Improved Estimation of Rare Sensitive Attribute in a Stratified Sampling Using Poisson Distribution

In this study, we propose a two stage randomized response model. Improved unbiased estimators of the mean number of persons possessing a rare sensitive attribute under two different situations are proposed. The proposed estimators are evaluated using a relative efficiency comparison. It is shown that our estimators are efficient as compared to existing estimators when the parameter of rare unrelated attribute is known and in unknown case, depending on the probability of selecting a question.

L-Moments Based Calibrated Variance Estimators Using Double Stratified Sampling

Variance is one of the most vital measures of dispersion widely employed in practical aspects.A commonly used approach for variance estimation is the traditional method of moments that is strongly influenced by the presence of extreme values,and thus its results cannot be relied on.Finding momentum from Koyuncu’s recent work,the present paper focuses first on proposing two classes of variance estimators based on linear moments(L-moments),and then employing them with auxiliary data under double stratified sampling to introduce a new class of calibration variance estimators using important properties of L-moments(L-location,L-cv,L-variance).Three populations are taken into account to assess the efficiency of the new estimators.The first and second populations are concerned with artificial data,and the third populations is concerned with real data.The percentage relative efficiency of the proposed estimators over existing ones is evaluated.In the presence of extreme values,our findings depict the superiority and high efficiency of the proposed classes over traditional classes.Hence,when auxiliary data is available along with extreme values,the proposed classes of estimators may be implemented in an extensive variety of sampling surveys.

Sequential stratified sampling belief propagation for multiple targets tracking

Rather than the difficulties of highly non-linear and non-Gaussian observation process and the state distribution in single target tracking, the presence of a large, varying number of targets and their interactions place more challenge on visual tracking. To overcome these difficulties, we formulate multiple targets tracking problem in a dynamic Markov network which consists of three coupled Markov random fields that model the following： a field for joint state of multi-target, one binary process for existence of individual target, and another binary process for occlusion of dual adjacent targets. By introducing two robust functions, we eliminate the two binary processes, and then apply a novel version of belief propagation called sequential stratified sampling belief propagation algorithm to obtain the maximum a posteriori （MAP） estimation in the dynamic Markov network, By using stratified sampler, we incorporate bottom-up information provided by a learned detector （e.g. SVM classifier） and belief information for the messages updating. Other low-level visual cues （e.g. color and shape） can be easily incorporated in our multi-target tracking model to obtain better tracking results. Experimental results suggest that our method is comparable to the state-of-the-art multiple targets tracking methods in several test cases.

Using a simulation analysis to evaluate the impact of crop mapping error on crop area estimation from stratified sampling

To analyze the efficiency of area estimations(i.e.estimation accuracy and variation of estimation)impacted by crop mapping error,we simulated error at eight levels for thematic maps using a stratified sampling estimation methodology.The results show that the estimation efficiency is influenced by the combination of the sample size and the error level.Evaluating the trade-offs between sample size and error level showed that reducing the crop mapping error level provides the most benefit(i.e.higher estimation efficiency).Further,sampling performance differed based on the heterogeneity of the crop area.The results demonstrated that the influence of increasing the error level on estimation efficiency is more detrimental in heterogeneous areas than in homogeneous ones.Therefore,to obtain higher estimation efficiency,a larger sample size and lower error level or both are needed,especially in heterogeneous areas.We suggest that existing land-cover maps should first be used to determine the heterogeneity of the area.The appropriate sample size for these areas then can be determined according to all three factors:heterogeneity,expected estimation efficiency,and sampling budget.Overall,extending our understanding of the impacts of crop mapping error is necessary for decision making to improve our ability to effectively estimate crop area.

Sampling Error Estimation in Stratified Surveys

Many operations carried out by official statistical institutes use large-scale surveys obtained by stratified random sampling without replacement. Variables commonly examined in this type of surveys are binary, categorical and continuous, and hence, the estimates of interest involve estimates of proportions, totals and means. The problem of approximating the sampling relative error of this kind of estimates is studied in this paper. Some new jackknife methods are proposed and compared with plug-in and bootstrap methods. An extensive simulation study is carried out to compare the behavior of all the methods considered in this paper.

On the Impact of Bootstrap in Stratified Random Sampling

In general the accuracy of mean estimator can be improved by stratified random sampling. In this paper, we provide an idea different from empirical methods that the accuracy can be more improved through bootstrap resampling method under some conditions. The determination of sample size by bootstrap method is also discussed, and a simulation is made to verify the accuracy of the proposed method. The simulation results show that the sample size based on bootstrapping is smaller than that based on central limit theorem.

