Smoothed bootstrap bandwidth selection for nonparametric hazard rate estimation

A smoothed bootstrap method is presented for the purpose of bandwidth selection in nonparametric hazard rate estimation for iid data. In this context, two new bootstrap bandwidth selectors are established based on the exact expression of the bootstrap version of the mean integrated squared error of some approximations of the kernel hazard rate estimator. This is very useful since Monte Carlo approximation is no longer needed for the implementation of the two bootstrap selectors. A simulation study is carried out in order to show the empirical performance of the new bootstrap bandwidths and to compare them with other existing selectors. The methods are illustrated by applying them to a diabetes data set.     

Assessing reporting patterns of child sexual abuse within the Catholic Church using discontinuities in model parameter timeseries

Prior to 2002, little was known about sexual abuse within the Catholic Church. After the Boston Globe broke the story about John Geoghan - a priest in the Boston Archdiocese who was accused of abusing numerous children, convicted of one count of indecent assault, and eventually murdered in prison - the Church had many questions to answer. To this end, the United States Conference of Catholic Bishops (USCCB) commissioned John Jay College of Criminal Justice to research the nature and scope, as well as the causes and context of child sexual abuse within the Catholic Church.This research analyzes the data from the John Jay studies using a new quantitative technique, capable of adjusting for distortions introduced by delays in abuse reporting. By isolating discontinuities in model parameter timeseries, we determine changes in reporting patterns occurred during the period 1982-1988. A posteriori to the analysis, we provide some possible explanations for the changes in abuse reporting associated with the change-point. While the scope of this paper is limited to presenting a new methodological approach within the frame of a particular case study, the techniques are more broadly applicable in settings where reporting lag is manifested.     

一类稀疏投资组合双层参数估计模型及其应用

带基约束的投资组合问题是近年来投资组合领域的热点问题,但是参数不确定性直接影响了模型的效果。带基约束的投资组合问题所涉及的参数不仅包括以往研究认为非常重要的预期收益率,还包括控制投资组合规模的稀疏度,尤其是最优稀疏度估计方面的专门研究还十分匮乏。为了使带基约束的投资组合模型更好地为投资决策服务,本文从投资者效用出发,用双层规划的思想构建了带基约束的投资组合双层参数估计模型。然后根据模型的特点,设计了无导数优化算法框架,并基于ADMM对算法子问题进行求解。本文实验针对真实的市场数据给出了预期收益率和最优稀疏度的估计,接着通过与等权重策略和含上下界约束的均值-方差模型进行比较,说明了模型及算法的有效性和实用性。最后,将本文提出的双层参数估计模型推广到了更一般的形式。     

一种简单有效的二项分布比例参数似然比置信区间的求法

对二项分布比例参数p的似然比置信区间,提出一种简便求解方法。在平均覆盖率、平均区间长度及区间长度的95%置信区间准则下与WScore、Plus4、Jeffreys置信区间进行模拟比较。试验表明,在二项分布b(n,p)的参数n≥20且p∈(0.1,0.9)时,该方法获取的似然比置信区间性能优良。当点估计p值不是接近于0或1且n≥20时,推荐使用本方法获取p的置信区间。     

Quantile dispersion graphs to compare the efficiencies of cluster randomized designs

The purpose of this article is to compare efficiencies of several cluster randomized designs using the method of quantile dispersion graphs (QDGs). A cluster randomized design is considered whenever subjects are randomized at a group level but analyzed at the individual level. A prior knowledge of the correlation existing between subjects within the same cluster is necessary to design these cluster randomized trials. Using the QDG approach, we are able to compare several cluster randomized designs without requiring any information on the intracluster correlation. For a given design, several quantiles of the power function, which are directly related to the effect size, are obtained for several effect sizes. The quantiles depend on the intracluster correlation present in the model. The dispersion of these quantiles over the space of the unknown intracluster correlation is determined, and then depicted by the QDGs. Two applications of the proposed methodology are presented.     

Transformed generalized linear models

The estimation of data transformation is very useful to yield response variables satisfying closely a normal linear model. Generalized linear models enable the fitting of models to a wide range of data types. These models are based on exponential dispersion models. We propose a new class of transformed generalized linear models to extend the Box and Cox models and the generalized linear models. We use the generalized linear model framework to fit these models and discuss maximum likelihood estimation and inference. We give a simple formula to estimate the parameter that index the transformation of the response variable for a subclass of models. We also give a simple formula to estimate the r$r$th moment of the original dependent variable. We explore the possibility of using these models to time series data to extend the generalized autoregressive moving average models discussed by Benjamin et al. [Generalized autoregressive moving average models. J. Amer. Statist. Assoc. 98, 214–223]. The usefulness of these models is illustrated in a simulation study and in applications to three real data sets.     

The discrepancy of P-values and posterior probability: Two-sided hypothesis of variance of normal distribution with unknown mean

This article is concerned with the comparison of P-value and Bayesian measure in point null hypothesis for the variance of Normal distribution with unknown mean. First, using fixed prior for test parameter, the posterior probability is obtained and compared with the P-value when an appropriate prior is used for the mean parameter. In the second, lower bounds of the posterior probability of H₀ under a reasonable class of prior are compared with the P-value. It has been shown that even in the presence of nuisance parameters, these two approaches can lead to different results in the statistical inference.     

The Bayes rule of the variance parameter of the hierarchical normal and inverse gamma model under Stein's loss

For the variance parameter of the hierarchical normal and inverse gamma model, we analytically calculate the Bayes rule (estimator) with respect to a prior distribution IG (alpha, beta) under Stein's loss function. This estimator minimizes the posterior expected Stein's loss (PESL). We also analytically calculate the Bayes rule and the PESL under the squared error loss. Finally, the numerical simulations exemplify that the PESLs depend only on alpha and the number of observations. The Bayes rules and PESLs under Stein's loss are unanimously smaller than those under the squared error loss.     

Extended scaled prediction variance optimality for modified central composite design

Robust parameter designs (RPDs) enable the experimenter to discover how to modify the design of the product to minimize the effect due to variation from noise sources. The aim of this article is to show how this amount of work can be reduced under modified central composite design (MCCD). We propose a measure of extended scaled prediction variance (ESPV) for evaluation of RPDs on MCCD. Using these measures, we show that we can check the error or bias associated with estimating the model parameters and suggest the values of α recommended for MCCS under minimum ESPV.     

A new confidence interval in measurement error model with the reliability ratio known

For the slope parameter of the measurement error model with the reliability ratio known, this article constructs a fiducial generalized confidence interval (FGCI) which is proved to have correct asymptotic coverage. Simulation results demonstrate that the FGCI often outperforms the existing intervals in terms of empirical coverage probability, average interval length, and false parameter coverage rate. Two examples are also provided to illustrate our approach.