Background:Large area forest inventories often use regular grids(with a single random start)of sample locations to ensure a uniform sampling intensity across the space of the surveyed populations.A design-unbiased est...Background:Large area forest inventories often use regular grids(with a single random start)of sample locations to ensure a uniform sampling intensity across the space of the surveyed populations.A design-unbiased estimator of variance does not exist for this design.Oftentimes,a quasi-default estimator applicable to simple random sampling(SRS)is used,even if it carries with it the likely risk of overestimating the variance by a practically important margin.To better exploit the precision of systematic sampling we assess the performance of five estimators of variance,including the quasi default.In this study,simulated systematic sampling was applied to artificial populations with contrasting covariance structures and with or without linear trends.We compared the results obtained with the SRS,Matern’s,successive difference replication,Ripley’s,and D’Orazio’s variance estimators.Results:The variances obtained with the four alternatives to the SRS estimator of variance were strongly correlated,and in all study settings consistently closer to the target design variance than the estimator for SRS.The latter always produced the greatest overestimation.In populations with a near zero spatial autocorrelation,all estimators,performed equally,and delivered estimates close to the actual design variance.Conclusion:Without a linear trend,the SDR and DOR estimators were best with variance estimates more narrowly distributed around the benchmark;yet in terms of the least average absolute deviation,Matern’s estimator held a narrow lead.With a strong or moderate linear trend,Matern’s estimator is choice.In large populations,and a low sampling intensity,the performance of the investigated estimators becomes more similar.展开更多
Generalized Least Squares (least squares with prior information) requires the correct assignment of two prior covariance matrices: one associated with the uncertainty of measurements;the other with the uncertainty of ...Generalized Least Squares (least squares with prior information) requires the correct assignment of two prior covariance matrices: one associated with the uncertainty of measurements;the other with the uncertainty of prior information. These assignments often are very subjective, especially when correlations among data or among prior information are believed to occur. However, in cases in which the general form of these matrices can be anticipated up to a set of poorly-known parameters, the data and prior information may be used to better-determine (or “tune”) the parameters in a manner that is faithful to the underlying Bayesian foundation of GLS. We identify an objective function, the minimization of which leads to the best-estimate of the parameters and provide explicit and computationally-efficient formula for calculating the derivatives needed to implement the minimization with a gradient descent method. Furthermore, the problem is organized so that the minimization need be performed only over the space of covariance parameters, and not over the combined space of model and covariance parameters. We show that the use of trade-off curves to select the relative weight given to observations and prior information is not a form of tuning, because it does not, in general maximize the posterior probability of the model parameters, and can lead to a different weighting than the procedure described here. We also provide several examples that demonstrate the viability, and discuss both the advantages and limitations of the method.展开更多
Background:A new variance estimator is derived and tested for big BAF(Basal Area Factor)sampling which is a forest inventory system that utilizes Bitterlich sampling(point sampling)with two BAF sizes,a small BAF for t...Background:A new variance estimator is derived and tested for big BAF(Basal Area Factor)sampling which is a forest inventory system that utilizes Bitterlich sampling(point sampling)with two BAF sizes,a small BAF for tree counts and a larger BAF on which tree measurements are made usually including DBHs and heights needed for volume estimation.Methods:The new estimator is derived using the Delta method from an existing formulation of the big BAF estimator as consisting of three sample means.The new formula is compared to existing big BAF estimators including a popular estimator based on Bruce’s formula.Results:Several computer simulation studies were conducted comparing the new variance estimator to all known variance estimators for big BAF currently in the forest inventory literature.In simulations the new estimator performed well and comparably to existing variance formulas.Conclusions:A possible advantage of the new estimator is that it does not require the assumption of negligible correlation between basal area counts on the small BAF factor and volume-basal area ratios based on the large BAF factor selection trees,an assumption required by all previous big BAF variance estimation formulas.Although this correlation was negligible on the simulation stands used in this study,it is conceivable that the correlation could be significant in some forest types,such as those in which the DBH-height relationship can be affected substantially by density perhaps through competition.We derived a formula that can be used to estimate the covariance between estimates of mean basal area and the ratio of estimates of mean volume and mean basal area.We also mathematically derived expressions for bias in the big BAF estimator that can be used to show the bias approaches zero in large samples on the order of 1n where n is the number of sample points.展开更多
