Finite mixture of regression models for a stratified sample

Despite the popularity and importance, there is limited work on modelling data which come from complex survey design using finite mixture models. In this work, we explored the use of finite mixture regression models when the samples were drawn using a complex survey design. In particular, we considered modelling data collected based on stratified sampling design. We developed a new design-based inference where we integrated sampling weights in the complete-data log-likelihood function. The expectation–maximisation algorithm was developed accordingly. A simulation study was conducted to compare the new methodology with the usual finite mixture of a regression model. The comparison was done using bias-variance components of mean square error. Additionally, a simulation study was conducted to assess the ability of the Bayesian information criterion to select the optimal number of components under the proposed modelling approach. The methodology was implemented on real data with good results.     

A new aging concept derived from the increasing convex ordering

In this paper, a comparison between the life distribution of a new unit with that of a used unit in the increasing convex order is made leading to a new class of life distributions which we call “new better than used in convex ordering of second order”. This class includes as subclasses the NBU and the NBUC and is a subclass of the NBUCA class. Preservation properties under convolution, random maxima, mixing and formation of coherent structures are established. Stochastic comparisons of the excess lifetime when the inter-arrival times belong to the NBUC(2) class are developed. Some applications of Poisson shock models and a test of exponentiality against NBUC(2) alternative are presented.     

Inferences for a Partially Varying Coefficient Model With Endogenous Regressors

In this article, we propose a new class of semiparametric instrumental variable models with partially varying coefficients, in which the structural function has a partially linear form and the impact of endogenous structural variables can vary over different levels of some exogenous variables. We propose a three-step estimation procedure to estimate both functional and constant coefficients. The consistency and asymptotic normality of these proposed estimators are established. Moreover, a generalized F-test is developed to test whether the functional coefficients are of particular parametric forms with some underlying economic intuitions, and furthermore, the limiting distribution of the proposed generalized F-test statistic under the null hypothesis is established. Finally, we illustrate the finite sample performance of our approach with simulations and two real data examples in economics.     

Efficient Bayesian inference in generalized inverse gamma processes for stochastic volatility

This paper develops a novel and efficient algorithm for Bayesian inference in inverse Gamma stochastic volatility models. It is shown that by conditioning on auxiliary variables, it is possible to sample all the volatilities jointly directly from their posterior conditional density, using simple and easy to draw from distributions. Furthermore, this paper develops a generalized inverse gamma process with more flexible tails in the distribution of volatilities, which still allows for simple and efficient calculations. Using several macroeconomic and financial datasets, it is shown that the inverse gamma and generalized inverse gamma processes can greatly outperform the commonly used log normal volatility processes with Student’s t errors or jumps in the mean equation.     

On approximations via convolution-defined mixture models

An often-cited fact regarding mixing or mixture distributions is that their density functions are able to approximate the density function of any unknown distribution to arbitrary degrees of accuracy, provided that the mixing or mixture distribution is sufficiently complex. This fact is often not made concrete. We investigate and review theorems that provide approximation bounds for mixing distributions. Connections between the approximation bounds of mixing distributions and estimation bounds for the maximum likelihood estimator of finite mixtures of location-scale distributions are reviewed.     

Cytometry inference through adaptive atomic deconvolution

In this paper, we consider a statistical estimation problem known as atomic deconvolution. Introduced in reliability, this model has a direct application when considering biological data produced by flow cytometers. From a statistical point of view, we aim at inferring the percentage of cells expressing the selected molecule and the probability distribution function associated with its fluorescence emission. We propose here an adaptive estimation procedure based on a previous deconvolution procedure introduced by Es, Gugushvili, and Spreij [(2008), ‘Deconvolution for an atomic distribution’, Electronic Journal of Statistics, 2, 265–297] and Gugushvili, Es, and Spreij [(2011), ‘Deconvolution for an atomic distribution: rates of convergence’, Journal of Nonparametric Statistics, 23, 1003–1029]. For both estimating the mixing parameter and the mixing density automatically, we use the Lepskii method based on the optimal choice of a bandwidth using a bias-variance decomposition. We then derive some convergence rates that are shown to be minimax optimal (up to some log terms) in Sobolev classes. Finally, we apply our algorithm on the simulated and real biological data.     

Bayesian density regression for discrete outcomes

We develop Bayesian models for density regression with emphasis on discrete outcomes. The problem of density regression is approached by considering methods for multivariate density estimation of mixed scale variables, and obtaining conditional densities from the multivariate ones. The approach to multivariate mixed scale outcome density estimation that we describe represents discrete variables, either responses or covariates, as discretised versions of continuous latent variables. We present and compare several models for obtaining these thresholds in the challenging context of count data analysis where the response may be over‐ and/or under‐dispersed in some of the regions of the covariate space. We utilise a nonparametric mixture of multivariate Gaussians to model the directly observed and the latent continuous variables. The paper presents a Markov chain Monte Carlo algorithm for posterior sampling, sufficient conditions for weak consistency, and illustrations on density, mean and quantile regression utilising simulated and real datasets.     

禅宗“斗机锋”交际的核心思维模式

“斗机锋”在行为表层体现为双人或多人参与的言语、副言语互动交际。“斗机锋”与一般交际行为存在共性,同时也存在显著差异。“斗机锋”是由禅宗逻辑下的思维系统驱动的,在一般理性下显得不可理喻。“斗机锋”展现出令人眼花缭乱的互动,若剥离其行为表层,则可还原为不同思维模式之间的对垒,涉及的思维模式主要有五类：“一切现成”思维、“不二”思维、“究竟本缘”思维、“离杀”思维、“空空”思维。“斗机锋”训练的基本目标是消除参与者对固化思维程式的执著,开发更广泛的思维途径。经过训练,参与者可以提升思维的创造性、灵活性和迅捷性,也可能被偶然地诱导发生顿悟。     

中国生育率研究方法:30年回眸

改革开放30年是我国人口学及人口研究迅速成长的30年。生育率研究方法从一个侧面反映出改革开放以来我国人口学研究方法的发展。中国的生育率研究方法既有从西方引进的各种生育率指标和模型,也有中国学者为了适应自己的需要而改进和创建的方法和模型。笔者从生育率度量指标和生育率模型两个方面总结我国生育率研究方法的应用及变化。对在中国生育率研究中所使用的主要方法进行回顾并对这些方法对我国生育率研究的贡献进行总结。     

上海市人口老龄化：现状、影响及对策思考

人口老龄化已成为当今世界各国经济发展过程面临的共同性话题,就上海而言．未来上海市人口老龄化带来的影响已逐渐凸显,人口老龄化带来的养老金匮乏,劳动力不足以及社区为老服务发展滞后的矛盾已开始成为制约上海市经济发展的瓶颈,老龄化带来的影响将在未来很长一段时间内长期存在．缓解人口老龄化带来的影响以及寻求可行性办法解决老龄化人口的赡养问题已成为政府和社会必须要解决的问题。