In this paper we propose an absolute error loss EB estimator for parameter of one-side truncation distribution families. Under some conditions we have proved that the convergence rates of its Bayes risk is o, where 0&...In this paper we propose an absolute error loss EB estimator for parameter of one-side truncation distribution families. Under some conditions we have proved that the convergence rates of its Bayes risk is o, where 0<λ,r≤1,Mn≤lnln n (for large n),Mn→∞ as n→∞.展开更多
Starting with the Aalen （1989） version of Cox （1972） ＇regression model＇ we show the method for construction of ＂any＂ joint survival function given marginal survival functions. Basically, however, we restrict o...Starting with the Aalen （1989） version of Cox （1972） ＇regression model＇ we show the method for construction of ＂any＂ joint survival function given marginal survival functions. Basically, however, we restrict ourselves to model positive stochastic dependences only with the general assumption that the underlying two marginal random variables are centered on the set of nonnegative real values. With only these assumptions we obtain nice general characterization of bivariate probability distributions that may play similar role as the copula methodology. Examples of reliability and biomedical applications are given.展开更多
The grain yield per unit area in China has been increasing from 1949 to 1992 with annual fluctuations, which was caused by both policies and monsoon climate. The total grain yield is divided into trend yield, which r...The grain yield per unit area in China has been increasing from 1949 to 1992 with annual fluctuations, which was caused by both policies and monsoon climate. The total grain yield is divided into trend yield, which reflects the influence of economic factors, and climate yield, which reflects the impact of climate factors. The results of grain and climate yield by EOF (empirical orthogonal function) method show that the grain yield in the eastern China is higher and more fluctuating than that in the western region. The spatial and temporal distributions of climate yield were divided into four patterns. Regional unanimity of climate yield variation is the first and main spatial pattern, and then there are the spatial patterns of north-south difference and east-west difference in some years. Generally, climate conditions are good for grain yield during the 1950s and 1980s all over the country.展开更多
The Jarque-Bera’s fitting test for normality is a celebrated and powerful one. In this paper, we consider general Jarque-Bera tests for any distribution function (df) having at least 4k finite moments for k ≥ 2. The...The Jarque-Bera’s fitting test for normality is a celebrated and powerful one. In this paper, we consider general Jarque-Bera tests for any distribution function (df) having at least 4k finite moments for k ≥ 2. The tests use as many moments as possible whereas the JB classical test is supposed to test only skewness and kurtosis for normal variates. But our results unveil the relations between the coeffients in the JB classical test and the moments, showing that it really depends on the first eight moments. This is a new explanation for the powerfulness of such tests. General Chi-square tests for an arbitrary model, not only normal, are also derived. We make use of the modern functional empirical processes approach that makes it easier to handle statistics based on the high moments and allows the generalization of the JB test both in the number of involved moments and in the underlying distribution. Simulation studies are provided and comparison cases with the Kolmogorov-Smirnov’s tests and the classical JB test are given.展开更多
Let {vij}, i, j = 1, 2, …, be i.i.d, random variables with Ev11 = 0, Ev11^2 = 1 and a1 = （ai1,…, aiM） be random vectors with {aij} being i.i.d, random variables. Define XN =（x1,…, xk） and SN =XNXN^T,where xi=ai...Let {vij}, i, j = 1, 2, …, be i.i.d, random variables with Ev11 = 0, Ev11^2 = 1 and a1 = （ai1,…, aiM） be random vectors with {aij} being i.i.d, random variables. Define XN =（x1,…, xk） and SN =XNXN^T,where xi=ai×si and si=1/√N（v1i,…, vN,i）^T. The spectral distribution of SN is proven to converge, with probability one, to a nonrandom distribution function under mild conditions.展开更多
In this paper, the weighted Kolmogrov-Smirnov, Cramer von-Miss and the Anderson Darling test statistics are considered as goodness of fit tests for the generalized Rayleigh interval grouped data. An extensive simulati...In this paper, the weighted Kolmogrov-Smirnov, Cramer von-Miss and the Anderson Darling test statistics are considered as goodness of fit tests for the generalized Rayleigh interval grouped data. An extensive simulation process is conducted to evaluate their controlling of type 1 error and their power functions. Generally, the weighted Kolmogrov-Smirnov test statistics show a relatively better performance than both, the Cramer von-Miss and the Anderson Darling test statistics. For large sample values, the Anderson Darling test statistics cannot control type 1 error but for relatively small sample values it indicates a better performance than the Cramer von-Miss test statistics. Best selection of the test statistics and highlights for future studies are also explored.展开更多
The study of perturbed (smoothed) empirical distribution has received considerable at-tention. The monograph by Reiss gives a particularly lucid exposition of the mathematical attractions of smoothing the empirical di...The study of perturbed (smoothed) empirical distribution has received considerable at-tention. The monograph by Reiss gives a particularly lucid exposition of the mathematical attractions of smoothing the empirical distribution function (e.d.f.): it is intuitively appealing; it is easy to compute, it provides increased second-order efficiency (see refs. [2, 3]) and it improves the speed of convergence in Bootstrap (see refs. [4,5]).展开更多