In this study we have proposed a modified ratio type estimator for population variance of the study variable y under simple random sampling without replacement making use of coefficient of kurtosis and median of an au...In this study we have proposed a modified ratio type estimator for population variance of the study variable y under simple random sampling without replacement making use of coefficient of kurtosis and median of an auxiliary variable x. The estimator’s properties have been derived up to first order of Taylor’s series expansion. The efficiency conditions derived theoretically under which the proposed estimator performs better than existing estimators. Empirical studies have been done using real populations to demonstrate the performance of the developed estimator in comparison with the existing estimators. The proposed estimator as illustrated by the empirical studies performs better than the existing estimators under some specified conditions i.e. it has the smallest Mean Squared Error and the highest Percentage Relative Efficiency. The developed estimator therefore is suitable to be applied to situations in which the variable of interest has a positive correlation with the auxiliary variable.展开更多
Using lAP AGCM simulation results for the period 1961-2005, summer hot days in China were calculated and then compared with observations. Generally, the spatial pattern of hot days is reasonably reproduced, with more ...Using lAP AGCM simulation results for the period 1961-2005, summer hot days in China were calculated and then compared with observations. Generally, the spatial pattern of hot days is reasonably reproduced, with more hot days found in northern China, the Yangtze and Huaihe River basin, the Chuan-Yu region, and southern Xinjiang. However, the model tends to overestimate the number of hot days in the above-mentioned regions, particularly in the Yangtze and Huaihe River basin where the simulated summer-mean hot days is 13 days more than observed when averaged over the whole region, and the maximum overestimation of hot days can reach 23 days in the region. Analysis of the probability distribution of daily maximum temperature （Trnax） suggests that the warm bias in the model-simulated Tmax contributes largely to the overestimation of hot days in the model. Furthermore, the discrepancy in the simulated variance of the Tmax distribution also plays a non- negligible role in the overestimation of hot days. Indeed, the latter can even account for 22% of the total bias of simulated hot days in August in the Yangtze and Huaihe River basin. The quantification of model bias from the mean value and variability can provide more information for further model improvement.展开更多
Leaf economics spectrum(LES)describes the fundamental trade-offs between leaf structural,chemical,and physiological investments.Generally,structurally robust thick leaves with high leaf dry mass per unit area(LMA)exhi...Leaf economics spectrum(LES)describes the fundamental trade-offs between leaf structural,chemical,and physiological investments.Generally,structurally robust thick leaves with high leaf dry mass per unit area(LMA)exhibit lower photosynthetic capacity per dry mass(Amass).Paradoxically,“soft and thinleaved”mosses and spikemosses have very low Amass,but due to minute-size foliage elements,their LMA and its components,leaf thickness(LT)and density(LD),have not been systematically estimated.Here,we characterized LES and associated traits in cryptogams in unprecedented details,covering five evolutionarily different lineages.We found that mosses and spikemosses had the lowest LMA and LT values ever measured for terrestrial plants.Across a broad range of species from different lineages,Amass and LD were negatively correlated.In contrast,Amass was only related to LMA when LMA was greater than 14 g cm^(-2).In fact,low Amass reflected high LD and cell wall thickness in the studied cryptogams.We conclude that evolutionarily old plant lineages attained poorly differentiated,ultrathin mesophyll by increasing LD.Across plant lineages,LD,not LMA,is the trait that represents the trade-off between leaf robustness and physiology in the LES.展开更多
Obtaining the accurate value estimation and reducing the estimation bias are the key issues in reinforcement learning.However,current methods that address the overestimation problem tend to introduce underestimation,w...Obtaining the accurate value estimation and reducing the estimation bias are the key issues in reinforcement learning.However,current methods that address the overestimation problem tend to introduce underestimation,which face a challenge of precise decision-making in many fields.To address this issue,we conduct a theoretical analysis of the underestimation bias and propose the minmax operation,which allow for flexible control of the estimation bias.Specifically,we select the maximum value of each action from multiple parallel state-action networks to create a new state-action value sequence.Then,a minimum value is selected to obtain more accurate value estimations.Moreover,based on the minmax operation,we propose two novel algorithms by combining Deep Q-Network(DQN)and Double DQN(DDQN),named minmax-DQN and minmax-DDQN.Meanwhile,we conduct theoretical analyses of the estimation bias and variance caused by our proposed minmax operation,which show that this operation significantly improves both underestimation and overestimation biases and leads to the unbiased estimation.Furthermore,the variance is also reduced,which is helpful to improve the network training stability.Finally,we conduct numerous comparative experiments in various environments,which empirically demonstrate the superiority of our method.展开更多
