Geometric consistency of principal component scores for high-dimensional mixture models and its application

In this article, we consider clustering based on principal component analysis (PCA) for high-dimensional mixture models. We present theoretical reasons why PCA is effective for clustering high-dimensional data. First, we derive a geometric representation of high-dimension, low-sample-size (HDLSS) data taken from a two-class mixture model. With the help of the geometric representation, we give geometric consistency properties of sample principal component scores in the HDLSS context. We develop ideas of the geometric representation and provide geometric consistency properties for multiclass mixture models. We show that PCA can cluster HDLSS data under certain conditions in a surprisingly explicit way. Finally, we demonstrate the performance of the clustering using gene expression datasets.     

SMOOTH TESTS FOR THE BIVARIATE POISSON DISTRIBUTION

A theorem of Rayner & Best (1989) is generalised to permit the construction of smooth tests of goodness of fit without requiring a set of orthonormal functions on the hypothesised distribution. This result is used to construct smooth tests for the bivariate Poisson distribution. The test due to Crockett (1979) is similar to a smooth test that assesses the variance structure under the bivariate Poisson model; the test due to Loukas & Kemp (1986) is related to a smooth test that seeks to detect a particular linear relationship between the variances and covariance under the bivariate Poisson model. Using focused smooth tests may be more informative than using previously suggested tests. The distribution of the Loukas & Kemp (1986) statistic is not well approximated by the x²distribution for larger correlations, and a revised statistic is suggested.     

Efficient score tests for heteroskedasticity in micro-economics

This paper develops an artificial regression that can be employed to obtain efficient score test statistics for heteroskedasticity in the context of a variety of micro-econometric models     

Modeling Two-state Disease Processes with Random Effects

Many chronic medical conditions are manifested by alternating sojourns in symptom-free and symptomatic states. In many cases, in addition to their relapsing and remitting nature, these conditions lead to worsening disease patterns over time and may exhibit seasonal trends. We develop a mixed-effect two-state model for such disease processes in which covariate effects are modeled multiplicatively on transition intensities. The transition intensities, in turn, are functions of three time scales: the semi-Markov scale involving the backward recurrence time for the cyclical component, the Markov scale for the time trend component, and a seasonal time scale. Multiplicative bivariate log-normal random effects are introduced to accommodate heterogeneity in disease activity between subjects and to admit a possible negative correlation between the transition intensities. Maximum likelihood estimation is carried out using Gauss-Hermite integration and a standard Newton-Raphson procedure. Tests of homogeneity are presented based on score statistics. An application of the methodology to data from a multi-center clinical trial of chronic bronchitis is provided for illustrative purposes.     

A Second-order Adjustment to the Profile Likelihood in the Case of a Multidimensional Parameter of Interest

Inference in the presence of nuisance parameters is often carried out by using the χ²-approximation to the profile likelihood ratio statistic. However, in small samples, the accuracy of such procedures may be poor, in part because the profile likelihood does not behave as a true likelihood, in particular having a profile score bias and information bias which do not vanish. To account better for nuisance parameters, various researchers have suggested that inference be based on an additively adjusted version of the profile likelihood function. Each of these adjustments to the profile likelihood generally has the effect of reducing the bias of the associated profile score statistic. However, these adjustments are not applicable outside the specific parametric framework for which they were developed. In particular, it is often difficult or even impossible to apply them where the parameter about which inference is desired is multidimensional. In this paper, we propose a new adjustment function which leads to an adjusted profile likelihood having reduced score and information biases and is readily applicable to a general parametric framework, including the case of vector-valued parameters of interest. Examples are given to examine the performance of the new adjusted profile likelihood in small samples, and also to compare its performance with other adjusted profile likelihoods.     

高校海归教师群体工作满意度的测量及影响因素分析——基于“学术职业发展状况第三次全球调查”的数据

近年来,中国高校中海归教师群体的比例不断扩大,高校海归教师正逐渐成为促进中国高等教育发展的重要力量。深入了解高校海归教师的工作满意度,并据此提出提升其工作满意度的政策建议具有一定的现实意义。基于“学术职业发展状况第三次全球调查”数据,对高校海归教师群体的工作满意度进行实证分析。研究发现,高校海归教师群体对聘任状态、工作环境、收入状况及整体职业环境的满意度呈现出较大差异。基于此,对提升高校海归教师群体工作满意度提出了若干建议。     

The Value of a Probability Forecast from Portfolio Theory

A probability forecast scored ex post using a probability scoring rule (e.g. Brier) is analogous to a risky financial security. With only superficial adaptation, the same economic logic by which securities are valued ex ante – in particular, portfolio theory and the capital asset pricing model (CAPM) – applies to the valuation of probability forecasts. Each available forecast of a given event is valued relative to each other and to the “market” (all available forecasts). A forecast is seen to be more valuable the higher its expected score and the lower the covariance of its score with the market aggregate score. Forecasts that score highly in trials when others do poorly are appreciated more than those with equal success in “easy” trials where most forecasts score well. The CAPM defines economically rational (equilibrium) forecast prices at which forecasters can trade shares in each other’s ex post score – or associated monetary payoff – thereby balancing forecast risk against return and ultimately forming optimally hedged portfolios. Hedging this way offers risk averse forecasters an “honest” alternative to the ruse of reporting conservative probability assessments.     

务农意愿对农户有机肥技术采纳行为的影响

基于我国非农就业不断加深的现实背景,利用湖北省５个县(区)７５３份样本 农户数据,通过倾向得分匹配法(PSM)进行实证,探讨了务农意愿对农户采纳有机肥技术 的影响.研究表明:务农意愿对农户采纳有机肥技术有显著的激励作用,也即务农意愿越强 的农户采纳有机肥技术的可能性越大.在具有务农意愿时,不同的规模调整预期也会导致 农户有机肥技术采纳行为差异.有机肥技术采纳的概率会随着农户的预期规模缩小而降 低,而预期规模增大时农户采纳有机肥技术的概率会增加.研究进一步发现,年龄较小、家 庭收入较高、家庭劳动力较多、耕地面积较大的农户务农意愿对其采纳有机肥技术有显著的 正向影响.因此,建议对农户进行差异化的技术培训和推广,优先考虑对相对规模种植户等 主体进行有机肥推广应用.     

基才平衡计分卡的公共部门战略管理

作为一种有效的战略管理工具,平衡计分卡能够实现多重管理因素的动态平衡。经过论证,平衡计分卡由私营领域引入到公共部门战略管理是可行的,而且对于中国公共部门的管理实践具有显而易见的现实意义。尽管基于平衡计分卡的公共部门还处于尝试和探索阶段,但若能将平衡计分卡与公共部门自身的内在属性结合起来,平衡计分卡将会在公共管理的实践中发挥更大的功用。     

区域经济社会发展水平的因子分析模糊综合评价

区域经济社会发展水平评价实践中，通常采用的方法除不能兼顾主客观性外，还忽略了评价指标之间的相关性，针对这一问题，提出了一种在因子分析基础上结合模糊评价的新方法，并将其用于湘潭市经济社会发展水平综合评价。