Large deviation for negatively dependent random variables under sublinear expectation

Abstract

In this article, first we give the definition of negatively dependent sequence of random variables under sublinear expectation then we establish large deviation principle for this kind of sequence. Moreover, we obtain the upper bound of moderate deviation principle.     

Moderate deviations for the moment estimators in Rayleigh distribution with two parameters

ABSTRACT

We study the moderate deviations of the moment estimators in Rayleigh distribution with two parameters. The moderate deviations are obtained by the delta method in large deviation principle.     

Moderate Deviation Principles for Empirical Covariance in the Neighbourhood of the Unit Root

In this paper, we consider the linear autoregressive model with varying coefficients θ_n∈[0,1). When θ_n tending to the unit root, the moderate deviation principle for empirical covariance is discussed, and as statistical applications, we provide the moderate deviation estimates of the least square and the Yule–Walker estimators of the parameter θ_n.     

Moderate deviations for quantile regression processes

This paper mainly discusses the asymptotic properties of quantile regression processes. In view of the exponential tightness and convexity argument, we prove the quantile regression estimators satisfy the functional moderate deviation principle. This method can be extended to a fair range of different statistical estimation problems such as quantile regression estimators with bridge penalized functions.     

Laws of the Iterated Logarithm and a Moderate Deviation of MLE for the Proportional Hazards Model with Incomplete Information

In this paper, we obtain a law of iterated logarithm, a Chung-type law of iterated logarithm, and a moderate deviation result of the maximum likelihood estimator (MLE) for the unknown regression parameter vector in a proportional hazards model with incomplete information.     

极差、平均差和标准差之间测度关系研究

极差（R）、平均差（AD）和标准差（δ）是描述离散程度所采用的三个测度值，通过证明，三者之间存在着R≥δ≥AD≥0的关系式。通过例证还得知，四分位差（Qd）与它们的关系并不确定。在具体运用三个测度值时，应考虑到各自的优缺点。     

Robustness of confidence intervals for scale parameters based on m-estimators

The robustness of confidence intervals for a scale parameter based on M-esimators is studied, especially in small size samples. The coverage probablity is used as measure of robustness. A theorem for a lower bound of the minimum coverage probability of M-estimators is presented and it is applied in order to examine the behavior of the standard deviation and the median absolute deviation, as interval estimators. This bound can confirm the robustness of any other scale M-estimator in interval estimation. The idea of stretching is used to formulate the family of distributions that are considered as underlying. Critical values for the confidence interval are computed where it is needed, that is for the median absolute deviation in the Normal, Uniform and Cauchy distribution and for the standard deviation in the Uniform and Cauchy distribution. Simulation results have been achieved for the estimation of the coverage probabilities and the critical values.     

A Multivariate Synthetic Control Chart for Monitoring the Process Mean Vector of Skewed Populations Using Weighted Standard Deviations

This article proposes a multivariate synthetic control chart for skewed populations based on the weighted standard deviation method. The proposed chart incorporates the weighted standard deviation method into the standard multivariate synthetic control chart. The standard multivariate synthetic chart consists of the Hotelling's T ² chart and the conforming run length chart. The weighted standard deviation method adjusts the variance–covariance matrix of the quality characteristics and approximates the probability density function using several multivariate normal distributions. The proposed chart reduces to the standard multivariate synthetic chart when the underlying distribution is symmetric. In general, the simulation results show that the proposed chart performs better than the existing multivariate charts for skewed populations and the standard T ² chart, in terms of false alarm rates as well as moderate and large mean shift detection rates based on the various degrees of skewnesses.     

Graphical Demonstration of an Optimality Property of the Median

The property that the mean absolute deviation is a minimum when measured from a median is demonstrated with graphs. Deficiencies of the usual proof of the property are pointed out, and a new, general proof is suggested.     

Finite sample correction factors for several simple robust estimators of normal standard deviation

Estimation of the standard deviation of a normal population is an important practical problem that in industrial practice must often be done from small and possibly contaminated data sets. Using multiple estimators is useful, as differences in the estimates may indicate whether the data set is contaminated and the form of the contamination. In this paper, finite sample correction factors have been estimated by simulation for several simple robust estimators of the standard deviation of a normal population. The estimators are the median absolute deviation, interquartile range, shortest half interval (Shorth), and median moving range. Finite sample correction factors have also been estimated for the commonly used non-robust estimators: mean absolute deviation and mean moving range. The simulation has been benchmarked against finite sample correction factors for the sample standard deviation and the sample range.     