Ordinary least squares(OLS) algorithm is widely applied in process measurement, because the sensor model used to estimate unknown parameters can be approximated through multivariate linear model. However, with few or ...Ordinary least squares(OLS) algorithm is widely applied in process measurement, because the sensor model used to estimate unknown parameters can be approximated through multivariate linear model. However, with few or noisy data or multi-collinearity, unbiased OLS leads to large variance. Biased estimators, especially ridge estimator, have been introduced to improve OLS by trading bias for variance. Ridge estimator is feasible as an estimator with smaller variance. At the same confidence level, with additive noise as the normal random variable, the less variance one estimator has, the shorter the two-sided symmetric confidence interval is. However, this finding is limited to the unbiased estimator and few studies analyze and compare the confidence levels between ridge estimator and OLS. This paper derives the matrix of ridge parameters under necessary and sufficient conditions based on which ridge estimator is superior to OLS in terms of mean squares error matrix, rather than mean squares error.Then the confidence levels between ridge estimator and OLS are compared under the condition of OLS fixed symmetric confidence interval, rather than the criteria for evaluating the validity of different unbiased estimators. We conclude that the confidence level of ridge estimator can not be directly compared with that of OLS based on the criteria available for unbiased estimators, which is verified by a simulation and a laboratory scale experiment on a single parameter measurement.展开更多
文摘Background:Large area forest inventories often use regular grids(with a single random start)of sample locations to ensure a uniform sampling intensity across the space of the surveyed populations.A design-unbiased estimator of variance does not exist for this design.Oftentimes,a quasi-default estimator applicable to simple random sampling(SRS)is used,even if it carries with it the likely risk of overestimating the variance by a practically important margin.To better exploit the precision of systematic sampling we assess the performance of five estimators of variance,including the quasi default.In this study,simulated systematic sampling was applied to artificial populations with contrasting covariance structures and with or without linear trends.We compared the results obtained with the SRS,Matern’s,successive difference replication,Ripley’s,and D’Orazio’s variance estimators.Results:The variances obtained with the four alternatives to the SRS estimator of variance were strongly correlated,and in all study settings consistently closer to the target design variance than the estimator for SRS.The latter always produced the greatest overestimation.In populations with a near zero spatial autocorrelation,all estimators,performed equally,and delivered estimates close to the actual design variance.Conclusion:Without a linear trend,the SDR and DOR estimators were best with variance estimates more narrowly distributed around the benchmark;yet in terms of the least average absolute deviation,Matern’s estimator held a narrow lead.With a strong or moderate linear trend,Matern’s estimator is choice.In large populations,and a low sampling intensity,the performance of the investigated estimators becomes more similar.
文摘Generalized Least Squares (least squares with prior information) requires the correct assignment of two prior covariance matrices: one associated with the uncertainty of measurements;the other with the uncertainty of prior information. These assignments often are very subjective, especially when correlations among data or among prior information are believed to occur. However, in cases in which the general form of these matrices can be anticipated up to a set of poorly-known parameters, the data and prior information may be used to better-determine (or “tune”) the parameters in a manner that is faithful to the underlying Bayesian foundation of GLS. We identify an objective function, the minimization of which leads to the best-estimate of the parameters and provide explicit and computationally-efficient formula for calculating the derivatives needed to implement the minimization with a gradient descent method. Furthermore, the problem is organized so that the minimization need be performed only over the space of covariance parameters, and not over the combined space of model and covariance parameters. We show that the use of trade-off curves to select the relative weight given to observations and prior information is not a form of tuning, because it does not, in general maximize the posterior probability of the model parameters, and can lead to a different weighting than the procedure described here. We also provide several examples that demonstrate the viability, and discuss both the advantages and limitations of the method.