Local Polynomial Regression Estimator of the Finite Population Total under Stratified Random Sampling: A Model-Based Approach

In this paper, auxiliary information is used to determine an estimator of finite population total using nonparametric regression under stratified random sampling. To achieve this, a model-based approach is adopted by making use of the local polynomial regression estimation to predict the nonsampled values of the survey variable y. The performance of the proposed estimator is investigated against some design-based and model-based regression estimators. The simulation experiments show that the resulting estimator exhibits good properties. Generally, good confidence intervals are seen for the nonparametric regression estimators, and use of the proposed estimator leads to relatively smaller values of RE compared to other estimators.

Efficient slope reliability analysis under soil spatial variability using maximum entropy distribution with fractional moments

Spatial variability of soil properties imposes a challenge for practical analysis and design in geotechnical engineering.The latter is particularly true for slope stability assessment,where the effects of uncertainty are synthesized in the so-called probability of failure.This probability quantifies the reliability of a slope and its numerical calculation is usually quite involved from a numerical viewpoint.In view of this issue,this paper proposes an approach for failure probability assessment based on Latinized partially stratified sampling and maximum entropy distribution with fractional moments.The spatial variability of geotechnical properties is represented by means of random fields and the Karhunen-Loève expansion.Then,failure probabilities are estimated employing maximum entropy distribution with fractional moments.The application of the proposed approach is examined with two examples:a case study of an undrained slope and a case study of a slope with cross-correlated random fields of strength parameters under a drained slope.The results show that the proposed approach has excellent accuracy and high efficiency,and it can be applied straightforwardly to similar geotechnical engineering problems.

STRATIFIED MODEL FOR ESTIMATING FATIGUE CRACK GROWTH RATE OF METALLIC MATERIALS

The curve of relationship between fatigue crack growth rate and the stress strength factor amplitude represented an important fatigue property in designing of damage tolerance limits and predicting life of metallic component parts. In order to have a more reasonable use of testing data, samples from population were stratified suggested by the stratified random sample model (SRAM). The data in each stratum corresponded to the same experiment conditions. A suitable weight was assigned to each stratified sample according to the actual working states of the pressure vessel, so that the estimation of fatigue crack growth rate equation was more accurate for practice. An empirical study shows that the SRAM estimation by using fatigue crack growth rate data from different stoves is obviously better than the estimation from simple random sample model.

SOME PROBLEMS ON FOREST SAMPLING TECHNIQUES

This paper reveaed some problems of the forest samling investigation from application.and pointed out the defects. Determining sample size method was precisely put forward from formla's origin in simple random Samling procedure In stratified random samgling, two cases were distinguished: the variances Sh2 are equal for all h and not all Sh2 are equal This method made the assertion of making confidence interval more reliable.

Climate Change Perceptions , Impacts and Adaptation Strategies of F arm Households in Potohar Region of Punjab, Pakistan

Climate change has become a global phenomenon and is adversely affecting agricultural development across the globe.Developing countries like Pakistan where 18.9%of the GDP(gross domestic product)came from the agriculture sector and also 42%of the labor force involved in agriculture.They are directly and indirectly affected by climate change due to an increase in the frequency and intensity of climatic extreme events such as floods,droughts and extreme weather events.In this paper,we have focused on the impact of climate change on farm households and their adaptation strategies to cope up the climatic extremes.For this purpose,we have selected farm households by using multistage stratified random sampling from four districts of the Potohar region i.e.Attock,Rawalpindi,Jhelum and Chakwal.These districts were selected by dividing the Potohar region into rain-fed areas.We have employed logistic regression to assess the determinants of adaptation to climate change and its impact.We have also calculated the marginal effect of each independent variable of the logistic regression to measure the immediate rate of change in the model.In order to check the significance of our suggested model,we have used hypothesis testing.

Reliability Sensitivity Algorithm Based on Stratified Importance Sampling Method for Multiple Failure Modes Systems

Combining the advantages of the stratified sampling and the importance sampling, a stratified importance sampling method （SISM） is presented to analyze the reliability sensitivity for structure with multiple failure modes. In the presented method, the variable space is divided into several disjoint subspace by n-dimensional coordinate planes at the mean point of the random vec- tor, and the importance sampling functions in the subspaces are constructed by keeping the sampling center at the mean point and augmenting the standard deviation by a factor of 2. The sample size generated from the importance sampling function in each subspace is determined by the contribution of the subspace to the reliability sensitivity, which can be estimated by iterative simulation in the sampling process. The formulae of the reliability sensitivity estimation, the variance and the coefficient of variation are derived for the presented SISM. Comparing with the Monte Carlo method, the stratified sampling method and the importance sampling method, the presented SISM has wider applicability and higher calculation efficiency, which is demonstrated by numerical examples. Finally, the reliability sensitivity analysis of flap structure is illustrated that the SISM can be applied to engineering structure.