Comparison of Robust Estimators of Standard Deviation in Normal Distributions Within the Context of Quality Control

Pitman criterion is used in simulation to determine the “closer” estimator of the standard deviation among selected choices. The initial simulation utilizes a standard normal distribution from which samples are taken of specific sizes. Popular and commonly used estimators of standard deviation are compared with the known population standard deviation in this study. Closeness criterion is calculated for each comparison and sample size. A secondary simulation applies the findings to variables control charts, in order to verify the ability of each estimator to identify out-of-control conditions.     

Robust analogs to the coefficient of variation

The coefficient of variation (CV) is commonly used to measure relative dispersion. However, since it is based on the sample mean and standard deviation, outliers can adversely affect it. Additionally, for skewed distributions the mean and standard deviation may be difficult to interpret and, consequently, that may also be the case for the CV. Here we investigate the extent to which quantile-based measures of relative dispersion can provide appropriate summary information as an alternative to the CV. In particular, we investigate two measures, the first being the interquartile range (in lieu of the standard deviation), divided by the median (in lieu of the mean), and the second being the median absolute deviation, divided by the median, as robust estimators of relative dispersion. In addition to comparing the influence functions of the competing estimators and their asymptotic biases and variances, we compare interval estimators using simulation studies to assess coverage.     

Tests for assessment of agreement using probability criteria

For the assessment of agreement using probability criteria, we obtain an exact test, and for sample sizes exceeding 30, we give a bootstrap-t$t$ test that is remarkably accurate. We show that for assessing agreement, the total deviation index approach of Lin [2000. Total deviation index for measuring individual agreement with applications in laboratory performance and bioequivalence. Statist. Med. 19, 255–270] is not consistent and may not preserve its asymptotic nominal level, and that the coverage probability approach of Lin et al. [2002. Statistical methods in assessing agreement: models, issues and tools. J. Amer. Statist. Assoc. 97, 257–270] is overly conservative for moderate sample sizes. We also show that the nearly unbiased test of Wang and Hwang [2001. A nearly unbiased test for individual bioequivalence problems using probability criteria. J. Statist. Plann. Inference 99, 41–58] may be liberal for large sample sizes, and suggest a minor modification that gives numerically equivalent approximation to the exact test for sample sizes 30 or less. We present a simple and accurate sample size formula for planning studies on assessing agreement, and illustrate our methodology with a real data set from the literature.     

工业结构变动率计算方法探讨

 目前,工业结构变动率的计算方法主要有两种：绝对变动率和平均偏差变动率。我们认为前者直观简单,但不能体现行业自身变动的大小;后者能反映行业自身变动的大小,但忽略了大行业与小行业之间的差别。为此,本文提出了两种改进的方法：加权平均偏差变动率和修正加权平均偏差变动率,并以实例进行了分析比较。     

The Discounted Large Deviation Principle for Autoregressive Processes

In this article, the discounted large deviation principle for autoregressive processes is obtained under the Bernstein condition.     

Conditional median absolute deviation

We introduce conditional median absolute deviation to characterize how the local variability of one quantitative random variable varies with another one. A two-step estimation procedure is proposed and the resultant estimator possesses an adaptiveness property. Simulation indicates that this estimator is much more efficient than its competitors such as the conditional semi-interquartile range.     

Moderate deviations for the total population arising from a nearly unstable sub-critical Galton-Watson process with immigration

Abstract

In this paper, we consider the moderate deviation of the nearly unstable sub-critical Galton-Waston process with immigration for the centered total population arising. We discuss the main influence factors for the form of moderate deviation in different stochastic processes. Moreover, we compute the exact rate function in every different situation of MDP.     

Recursive M-estimators of location

This paper deals with recursive M-estimators of a location parameter θ in stationary processes when scale is regarded as a nuisance parameter. For the nonrecursive M-estimators, the median absolute deviation is a useful estimator of scale. Two recursive variants of the median absolute deviation are proposed and the performance of the resulting recursive estimators is examined in a numerical study.     

中国能源消费水平空间差异及成因研究

本文运用离差指标来测度中国能源消费水平空间差异,并将离差平方之和分解为地区内差异和地区间差异,使得能够测算总体差异的地区构成;将离差绝对值之和分解为各影响因素贡献份额,使得能够找出影响地区差异的主要影响因素。研究结果表明中国能源消费水平空间差异不断扩大;能源消费水平总体差异主要是由三大地区内部差异引起的,其中地区内部差异主要来自于东部地区;人均资本存量是影响我国能源消费水平空间差异的主要因素。本文据此提出相应的政策建议。     

Strong convergence rate of the least median absolute estimator in linear regression models

We propose a least median of absolute (LMA) estimator for a linear regression model, based on minimizing the median absolute deviation of the residuals. Under some regularity conditions on the design points and disturbances, the strong convergence rate of the LMA estimator is established.