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.     

陶渊明的诗化人格

作家的人格是其作品风格的内在因素 ,往往决定着其作品的风格。我们在研究作品风格的时候 ,不能不关注作家的人格。只有对作家的人格进行全面深入的审视 ,才能更准确地理解和把握其作品的风格。探讨陶渊明的人格魅力及其特征 ,是深入研究陶渊明作品风格的至关重要的途径。从陶渊明的作品中 ,从他的言行中 ,我们可以领悟到他的情趣和胸襟 ,领悟到一种具体的人格。陶渊明自然率真平和旷达的个性特征构筑了他的诗化人格 ,即未经世俗异化的高尚贞洁的人格。这种人格的内在思想根源是自然化迁的宇宙观和委运自然的人生观。这种人格的外在表现形式是他任真自得和固穷守节的行为方式。他的作品中常见的酒与菊、孤松、孤云与归鸟等艺术形象组成了陶渊明诗化人格的象征系列     

从"唐人选唐诗"看王昌龄在唐代诗坛地位的变迁

“唐人选唐诗”录王昌龄诗歌作品的情况反映出唐代不同时期人们对王昌龄诗歌接受态度及其在唐代诗坛地位的升降变迁。总体而言 ,昌龄因其五言古诗对盛唐诗风的开拓之功而受到当时选家普遍重视 ,有“诗家夫子”之称 ,中唐以后选家则独重昌龄七言绝句 ,虽以“七绝圣手”誉之 ,但其诗歌地位已非显著。文章同时指出 ,作为古代诗歌批评的一种特殊形态 ,唐诗选本所蕴含的诗学价值应受到重视 ,成为唐诗学研究的一个方向     

Empirical likelihood confidence intervals for the mean of a population containing many zero values

If a population contains many zero values and the sample size is not very large, the traditional normal approximation‐based confidence intervals for the population mean may have poor coverage probabilities. This problem is substantially reduced by constructing parametric likelihood ratio intervals when an appropriate mixture model can be found. In the context of survey sampling, however, there is a general preference for making minimal assumptions about the population under study. The authors have therefore investigated the coverage properties of nonparametric empirical likelihood confidence intervals for the population mean. They show that under a variety of hypothetical populations, these intervals often outperformed parametric likelihood intervals by having more balanced coverage rates and larger lower bounds. The authors illustrate their methodology using data from the Canadian Labour Force Survey for the year 2000.     

Non-ignorable missing covariate data in survival analysis: a case-study of an International Breast Cancer Study Group trial

Summary.  Non-ignorable missing data, a serious problem in both clinical trials and observational studies, can lead to biased inferences. Quality-of-life measures have become increasingly popular in clinical trials. However, these measures are often incompletely observed, and investigators may suspect that missing quality-of-life data are likely to be non-ignorable. Although several recent references have addressed missing covariates in survival analysis, they all required the assumption that missingness is at random or that all covariates are discrete. We present a method for estimating the parameters in the Cox proportional hazards model when missing covariates may be non-ignorable and continuous or discrete. Our method is useful in reducing the bias and improving efficiency in the presence of missing data. The methodology clearly specifies assumptions about the missing data mechanism and, through sensitivity analysis, helps investigators to understand the potential effect of missing data on study results.     

Merging information for semiparametric density estimation

Summary.  The density ratio model specifies that the likelihood ratio of m −1 probability density functions with respect to the m th is of known parametric form without reference to any parametric model. We study the semiparametric inference problem that is related to the density ratio model by appealing to the methodology of empirical likelihood. The combined data from all the samples leads to more efficient kernel density estimators for the unknown distributions. We adopt variants of well-established techniques to choose the smoothing parameter for the density estimators proposed.     

Assessing goodness-of-fit of categorical regression models based on case-control data

Demonstrated equivalence between a categorical regression model based on case‐control data and an I‐sample semiparametric selection bias model leads to a new goodness‐of‐fit test. The proposed test statistic is an extension of an existing Kolmogorov–Smirnov‐type statistic and is the weighted average of the absolute differences between two estimated distribution functions in each response category. The paper establishes an optimal property for the maximum semiparametric likelihood estimator of the parameters in the I‐sample semiparametric selection bias model. It also presents a bootstrap procedure, some simulation results and an analysis of two real datasets.     

A Bayesian method for classification and discrimination

We discuss Bayesian analyses of traditional normal-mixture models for classification and discrimination. The development involves application of an iterative resampling approach to Monte Carlo inference, commonly called Gibbs sampling, and demonstrates routine application. We stress the benefits of exact analyses over traditional classification and discrimination techniques, including the ease with which such analyses may be performed in a quite general setting, with possibly several normal-mixture components having different covariance matrices, the computation of exact posterior classification probabilities for observed data and for future cases to be classified, and posterior distributions for these probabilities that allow for assessment of second-level uncertainties in classification.     

Generating random variates from D-distributions via substitution sampling

Laud et al. (1993) describe a method for random variate generation from D-distributions. In this paper an alternative method using substitution sampling is given. An algorithm for the random variate generation from SD-distributions is also given.     

Divergence-based estimation and testing with misclassified data

The well-known chi-squared goodness-of-fit test for a multinomial distribution is generally biased when the observations are subject to misclassification. In Pardo and Zografos (2000) the problem was considered using a double sampling scheme and ø-divergence test statistics. A new problem appears if the null hypothesis is not simple because it is necessary to give estimators for the unknown parameters. In this paper the minimum ø-divergence estimators are considered and some of their properties are established. The proposed ø-divergence test statistics are obtained by calculating ø-divergences between probability density functions and by replacing parameters by their minimum ø-divergence estimators in the derived expressions. Asymptotic distributions of the new test statistics are also obtained. The testing procedure is illustrated with an example.