By the well-known large and small blocks parting method for dependent situations, we establish the asymptotic normality of the Empirical Distribution Function under Negatively Associated Sequences. As its application ...By the well-known large and small blocks parting method for dependent situations, we establish the asymptotic normality of the Empirical Distribution Function under Negatively Associated Sequences. As its application in reliablity problems, a natural estimate Fn（x） for the survival function F（x） = P（X 〉 x） is proposed, and the asymptotic normality of n^1/2 [Fn（x） - F（x）] is established.展开更多
As one of optical isomers of zeaxanthin, meso-zeaxanthin is an important ingredient of macular pigment. Compared with lutein and zeaxanthin, meso-zeaxanthin may display strong functions as antioxidant and filtering sh...As one of optical isomers of zeaxanthin, meso-zeaxanthin is an important ingredient of macular pigment. Compared with lutein and zeaxanthin, meso-zeaxanthin may display strong functions as antioxidant and filtering short-wavelength, for example, the blue light. Comparisons among lutein, zeaxanthin and meso-zeaxanthin as well as functions and distributions together with the source of meso-zeaxanthin were discussed. The application as a supplement of diet and issues should be studied in the future for mesozeaxanthin were also analyzed.展开更多
This paper considers the convergence rates for nonparametric estimators of the error distribution in semi-parametric regression models. By establishing some general laws of the iterated logarithm, it shows that the ra...This paper considers the convergence rates for nonparametric estimators of the error distribution in semi-parametric regression models. By establishing some general laws of the iterated logarithm, it shows that the rates of convergence of either the empirical distribution or a smoothed version of the empirical distribution function matches exactly the rates obtained for an independent sample from the error distribution.展开更多
A microcomputerized measurement system is developed.This system automatically acquiresan I-V characteristic curve in 5 seconds with the accuracy of 0.05％ FSR(full scale range).The Schottkyextrapolation field-free emi...A microcomputerized measurement system is developed.This system automatically acquiresan I-V characteristic curve in 5 seconds with the accuracy of 0.05％ FSR(full scale range).The Schottkyextrapolation field-free emission,the inflection-point emission,the flection-point emission,the average effec-tive work function.the Richardson work function,the work function distribution at the operation tempera-ture and other important information that reflects properties of cathodes are obtained by this system.The re-sults of analysing four types of cathodes demonstrate that this system is very suitable for measuring the activi-ty changes of the cathode in the processes of activation,ageing,poisoning and life test.It is proved that thissystem can also be used to monitor the actlvity of the cathode in the assembled tube by measuring a gridcontrolled travelling-wave tube.展开更多
Temperature series of the original individual measurements of the minimum and maximum daily temperatures from 24 stations located in different regions of Europe are considered with the objective of studying the stabil...Temperature series of the original individual measurements of the minimum and maximum daily temperatures from 24 stations located in different regions of Europe are considered with the objective of studying the stability or the variability of the “climate” in time and space. The patterns of the temperature statistics, the shapes of probability density functions, in particular, at different places and times allow comparisons based on the Kolmogorov-Smirnov test, the Shannon entropy, and cluster analysis, used separately or in combination for the purposes of quantitative climate classification.展开更多
We propose a nonparametric change point estimator in the distributions of a sequence of independent observations in terms of the test statistics given by Huˇskov′a and Meintanis(2006) that are based on weighted empi...We propose a nonparametric change point estimator in the distributions of a sequence of independent observations in terms of the test statistics given by Huˇskov′a and Meintanis(2006) that are based on weighted empirical characteristic functions. The weight function ω(t; a) under consideration includes the two weight functions from Huˇskov′a and Meintanis(2006) plus the weight function used by Matteson and James(2014),where a is a tuning parameter. Under the local alternative hypothesis, we establish the consistency, convergence rate, and asymptotic distribution of this change point estimator which is the maxima of a two-side Brownian motion with a drift. Since the performance of the change point estimator depends on a in use, we thus propose an algorithm for choosing an appropriate value of a, denoted by a_s which is also justified. Our simulation study shows that the change point estimate obtained by using a_s has a satisfactory performance. We also apply our method to a real dataset.展开更多
文摘In this paper we propose an absolute error loss EB estimator for parameter of one-side truncation distribution families. Under some conditions we have proved that the convergence rates of its Bayes risk is o, where 0<λ,r≤1,Mn≤lnln n (for large n),Mn→∞ as n→∞.