基金Support was provided by Research Joint Venture Agreement 17-JV-11242306045,“Old Growth Forest Dynamics and Structure,”between the USDA Forest Service and the University of New HampshireAdditional support to MJD was provided by the USDA National Institute of Food and Agriculture McIntire-Stennis Project Accession Number 1020142,“Forest Structure,Volume,and Biomass in the Northeastern United States.”+1 种基金supported by the USDA National Institute of Food and Agriculture,McIntire-Stennis project OKL02834the Division of Agricultural Sciences and Natural Resources at Oklahoma State University.
文摘Background:A new variance estimator is derived and tested for big BAF(Basal Area Factor)sampling which is a forest inventory system that utilizes Bitterlich sampling(point sampling)with two BAF sizes,a small BAF for tree counts and a larger BAF on which tree measurements are made usually including DBHs and heights needed for volume estimation.Methods:The new estimator is derived using the Delta method from an existing formulation of the big BAF estimator as consisting of three sample means.The new formula is compared to existing big BAF estimators including a popular estimator based on Bruce’s formula.Results:Several computer simulation studies were conducted comparing the new variance estimator to all known variance estimators for big BAF currently in the forest inventory literature.In simulations the new estimator performed well and comparably to existing variance formulas.Conclusions:A possible advantage of the new estimator is that it does not require the assumption of negligible correlation between basal area counts on the small BAF factor and volume-basal area ratios based on the large BAF factor selection trees,an assumption required by all previous big BAF variance estimation formulas.Although this correlation was negligible on the simulation stands used in this study,it is conceivable that the correlation could be significant in some forest types,such as those in which the DBH-height relationship can be affected substantially by density perhaps through competition.We derived a formula that can be used to estimate the covariance between estimates of mean basal area and the ratio of estimates of mean volume and mean basal area.We also mathematically derived expressions for bias in the big BAF estimator that can be used to show the bias approaches zero in large samples on the order of 1n where n is the number of sample points.
文摘In this study we have proposed a modified ratio type estimator for population variance of the study variable y under simple random sampling without replacement making use of coefficient of kurtosis and median of an auxiliary variable x. The estimator’s properties have been derived up to first order of Taylor’s series expansion. The efficiency conditions derived theoretically under which the proposed estimator performs better than existing estimators. Empirical studies have been done using real populations to demonstrate the performance of the developed estimator in comparison with the existing estimators. The proposed estimator as illustrated by the empirical studies performs better than the existing estimators under some specified conditions i.e. it has the smallest Mean Squared Error and the highest Percentage Relative Efficiency. The developed estimator therefore is suitable to be applied to situations in which the variable of interest has a positive correlation with the auxiliary variable.
基金supported by the Special Scientific Research Fund of the Meteorological Public Welfare Profession of China[grant number GYHY01406021]National Key Research and Development Program[grant number 2016YFC0402702]the National Natural Science Foundation of China[grant numbers 41575095,41175073]
文摘Using lAP AGCM simulation results for the period 1961-2005, summer hot days in China were calculated and then compared with observations. Generally, the spatial pattern of hot days is reasonably reproduced, with more hot days found in northern China, the Yangtze and Huaihe River basin, the Chuan-Yu region, and southern Xinjiang. However, the model tends to overestimate the number of hot days in the above-mentioned regions, particularly in the Yangtze and Huaihe River basin where the simulated summer-mean hot days is 13 days more than observed when averaged over the whole region, and the maximum overestimation of hot days can reach 23 days in the region. Analysis of the probability distribution of daily maximum temperature （Trnax） suggests that the warm bias in the model-simulated Tmax contributes largely to the overestimation of hot days in the model. Furthermore, the discrepancy in the simulated variance of the Tmax distribution also plays a non- negligible role in the overestimation of hot days. Indeed, the latter can even account for 22% of the total bias of simulated hot days in August in the Yangtze and Huaihe River basin. The quantification of model bias from the mean value and variability can provide more information for further model improvement.
