Efficiency of the generalized-difference-based weighted mixed almost unbiased two-parameter estimator in partially linear model

In this paper, a generalized difference-based estimator is introduced for the vector parameter β in partially linear model when the errors are correlated. A generalized-difference-based almost unbiased two-parameter estimator is defined for the vector parameter β. Under the linear stochastic constraint r = Rβ + e, we introduce a new generalized-difference-based weighted mixed almost unbiased two-parameter estimator. The performance of this new estimator over the generalized-difference-based estimator and generalized- difference-based almost unbiased two-parameter estimator in terms of the MSEM criterion is investigated. The efficiency properties of the new estimator is illustrated by a simulation study. Finally, the performance of the new estimator is evaluated for a real dataset.     

Marginal zero-inflated regression models for count data

Data sets with excess zeroes are frequently analyzed in many disciplines. A common framework used to analyze such data is the zero-inflated (ZI) regression model. It mixes a degenerate distribution with point mass at zero with a non-degenerate distribution. The estimates from ZI models quantify the effects of covariates on the means of latent random variables, which are often not the quantities of primary interest. Recently, marginal zero-inflated Poisson (MZIP; Long et al. [A marginalized zero-inflated Poisson regression model with overall exposure effects. Stat. Med. 33 (2014), pp. 5151–5165]) and negative binomial (MZINB; Preisser et al., 2016) models have been introduced that model the mean response directly. These models yield covariate effects that have simple interpretations that are, for many applications, more appealing than those available from ZI regression. This paper outlines a general framework for marginal zero-inflated models where the latent distribution is a member of the exponential dispersion family, focusing on common distributions for count data. In particular, our discussion includes the marginal zero-inflated binomial (MZIB) model, which has not been discussed previously. The details of maximum likelihood estimation via the EM algorithm are presented and the properties of the estimators as well as Wald and likelihood ratio-based inference are examined via simulation. Two examples presented illustrate the advantages of MZIP, MZINB, and MZIB models for practical data analysis.     

网络社区发现算法在流动表建模中的设计与应用

代际流动表可以统计子代与其父代社会地位配对数据的交互频数，反映了社会资源占有的优劣势在父子两代人之间的比较。对财富、阶级、特权等社会基本特征演变的实证考察，均依赖于代际流动表的量化分析。对数线性模型是流动表建模分析的基本工具，通过对列联表单元格频数进行拟合，可以识别流动表行分类与列分类之间的强弱交互效应，刻画父子社会地位间的交互结构。本文利用复杂网络社区发现算法分析父子社会地位的关联结构，针对简约对数线性模型拟合精度不够的问题，提出一种新的建模思路：利用社区发现算法对简约对数线性模型的残差列联表进行关联关系挖掘，将发现的社区效应作为附加参数约束引入原对数线性模型，以改善数据的拟合情况。由于该方法只在原简约对数线性模型中增加了一个参数约束，因此仍可以保证建模结果的简洁性及理论意义，同时社区效应补充了原对数线性模型对经验数据结构的解读。论文用此方法对来源于中国综合社会调查数据的经验代际职业流动表进行建模分析，较好地解释了子代职业阶层与父代职业阶层间的关联模式。     

Tail asymptotic of discounted aggregate claims with compound dependence under risky investment

This paper considers the tail asymptotic of discounted aggregate claims with compound dependence under risky investment. The price of risky investment is modeled by a geometric Lévy process, while claims are modeled by a one-sided linear process whose innovations further obeying a so-called upper tail asymptotic independence. When the innovations are heavy tailed, we derive some uniform asymptotic formulas. The results show that the linear dependence has significant impact on the tail asymptotic of discounted aggregate claims but the upper tail asymptotic independence is negligible.     

A class of partially linear transformation models for recurrent gap times

In this article, we propose a general class of partially linear transformation models for recurrent gap time data, which extends the linear transformation models by incorporating non linear covariate effects and includes the partially linear proportional hazards and the partially linear proportional odds models as special cases. Both global and local estimating equations are developed to estimate the parametric and non parametric covariate effects, and the asymptotic properties of the resulting estimators are established. The finite-sample behavior of the proposed estimators is evaluated through simulation studies, and an application to a clinic study on chronic granulomatous disease is provided.     

The beta generalized linear exponential distribution

In this paper, a new five-parameter lifetime distribution called beta generalized linear exponential distribution (BGLED) is introduced. It includes at least 17 popular sub-models as special cases such as the beta linear exponential, the beta generalized exponential, and the exponentiated generalized linear distributions. Mathematical and statistical properties of the proposed distribution are discussed in details. In particular, explicit expression for the density function, moments, asymptotics distributions for sample extreme statistics, and other statistical measures are obtained. The estimation of the parameters by the method of maximum-likelihood is discussed and the finite sample properties of the maximum-likelihood estimators (MLEs) are investigated numerically. A real data set is used to demonstrate its superior performance fit over several existing popular lifetime models.     

Quasi-minimax estimation in the partial linear model

This article discusses the minimax estimator in partial linear model y = Zβ + f + ε under ellipsoidal restrictions on the parameter space and quadratic loss function. The superiority of the minimax estimator over the two-step estimator is studied in the mean squared error matrix criterion.     

Why do we observe misclassification errors smaller than the Bayes error?

In simulation studies for discriminant analysis, misclassification errors are often computed using the Monte Carlo method, by testing a classifier on large samples generated from known populations. Although large samples are expected to behave closely to the underlying distributions, they may not do so in a small interval or region, and thus may lead to unexpected results. We demonstrate with an example that the LDA misclassification error computed via the Monte Carlo method may often be smaller than the Bayes error. We give a rigorous explanation and recommend a method to properly compute misclassification errors.