文摘Starting with the Aalen （1989） version of Cox （1972） ＇regression model＇ we show the method for construction of ＂any＂ joint survival function given marginal survival functions. Basically, however, we restrict ourselves to model positive stochastic dependences only with the general assumption that the underlying two marginal random variables are centered on the set of nonnegative real values. With only these assumptions we obtain nice general characterization of bivariate probability distributions that may play similar role as the copula methodology. Examples of reliability and biomedical applications are given.
文摘The grain yield per unit area in China has been increasing from 1949 to 1992 with annual fluctuations, which was caused by both policies and monsoon climate. The total grain yield is divided into trend yield, which reflects the influence of economic factors, and climate yield, which reflects the impact of climate factors. The results of grain and climate yield by EOF (empirical orthogonal function) method show that the grain yield in the eastern China is higher and more fluctuating than that in the western region. The spatial and temporal distributions of climate yield were divided into four patterns. Regional unanimity of climate yield variation is the first and main spatial pattern, and then there are the spatial patterns of north-south difference and east-west difference in some years. Generally, climate conditions are good for grain yield during the 1950s and 1980s all over the country.
文摘The Jarque-Bera’s fitting test for normality is a celebrated and powerful one. In this paper, we consider general Jarque-Bera tests for any distribution function (df) having at least 4k finite moments for k ≥ 2. The tests use as many moments as possible whereas the JB classical test is supposed to test only skewness and kurtosis for normal variates. But our results unveil the relations between the coeffients in the JB classical test and the moments, showing that it really depends on the first eight moments. This is a new explanation for the powerfulness of such tests. General Chi-square tests for an arbitrary model, not only normal, are also derived. We make use of the modern functional empirical processes approach that makes it easier to handle statistics based on the high moments and allows the generalization of the JB test both in the number of involved moments and in the underlying distribution. Simulation studies are provided and comparison cases with the Kolmogorov-Smirnov’s tests and the classical JB test are given.
文摘Let {vij}, i, j = 1, 2, …, be i.i.d, random variables with Ev11 = 0, Ev11^2 = 1 and a1 = （ai1,…, aiM） be random vectors with {aij} being i.i.d, random variables. Define XN =（x1,…, xk） and SN =XNXN^T,where xi=ai×si and si=1/√N（v1i,…, vN,i）^T. The spectral distribution of SN is proven to converge, with probability one, to a nonrandom distribution function under mild conditions.
文摘In this paper, the weighted Kolmogrov-Smirnov, Cramer von-Miss and the Anderson Darling test statistics are considered as goodness of fit tests for the generalized Rayleigh interval grouped data. An extensive simulation process is conducted to evaluate their controlling of type 1 error and their power functions. Generally, the weighted Kolmogrov-Smirnov test statistics show a relatively better performance than both, the Cramer von-Miss and the Anderson Darling test statistics. For large sample values, the Anderson Darling test statistics cannot control type 1 error but for relatively small sample values it indicates a better performance than the Cramer von-Miss test statistics. Best selection of the test statistics and highlights for future studies are also explored.
文摘The study of perturbed (smoothed) empirical distribution has received considerable at-tention. The monograph by Reiss gives a particularly lucid exposition of the mathematical attractions of smoothing the empirical distribution function (e.d.f.): it is intuitively appealing; it is easy to compute, it provides increased second-order efficiency (see refs. [2, 3]) and it improves the speed of convergence in Bootstrap (see refs. [4,5]).