基金funded by the EU Regional Development Fund within the framework of the Centre of Excellence EcolChange(2014-2020.4.01.15-0002),the European Commission through the European Research Council(advanced grant 322603,SIPVOL+),the Estonian Research Council(personal grant PSG884)base funding nr 190200,the National Natural Science foundation of China(31711530648)+2 种基金the Personnel Startup Project of the Scientific Research and Development Foundation of Zhejiang A&F University(2021FR041)the study was partly purchased from funding by the EU Regional Development Fund(AnaEE Estonia,2014-2020.4.01.20-0285,and the project“Plant Biology Infrastructure-TAIM”,2014-2020.4.01.20-0282)the Estonian Research Council(“Plant Biology Infrastructure-TAIM”,TT5).
文摘Leaf economics spectrum(LES)describes the fundamental trade-offs between leaf structural,chemical,and physiological investments.Generally,structurally robust thick leaves with high leaf dry mass per unit area(LMA)exhibit lower photosynthetic capacity per dry mass(Amass).Paradoxically,“soft and thinleaved”mosses and spikemosses have very low Amass,but due to minute-size foliage elements,their LMA and its components,leaf thickness(LT)and density(LD),have not been systematically estimated.Here,we characterized LES and associated traits in cryptogams in unprecedented details,covering five evolutionarily different lineages.We found that mosses and spikemosses had the lowest LMA and LT values ever measured for terrestrial plants.Across a broad range of species from different lineages,Amass and LD were negatively correlated.In contrast,Amass was only related to LMA when LMA was greater than 14 g cm^(-2).In fact,low Amass reflected high LD and cell wall thickness in the studied cryptogams.We conclude that evolutionarily old plant lineages attained poorly differentiated,ultrathin mesophyll by increasing LD.Across plant lineages,LD,not LMA,is the trait that represents the trade-off between leaf robustness and physiology in the LES.
基金supported by the National Natural Science Foundation of China(No.62173272).
文摘Obtaining the accurate value estimation and reducing the estimation bias are the key issues in reinforcement learning.However,current methods that address the overestimation problem tend to introduce underestimation,which face a challenge of precise decision-making in many fields.To address this issue,we conduct a theoretical analysis of the underestimation bias and propose the minmax operation,which allow for flexible control of the estimation bias.Specifically,we select the maximum value of each action from multiple parallel state-action networks to create a new state-action value sequence.Then,a minimum value is selected to obtain more accurate value estimations.Moreover,based on the minmax operation,we propose two novel algorithms by combining Deep Q-Network(DQN)and Double DQN(DDQN),named minmax-DQN and minmax-DDQN.Meanwhile,we conduct theoretical analyses of the estimation bias and variance caused by our proposed minmax operation,which show that this operation significantly improves both underestimation and overestimation biases and leads to the unbiased estimation.Furthermore,the variance is also reduced,which is helpful to improve the network training stability.Finally,we conduct numerous comparative experiments in various environments,which empirically demonstrate the superiority of our method.
基金Supported by the National Natural Science Foundation of China （21006127） and the National Basic Research Program of China （2012CB720500）.
文摘Ordinary least squares(OLS) algorithm is widely applied in process measurement, because the sensor model used to estimate unknown parameters can be approximated through multivariate linear model. However, with few or noisy data or multi-collinearity, unbiased OLS leads to large variance. Biased estimators, especially ridge estimator, have been introduced to improve OLS by trading bias for variance. Ridge estimator is feasible as an estimator with smaller variance. At the same confidence level, with additive noise as the normal random variable, the less variance one estimator has, the shorter the two-sided symmetric confidence interval is. However, this finding is limited to the unbiased estimator and few studies analyze and compare the confidence levels between ridge estimator and OLS. This paper derives the matrix of ridge parameters under necessary and sufficient conditions based on which ridge estimator is superior to OLS in terms of mean squares error matrix, rather than mean squares error.Then the confidence levels between ridge estimator and OLS are compared under the condition of OLS fixed symmetric confidence interval, rather than the criteria for evaluating the validity of different unbiased estimators. We conclude that the confidence level of ridge estimator can not be directly compared with that of OLS based on the criteria available for unbiased estimators, which is verified by a simulation and a laboratory scale experiment on a single parameter measurement.
