排序集抽样下Inverse Rayleigh分布的Fisher信息量及其在参数估计中的应用

文章分别在简单随机抽样和排序集抽样下研究了Inverse Rayleigh分布中对应样本所含刻度参数θ的Fisher信息量.数值结果表示,同等样本容量的排序集样本比简单随机样本提供更多关于θ的信息.接着分别基于简单随机样本和排序集样本构造了θ的一些优良估计,并对估计结果进行了数值比较.     

Estimation of a quantile in some nonstandard cases

A necessary condition for the asymptotic normality of the sample quantile estimator isf(Q(p))=F(Q(p))>0, whereQ(p) is thep-th quantile of the distribution functionF(x). In this paper, we estimate a quantile by a kernel quantile estimator when this condition is violated. We have shown that the kernel quantile estimator is asymptotically normal in some nonstandard cases. The optimal convergence rate of the mean squared error for the kernel estimator is obtained with respect to the asymptotically optimal bandwidth. A law of the iterated logarithm is also established.This research was partially supported by the new faculty award from the University of Oregon.     

Sequential estimation of a parameter of an exponential distribution

We consider the problem of minimum risk point estimation for the parameter =a+b of the exponential distribution with unknown location parameter and scale parameter when the loss function is squared error plus linear cost. In this paper, we propose a sequential estimator of and show that the associated risk is asymptotically one cost less than that given by Ghosh and Mukhopadhyay (1989,South African Statist. J.,23, 251–268).     

Evaluation of the use of consensus values in proficiency testing programmes

Proficiency testing (PT) is an essential tool used by laboratory accreditation bodies to assess the competency of laboratories. Because of limited resources of PT providers or for other reasons, the assigned reference value used in the calculation of z-score values has usually been derived from some sort of consensus value obtained by central tendency estimators such as the arithmetic mean or robust mean. However, if the assigned reference value deviates significantly from the ‘true value’ of the analyte in the test material, laboratories’ performance will be evaluated incorrectly. This paper evaluates the use of consensus values in proficiency testing programmes using the Monte Carlo simulation technique. The results indicated that the deviation of the assigned value from the true value could be as large as 40%, depending on the parameters of the proficiency testing programmes under investigation such as sample homogeneity, number of participant laboratories, concentration level, method precision and laboratory bias. To study how these parameters affect the degree of discrepancy between the consensus value and the true value, a fractional factorial design was also applied. The findings indicate that the number of participating laboratories and the distribution of laboratory bias were the prime two factors affecting the deviation of the consensus value from the true value.     

Durbin-Watson statistic as a morphological estimator of information content

The present work proposes a new approach for the evaluation of the information content in latent variables, and therefore, for the determination of the regression model dimensionality. Several examples are provided, using simulated, real-world, and reference datasets. The results showed that the application of the Durbin-Watson (DW) criterion could be used for the determination of the number of latent variables. Moreover, the method is straightforward in its implementation and could help in the understanding of model behaviour, particularly in complex datasets. A comparison is made with cross-validation techniques for the case of reference datasets, showing the potential of the Durbin-Watson criterion in the characterisation of the regression model. The advantages and disadvantages of this procedure (compared to cross-validation) are discussed. The properties of the information content of the regression vectors (loadings p, w and b vectors) are shown as well as how to use them for the current purpose.     

一般增长曲线模型参数阵的BLU估计

考虑一般增长曲线模型：Ｙ＝Ｘ１ＢＸ２＋εＥ（Ｖｅｃ（ε））＝０Ｖ（Ｖｅｃ（ε））＝σ２ＶＩｎ（Ｖ０）本文对任一可估函数ＫＢＬ给出了它的ＢＬＵ估计（最佳线性无偏估计），并得到了方差σ２的一个无偏估计．     

The a posteriori error estimates of Chebyshev–Petrov–Galerkin methods for second-order equations

In this paper, the a posteriori error estimates of Chebyshev–Petrov–Galerkin approximations are investigated. For simplicity, we choose the Poisson equation with Dirichlet boundary conditions to discuss the a posteriori error estimators, and deduce their efficient and reliable properties. Some numerical experiments are performed to verify the theoretical analysis for the a posteriori error estimators.     

Limit theorems for the pre-averaged Hayashi–Yoshida estimator with random sampling

We will focus on estimating the integrated covariance of two diffusion processes observed in a nonsynchronous manner. The observation data is contaminated by some noise, which possibly depends on the time and the latent diffusion processes, while the sampling times also possibly depend on the observed processes. In a high-frequency setting, we consider a modified version of the pre-averaged Hayashi–Yoshida estimator, and we show that such a kind of estimator has the consistency and the asymptotic mixed normality, and attains the optimal rate of convergence.     

Folded overlapping variance estimators for simulation

We propose and analyze a new class of estimators for the variance parameter of a steady-state simulation output process. The new estimators are computed by averaging individual estimators from “folded” standardized time series based on overlapping batches composed of consecutive observations. The folding transformation on each batch can be applied more than once to produce an entire set of estimators. We establish the limiting distributions of the proposed estimators as the sample size tends to infinity while the ratio of the sample size to the batch size remains constant. We give analytical and Monte Carlo results showing that, compared to their counterparts computed from nonoverlapping batches, the new estimators have roughly the same bias but smaller variance. In addition, these estimators can be computed with order-of-sample-size work.