Bootstrap confidence interval for a correlation curve

A correlation curve measures the strength of the association between two variables locally at different values of x. The purpose of this study is to obtain point-wise confidence intervals for a correlation curve using wild bootstrap techniques. Empirical coverage probabilities are found to be close to the specified nominal level. Bootstrapping is an attractive alternative to confidence intervals based on asymptotic expressions that have slow rate of convergence.     

统计方法在大学英语四级成绩分析中的应用

本文以本校2005级本科生为调查对象,考察影响大学生四级考试（College English Test Band Four,简称CET-4）CET-4成绩的因素。采用Bootstrap方法与T检验方法,分析得出：来自城市和农村的大学生CET-4成绩存在差异;大一大二四学期英语水平不同的人CET-4成绩存在显著差异;文、理科大学生CET-4成绩也存在差异。进一步,我们运用多元统计中回归分析的方法建立了CET-4成绩的回归模型,并利用Logistic模型对四级通过率进行了预测。     

Computational Tools for Evaluating Phylogenetic and Hierarchical Clustering Trees

This article presents an alternative derivation of the generalized approximate crossvalidation (GACV) score of Xiang and Wahba (1996) for smoothing parameter selection in penalized likelihood regression. The new derivation suggests a simple numerical solution that is stable for all sample sizes. Also suggested is a variant of the score that can be computationally more convenient. Simple simulations are presented to illustrate the effectiveness of the scores.     

A Method for the Computer Calculation of Edgeworth Expansions for Smooth Function Models

Abstract

In this article I describe, in detail, a method for the computer calculation of Edgeworth expansions for a smooth function model accurate in the O(n ^–1) term. For such models, these expansions are an important tool for the analysis of normalizing transformations, the correction of an approximately normally distributed quantity for skewness, and the comparison of bootstrap inference procedures. The method is straightforward and is efficient in a sense described in the article. The implementation of the method in general is clear from its implementation in the Mathematica program (available through StatLib) for the particular case of the studentized mean.     

Formal Hypothesis Tests for Additive Structure in Random Forests

While statistical learning methods have proved powerful tools for predictive modeling, the black-box nature of the models they produce can severely limit their interpretability and the ability to conduct formal inference. However, the natural structure of ensemble learners like bagged trees and random forests has been shown to admit desirable asymptotic properties when base learners are built with proper subsamples. In this work, we demonstrate that by defining an appropriate grid structure on the covariate space, we may carry out formal hypothesis tests for both variable importance and underlying additive model structure. To our knowledge, these tests represent the first statistical tools for investigating the underlying regression structure in a context such as random forests. We develop notions of total and partial additivity and further demonstrate that testing can be carried out at no additional computational cost by estimating the variance within the process of constructing the ensemble. Furthermore, we propose a novel extension of these testing procedures using random projections to allow for computationally efficient testing procedures that retain high power even when the grid size is much larger than that of the training set.     

Estimations from the exponentiated rayleigh distribution based on generalized Type-II hybrid censored data

In this article, unknown parameters of exponentiated Rayleigh distribution based on generalized Type II Hybrid censored data, survival function, failure rate function and coefficient of variation are derived by applying the maximum likelihood, Bayes and percentile bootstrap methods. Approximate confidence intervals for the unknown parameters, survival function, failure rate function and coefficient of variation are obtained. We study Bayes estimates under gamma priors distributions depending on symmetric and asymmetric loss functions via the Gibbs within Metropolis-Hasting samplers procedure. Finally, the proposed methods can be understood through illustrating the results of the real data analysis.     

基于随机加权的空间聚集性检验及其在基础教育师资均衡性评价中的应用

使用空间统计检验方法研究北京基础教育资源分配的均衡性问题.对于空间分布均匀性的检验,常用的统计量是Moran's I统计量.但基于Moran's I统计量做推断的时候,人们往往用渐进正态分布或者用Bootstrap反复抽样得到经验分布来进行.提出使用随机加权法进行统计量的经验检验.Jin和Lee(2014)文中得出基于Bootstrap的Moran's I统计量满足一致逼近和渐进正态等性质.采用类似的统计工具证明了基于随机加权得到的统计量的渐进分布也满足这些良好性质.填补了用随机加权法在空间统计量的推断中理论保证的空白.通过模拟研究,证明了所提算法的有效性.方法应用于北京基础教育的师资-适龄儿童数比例,师资-在校生数比例的空间聚集性检验中得到了良好的应用,并与其它检验方法所得结论进行比较.结论显示在不同相邻概念(地理相邻、政策空间相邻)下,方法得到的结论符合常理.     

On the asymptotic accuracy of the bootstrap under arbitrary resampling size

We study the order of convergence of the Kolmogorov-Smirnov distance for the bootstrap of the mean and the bootstrap of quantiles when an arbitrary bootstrap sample size is used. We see that for the bootstrap of the mean, the best order of the bootstrap sample is of the order ofn, wheren is the sample size. In the case of non-lattice distributions and the bootstrap of the sample mean; the bootstrap removes the effect of the skewness of the distribution only when the bootstrap sample equals the sample size. However, for the bootstrap of quantiles, the preferred order of the bootstrap sample isn ^2/3. For the bootstrap of quantiles, if the bootstrap sample is of ordern ² or bigger, the bootstrap is not consistent.     

Bayesian nonparametric predictive inference and bootstrap techniques

We address the question as to whether a prior distribution on the space of distribution functions exists which generates the posterior produced by Efron's and Rubin's bootstrap techniques, emphasizing the connection with the Dirichlet process. We also introduce a new resampling plan which has two advantages: prior opinions are taken into account and the predictive distribution of the future observations is not forced to be concentrated on observed values.     

Bootstrap approaches and confidence intervals for stationary and non-stationary long-range dependence processes

This paper deals with different bootstrap approaches and bootstrap confidence intervals in the fractionally autoregressive moving average (ARFIMA(p,d,q))$(\text{ARFIMA}(p,d,q))$ process [J. Hosking, Fractional differencing, Biometrika 68(1) (1981) 165–175] using parametric and semi-parametric estimation techniques for the memory parameter d. The bootstrap procedures considered are: the classical bootstrap in the residuals of the fitted model [B. Efron, R. Tibshirani, An Introduction to the Bootstrap, Chapman and Hall, New York, 1993], the bootstrap in the spectral density function [E. Paparoditis, D.N Politis, The local bootstrap for periodogram statistics. J. Time Ser. Anal. 20(2) (1999) 193–222], the bootstrap in the residuals resulting from the regression equation of the semi-parametric estimators [G.C Franco, V.A Reisen, Bootstrap techniques in semiparametric estimation methods for ARFIMA models: a comparison study, Comput. Statist. 19 (2004) 243–259] and the Sieve bootstrap [P. Bühlmann, Sieve bootstrap for time series, Bernoulli 3 (1997) 123–148]. The performance of these procedures and confidence intervals for d in the stationary and non-stationary ranges are empirically obtained through Monte Carlo experiments. The bootstrap confidence intervals here proposed are alternative procedures with some accuracy to obtain confidence intervals for d.