Optimization of stratification scheme for a fishery-independent survey with multiple objectives

Fishery-independent surveys are often used for collecting high quality biological and ecological data to support fisheries management. A careful optimization of fishery-independent survey design is necessary to improve the precision of survey estimates with cost-effective sampling efforts. We developed a simulation approach to evaluate and optimize the stratification scheme for a fishery-independent survey with multiple goals including estimation of abundance indices of individual species and species diversity indices. We compared the performances of the sampling designs with different stratification schemes for different goals over different months. Gains in precision of survey estimates from the stratification schemes were acquired compared to simple random sampling design for most indices. The stratification scheme with five strata performed the best. This study showed that the loss of precision of survey estimates due to the reduction of sampling efforts could be compensated by improved stratification schemes, which would reduce the cost and negative impacts of survey trawling on those species with low abundance in the fishery-independent survey. This study also suggests that optimization of a survey design differed with different survey objectives. A post-survey analysis can improve the stratification scheme of fishery-independent survey designs.

Comparison of sampling effort allocation strategies in a stratified random survey with multiple objectives

Stratified random survey is commonly used to estimate abundance indices of fish populations in multispecies survey,providing reliable data for stock assessment and fisheries management.In some cases,however,the sample size is relatively small because of the limitation of survey cost or other factors.The allocation methods of sampling efforts among strata in stratified random surveys with small sample size may need adjustment compared with traditional approaches.In this study,two sampling stations were allocated to each stratum first and then the remaining sampling units were allocated among strata using five traditional allocation methods.In order to distinguish them from traditional methods,we called them adjusted methods in this study.A simulation study was conducted to compare the performances of different allocation strategies of sampling efforts in a stratified random survey for estimating abundance indices of multiple target species.Relative estimation error(REE)and relative bias(RB)were used to measure the precision and accuracy of estimates of abundance indices under different allocation schemes of sampling efforts in the multispecies survey.The performances of different allocation schemes in estimating abundance indices varied greatly for different species over different seasons.The adjusted Neyman allocation scheme could significantly reduce the REE and RB of estimates of abundance index for single species survey.For multiple species surveys,the adjusted average-Neyman allocation method,the adjusted Yate allocation method,the adjusted proportional allocation method and current allocation method had relatively high accuracy and precision of estimates of abundance indices for four species in terms of the total_(REE) and total_(RB).Though the adjusted average-Neyman allocation scheme did not always have the best performance,it was the optimal one considering the accuracy and precision of estimates of abundance indices for all species simultaneously.The allocation of sampling efforts among strata in stratified random surveys targeting for estimating abundance indices of multiple species should comprehensively consider the variance of abundance of different species in stratum and the seasonal changes.

A New Class of L-Moments Based Calibration Variance Estimators

Variance is one of themost important measures of descriptive statistics and commonly used for statistical analysis.The traditional second-order central moment based variance estimation is a widely utilized methodology.However,traditional variance estimator is highly affected in the presence of extreme values.So this paper initially,proposes two classes of calibration estimators based on an adaptation of the estimators recently proposed by Koyuncu and then presents a new class of L-Moments based calibration variance estimators utilizing L-Moments characteristics(L-location,Lscale,L-CV)and auxiliary information.It is demonstrated that the proposed L-Moments based calibration variance estimators are more efficient than adapted ones.Artificial data is considered for assessing the performance of the proposed estimators.We also demonstrated an application related to apple fruit for purposes of the article.Using artificial and real data sets,percentage relative efficiency(PRE)of the proposed class of estimators with respect to adapted ones are calculated.The PRE results indicate to the superiority of the proposed class over adapted ones in the presence of extreme values.In this manner,the proposed class of estimators could be applied over an expansive range of survey sampling whenever auxiliary information is available in the presence of extreme values.

Calibration of a Confidence Interval for a Classification Accuracy

Coverage of nominal 95% confidence intervals of a proportion estimated from a sample obtained under a complex survey design, or a proportion estimated from a ratio of two random variables, can depart significantly from its target. Effective calibration methods exist for intervals for a proportion derived from a single binary study variable, but not for estimates of thematic classification accuracy. To promote a calibration of confidence intervals within the context of land-cover mapping, this study first illustrates a common problem of under and over-coverage with standard confidence intervals, and then proposes a simple and fast calibration that more often than not will improve coverage. The demonstration is with simulated sampling from a classified map with four classes, and a reference class known for every unit in a population of 160,000 units arranged in a square array. The simulations include four common probability sampling designs for accuracy assessment, and three sample sizes. Statistically significant over- and under-coverage was present in estimates of user’s (UA) and producer’s accuracy (PA) as well as in estimates of class area proportion. A calibration with Bayes intervals for UA and PA was most efficient with smaller sample sizes and two cluster sampling designs.