基金the National Natural Science Foundation of China (10161004)the Natural Science Foundation of Jiangxi (0611068)Science Foundation of Shangrao Normal Gollege.
文摘By the well-known large and small blocks parting method for dependent situations, we establish the asymptotic normality of the Empirical Distribution Function under Negatively Associated Sequences. As its application in reliablity problems, a natural estimate Fn（x） for the survival function F（x） = P（X 〉 x） is proposed, and the asymptotic normality of n^1/2 [Fn（x） - F（x）] is established.
文摘As one of optical isomers of zeaxanthin, meso-zeaxanthin is an important ingredient of macular pigment. Compared with lutein and zeaxanthin, meso-zeaxanthin may display strong functions as antioxidant and filtering short-wavelength, for example, the blue light. Comparisons among lutein, zeaxanthin and meso-zeaxanthin as well as functions and distributions together with the source of meso-zeaxanthin were discussed. The application as a supplement of diet and issues should be studied in the future for mesozeaxanthin were also analyzed.
基金supported by the National Science Foundation of China under Grant Nos.11201422,11301481,and 11371321Zhejiang Provincial Natural Science Foundation of China under Grant Nos.Y6110639,Y6110110,LQ12A01018,and LQ12A01017+2 种基金the National Statistical Science Research Project of China under Grant No.2012LY174Foundation for Young Talents of ZJGSU under Grant No.1020XJ1314019Zhejiang Provincial Key Research Base for Humanities and Social Science Research(Statistics)
文摘This paper considers the convergence rates for nonparametric estimators of the error distribution in semi-parametric regression models. By establishing some general laws of the iterated logarithm, it shows that the rates of convergence of either the empirical distribution or a smoothed version of the empirical distribution function matches exactly the rates obtained for an independent sample from the error distribution.
文摘A microcomputerized measurement system is developed.This system automatically acquiresan I-V characteristic curve in 5 seconds with the accuracy of 0.05％ FSR(full scale range).The Schottkyextrapolation field-free emission,the inflection-point emission,the flection-point emission,the average effec-tive work function.the Richardson work function,the work function distribution at the operation tempera-ture and other important information that reflects properties of cathodes are obtained by this system.The re-sults of analysing four types of cathodes demonstrate that this system is very suitable for measuring the activi-ty changes of the cathode in the processes of activation,ageing,poisoning and life test.It is proved that thissystem can also be used to monitor the actlvity of the cathode in the assembled tube by measuring a gridcontrolled travelling-wave tube.
文摘Temperature series of the original individual measurements of the minimum and maximum daily temperatures from 24 stations located in different regions of Europe are considered with the objective of studying the stability or the variability of the “climate” in time and space. The patterns of the temperature statistics, the shapes of probability density functions, in particular, at different places and times allow comparisons based on the Kolmogorov-Smirnov test, the Shannon entropy, and cluster analysis, used separately or in combination for the purposes of quantitative climate classification.
基金supported by Natural Sciences and the Engineering Research Council of Canada (Grant No. 105557-2012)National Natural Science Foundation for Young Scientists of China (Grant No. 11201108)+1 种基金the National Statistical Research Plan Project (Grant No. 2012LZ009)the Humanities and Social Sciences Project from Ministry of Education of China (Grant No. 12YJC910007)
文摘We propose a nonparametric change point estimator in the distributions of a sequence of independent observations in terms of the test statistics given by Huˇskov′a and Meintanis(2006) that are based on weighted empirical characteristic functions. The weight function ω(t; a) under consideration includes the two weight functions from Huˇskov′a and Meintanis(2006) plus the weight function used by Matteson and James(2014),where a is a tuning parameter. Under the local alternative hypothesis, we establish the consistency, convergence rate, and asymptotic distribution of this change point estimator which is the maxima of a two-side Brownian motion with a drift. Since the performance of the change point estimator depends on a in use, we thus propose an algorithm for choosing an appropriate value of a, denoted by a_s which is also justified. Our simulation study shows that the change point estimate obtained by using a_s has a satisfactory performance. We also apply our method to a real dataset.
