Normal approximation to the hypergeometric distribution in nonstandard cases and a sub-Gaussian Berry–Esseen theorem

In this paper, we consider simple random sampling without replacement from a dichotomous finite population. We investigate accuracy of the Normal approximation to the Hypergeometric probabilities for a wide range of parameter values, including the nonstandard cases where the sampling fraction tends to one and where the proportion of the objects of interest in the population tends to the boundary values, zero and one. We establish a non-uniform Berry–Esseen theorem for the Hypergeometric distribution which shows that in the nonstandard cases, the rate of Normal approximation to the Hypergeometric distribution can be considerably slower than the rate of Normal approximation to the Binomial distribution. We also report results from a moderately large numerical study and provide some guidelines for using the Normal approximation to the Hypergeometric distribution in finite samples.     

Rényi statistics for testing hypotheses in mixed linear regression models

Rényi divergences are used to propose some statistics for testing general hypotheses in mixed linear regression models. The asymptotic distribution of these tests statistics, of the Kullback–Leibler and of the likelihood ratio statistics are provided, assuming that the sample size and the number of levels of the random factors tend to infinity. A simulation study is carried out to analyze and compare the behavior of the proposed tests when the sample size and number of levels are small.     

On the detection of changes in autoregressive time series I. Asymptotics

Various test statistics are discussed which can be used for detecting changes in the parameters of an autoregressive time series. In this first part of our study, the limiting behavior of the test statistics is derived under the null hypothesis of no change as well as under alternatives. In a forthcoming second part of our investigation, these asymptotic results will be compared to some corresponding bootstrap procedures, and a small simulation study will be conducted.     

《101/2章世界史》中的反讽艺术

《10 1/2章世界史》是英国当代作家朱利安.巴恩斯的代表作之一。作者以《圣经》中的诺亚方舟为基本意象,敷衍出10 1/2章故事,同时以反讽的姿态重新审视神话传说和历史事件,在有限的篇幅内展现出了一幅独特的人类历史画卷。     

Robust estimating equation based on statistical depth

In this paper the estimating equation is constructed via statistical depth. The obtained estimating equation and parameter estimation have desirable robustness, which attain very high breakdown values close to 1/2. At the same time, the obtained parameter estimation still has ordinary asymptotic behaviours such as asymptotic normality. In particular, the robust quasi likelihood and depth-weighted LSE respectively for nonlinear and linear regression model are introduced. A suggestion for choosing weight function and a method of constructing depth-weighed quasi likelihood equation are given. This paper is supported by NNSF projects (10371059 and 10171051) of China.     

UNEMPLOYMENT INSURANCE AND CULTURAL TRANSMISSION: THEORY AND APPLICATION TO EUROPEAN UNEMPLOYMENT

This paper emphasizes the two‐way causality between the provision of unemployment insurance and the cultural transmission of civicness. The returns to being uncivic are increasing in the generosity of unemployment insurance; but this generosity is decreasing in the number of uncivic individuals. In this context, I determine the evolution of preferences across generations and show that cultural heterogeneity is sustained over the long‐run. The dynamics of cultural transmission can generate a long lag between the introduction of unemployment insurance and an increase in people's willingness to live off government‐provided benefits. Hence, it offers an explanation to the ‘European unemployment puzzle’ due to the coexistence of generous unemployment insurance and low unemployment in the 1950s and 1960s.     

永泰县城区空气中主要污染物类别及其影响因素分析

经监测,永泰县城区大气污染物主要为PMl0、PM2.5、O3,影响O3的因素主要有汽车尾气排放、日照,PMl0、PM2.5浓度大小除与车流量、烟花爆竹燃放相关外,还与降水、风速等气象因素密切关联。针对这些影响因素,该文提出了相应的防治措施。     

Do bootstrap confidence procedures behave well uniformly in P?

An important statistical problem is to construct a confidence set for some functional T(P) of some unknown probability distribution P. Typically, this involves approximating the sampling distribution J_n(P) of some pivot based on a sample of size n from P. A bootstrap procedure is to estimate J_n(P) by J_n(&Pcirc;_n), where P?_n is the empirical measure based on a sample of size n from P. Typically, one has that J_n(P) and J_n(P?_n) are close in an appropriate sense. Two questions are addressed in this note. Are J_n(P) and J_n(P?_n) uniformly close as P varies as well? If so, do confidence statements about T(P) possess a corresponding uniformity property? In the case T(P) = P, the answer to the first questions is yes; the answer to the second is no. However, bootstrap confidence statements about T(P) can be made uniform over a restricted, though large, class of P. Similar results apply to other functional T(P).     

Rate of strong uniform convergence of k-NN density estimates

Let f_n(x) be the univariate k-nearest neighbor (k-NN) density estimate proposed by Loftsgaarden and Quesenberry (1965). By using similar techniques as in Bahadur's representation of sample quantiles (1966), and by the recent results on the oscillation of empirical processes by Stute (1982), we derive the rate of strong uniform convergence of f_n(x) on some suitably chosen interval J_δ. Some comparison with the kernel estimates is given, as well as the choice of the bandwidth sequence relative to the sample size.     

Non-parametric recursive estimates of a probability density function and its derivatives

Recursive estimates of a probability density function (pdf) are known. This paper presents recursive estimates of a derivative of any desired order of a pdf. Let f be a pdf on the real line and p?0 be any desired integer. Based on a random sample of size n from f, estimators f^(p)_n of f^(p), the pth order derivatives of f, are exhibited. These estimators are of the form $\text{n}{}^{\mathrm{?1}}\text{∑n}\text{j=1}\text{δ}{}_{\mathrm{jp}}$, where δ_jp depends only on p and the jth observation in the sample, and hence can be computed recursively as the sample size increases. These estimators are shown to be asymptotically unbiased, mean square consistent and strongly consistent, both at a point and uniformly on the real line. For pointwise properties, the conditions on f^(p) have been weakened with a little stronger assumption on the kernel function.