Improved landscape sampling method for landscape character assessment

Landscape character assessment(LCA)is an effective tool for understanding people’s perceptions and preferences of landscape characteristics.Other than the assessment indicators and subjects,the reliability of photos as assessment objects is equally important for the LCA result.However,the commonly used onsite photos are mainly obtained at randomly selected locations by the researchers.We can neither know whether those photos represent the researchers’own preferences,nor,to our best knowledge,can their reliability be tested scientifically.This method is also difficult to apply in large-scale geographical areas.To address these issues,we(1)propose an improved method including the protocols of photography and the sampling of photography locations,in which the fractal principle and stratified random sampling method were combined to minimize the effects of the researchers’preferences and other factors;(2)apply the method to the Guanzhong region as an example,and obtain sampling photos and their geographical coordinates,which can be used as a data package for LCA;(3)use Fractalyse to test the sampled result and receive good validity.In conclusion,this study extends the methodological chain of the LCA and supports the application of LCA in large-scale regions.

An Efficient Class of Calibration Ratio Estimators of Domain Mean in Survey Sampling

This paper develops a new approach to domain estimation and proposes a new class of ratio estimators that is more efficient than the regression estimator and not depending on any optimality condition using the principle of calibration weightings.Some wellknown regression and ratio-type estimators are obtained and shown to be special members of the newclass of estimators.Results of analytical study showed that the new class of estimators is superior in both efficiency and biasedness to all related existing estimators under review.The relative performances of the new class of estimators with a corresponding global estimator were evaluated through a simulation study.Analysis and evaluation are presented.

Comparison of sampling designs for calibrating digital soil maps at multiple depths

Digital soil mapping (DSM) aims to produce detailed maps of soil properties or soil classes to improve agricultural management and soil quality assessment. Optimized sampling design can reduce the substantial costs and efforts associated with sampling, profile description, and laboratory analysis. The purpose of this study was to compare common sampling designs for DSM, including grid sampling (GS), grid random sampling (GRS), stratified random sampling (StRS), and conditioned Latin hypercube sampling (cLHS). In an agricultural field (11 ha) in Quebec, Canada, a total of unique 118 locations were selected using each of the four sampling designs (45 locations each), and additional 30 sample locations were selected as an independent testing dataset (evaluation dataset). Soil visible near-infrared (Vis-NIR) spectra were collected in situ at the 148 locations (1 m depth), and soil cores were collected from a subset of 32 locations and subdivided at 10-cm depth intervals, totaling 251 samples. The Cubist model was used to elucidate the relationship between Vis-NIR spectra and soil properties (soil organic matter (SOM) and clay), which was then used to predict the soil properties at all 148 sample locations. Digital maps of soil properties at multiple depths for the entire field (148 sample locations) were prepared using a quantile random forest model to obtain complete model maps (CM-maps). Soil properties were also mapped using the samples from each of the 45 locations for each sampling design to obtain sampling design maps (SD-maps). The SD-maps were evaluated using the independent testing dataset (30 sample locations), and the spatial distribution and model uncertainty of each SD-map were compared with those of the corresponding CM-map. The spatial and feature space coverage were compared across the four sampling designs. The results showed that GS resulted in the most even spatial coverage, cLHS resulted in the best coverage of the feature space, and GS and cLHS resulted in similar prediction accuracies and spatial distributions of soil properties. The SOM content was underestimated using GRS, with large errors at 0–50 cm depth, due to some values not being captured by this sampling design, whereas larger errors for the deeper soil layers were produced using StRS. Predictions of SOM and clay contents had higher accuracy for topsoil (0–30 cm) than for deep subsoil (60–100 cm). It was concluded that the soil sampling designs with either good spatial coverage or feature space coverage can provide good accuracy in 3D DSM, but their performances may be different for different soil properties.

A Class of Weighted Estimators for Additive Hazards Model in Case-cohort Studies

Case-cohort sampling is a commonly used and efficient method for studying large cohorts. In many situations, some covariates are easily measured on all cohort subjects, and surrogate measurements of the expensive covariates also may be observed. In this paper, to make full use of the covariate data collected outside the case-cohort sample, we propose＇a class of weighted estimators with general time-varying weights for the additive hazards model, and the estimators are shown to be consistent and asymptotically normal. We also identify the estimator within this class that maximizes efficiency, and simulation studies show that the efficiency gains of the proposed estimator over the existing ones can be substantial in practical situations. A real example is provided.