Testing for the Equality of Two Autoregressive Functions Using Quasi-Residuals

This article discusses the problem of testing the equality of two nonparametric autoregressive functions against one-sided alternatives. The heteroscedastic errors and stationary densities of the two independent strong mixing strictly stationary time series can be possibly different. The article adapts the idea of using sum of quasi-residuals to construct the test and derives its asymptotic null distributions. The article also shows that the test is consistent for general alternatives and obtains its limiting distributions under a sequence of local alternatives. Then a Monte Carlo simulation is conducted to study the finite sample level and power behavior of these tests at some alternatives. We also compare the test to an existing lag matched test theoretically and by Monte Carlo experiments.     

Bayesian Proportional Hazard Analysis of the Timing of High School Dropout Decisions

In this paper, I study the timing of high school dropout decisions using data from High School and Beyond. I propose a Bayesian proportional hazard analysis framework that takes into account the specification of piecewise constant baseline hazard, the time-varying covariate of dropout eligibility, and individual, school, and state level random effects in the dropout hazard. I find that students who have reached their state compulsory school attendance ages are more likely to drop out of high school than those who have not reached compulsory school attendance ages. Regarding the school quality effects, a student is more likely to drop out of high school if the school she attends is associated with a higher pupil–teacher ratio or lower district expenditure per pupil. An interesting finding of the paper that comes along with the empirical results is that failure to account for the time-varying heterogeneity in the hazard, in this application, results in upward biases in the duration dependence estimates. Moreover, these upward biases are comparable in magnitude to the well-known downward biases in the duration dependence estimates when the modeling of the time-invariant heterogeneity in the hazard is absent.     

Bayesian Approaches to Nonparametric Estimation of Densities on the Unit Interval

This paper investigates nonparametric estimation of density on [0, 1]. The kernel estimator of density on [0, 1] has been found to be sensitive to both bandwidth and kernel. This paper proposes a unified Bayesian framework for choosing both the bandwidth and kernel function. In a simulation study, the Bayesian bandwidth estimator performed better than others, and kernel estimators were sensitive to the choice of the kernel and the shapes of the population densities on [0, 1]. The simulation and empirical results demonstrate that the methods proposed in this paper can improve the way the probability densities on [0, 1] are presently estimated.     

Extreme Quantile Estimation for Autoregressive Models

ABSTRACT

A quantile autoregresive model is a useful extension of classical autoregresive models as it can capture the influences of conditioning variables on the location, scale, and shape of the response distribution. However, at the extreme tails, standard quantile autoregression estimator is often unstable due to data sparsity. In this article, assuming quantile autoregresive models, we develop a new estimator for extreme conditional quantiles of time series data based on extreme value theory. We build the connection between the second-order conditions for the autoregression coefficients and for the conditional quantile functions, and establish the asymptotic properties of the proposed estimator. The finite sample performance of the proposed method is illustrated through a simulation study and the analysis of U.S. retail gasoline price.     

Characterizations of the poisson process using,the variance

Let γ(t) be the residual life at time t of the renewal process {A(t), t > 0}, which has F as the common distribution function of the inter-arrival times. In this article we prove that if Var(γ(t)) is constant, then F will be exponentially or geometrically distributed under the assumption F is continuous or discrete respectively. An application and a related example also are given.     

论统计泄露控制问题

一、背景统计泄露控制 (ＳｔａｔｉｓｔｉｃａｌＤｉｓｃｌｏｓｕｒｅＣｏｎｔｒｏｌ)是指统计部门在为社会提供的统计资料中 ,不泄露任一单个个体 (如住户 ,企业等 )的资料。这里有两层意思 ,一层是统计泄露的问题 ,另一层是控制方法的问题 ,两者是密不可分的。世界上有关统计泄露控制的研究已有 2 0多年的历史 ,有专门的人员、项目、机构来从事这个问题的研究。1 统计泄露控制的需求众所周知 ,统计部门对外公布的资料 ,基本上来说有两种 ,即汇总 (综合 )资料和微观资料 (调查单位原始资料 )。事实上 ,原始数据是汇总数据的原材料 ,在计算…     

Shrinkage inverse regression estimation for model-free variable selection

Summary.  The family of inverse regression estimators that was recently proposed by Cook and Ni has proven effective in dimension reduction by transforming the high dimensional predictor vector to its low dimensional projections. We propose a general shrinkage estimation strategy for the entire inverse regression estimation family that is capable of simultaneous dimension reduction and variable selection. We demonstrate that the new estimators achieve consistency in variable selection without requiring any traditional model, meanwhile retaining the root n estimation consistency of the dimension reduction basis. We also show the effectiveness of the new estimators through both simulation and real data analysis.     

统计数据、统计安全与统计法治

 本文以《统计违法违纪行为处分规定》的施行为背景,以统计数据质量为切入点,讨论了统计法治问题。文章阐述了统计数据质量与国家统计安全、统计本质与统计法治的关系,并对实现统计法治的途径进行了探讨。     

Nonparametric and semiparametric estimation of the three way receiver operating characteristic surface

In many situations the diagnostic decision is not limited to a binary choice. Binary statistical tools such as receiver operating characteristic (ROC) curve and area under the ROC curve (AUC) need to be expanded to address three-category classification problem. Previous authors have suggest various ways to model the extension of AUC but not the ROC surface. Only simple parametric approaches are proposed for modeling the ROC measure under the assumption that test results all follow normal distributions. We study the estimation methods of three-dimensional ROC surfaces with nonparametric and semiparametric estimators. Asymptotical results are provided as a basis for statistical inference. Simulation studies are performed to assess the validity of our proposed methods in finite samples. We consider an Alzheimer's disease example from a clinical study in the US as an illustration. The nonparametric and semiparametric modelling approaches for the three way ROC analysis can be readily generalized to diagnostic problems with more than three classes.