Testing equality of two normal covariance matrices with monotone missing data

Abstract

The problem of testing equality of two multivariate normal covariance matrices is considered. Assuming that the incomplete data are of monotone pattern, a quantity similar to the Likelihood Ratio Test Statistic is proposed. A satisfactory approximation to the distribution of the quantity is derived. Hypothesis testing based on the approximate distribution is outlined. The merits of the test are investigated using Monte Carlo simulation. Monte Carlo studies indicate that the test is very satisfactory even for moderately small samples. The proposed methods are illustrated using an example.     

Random effects regression mixtures for analyzing infant habituation

Random effects regression mixture models are a way to classify longitudinal data (or trajectories) having possibly varying lengths. The mixture structure of the traditional random effects regression mixture model arises through the distribution of the random regression coefficients, which is assumed to be a mixture of multivariate normals. An extension of this standard model is presented that accounts for various levels of heterogeneity among the trajectories, depending on their assumed error structure. A standard likelihood ratio test is presented for testing this error structure assumption. Full details of an expectation-conditional maximization algorithm for maximum likelihood estimation are also presented. This model is used to analyze data from an infant habituation experiment, where it is desirable to assess whether infants comprise different populations in terms of their habituation time.     

双波长比值法测定水杨酸、间苯二酚、对氨基苯甲酸的含量

依据水杨酸、间苯二酚、对氨基苯甲酸三组分的比值光谱特征,以对氨基苯甲酸为干扰组分,选择241nm、278nm作为测定水杨酸的波长;以水杨酸作为干扰组分,选择214nm、240nm作为测定间苯二酚的波长;以间苯二酚作为干扰组分,选择222nm、279nm作为测定对氨基苯甲酸的波长.结果显示,水杨酸浓度在1~80mg/L,基本二酚浓度在0.8~40mg/L,对氨基苯甲酸浓度在0.4~40mg/L范围内具有良好的线性关系.本方法具有测定波长少,光谱分离能力强、计算简单、能在低档分光光度计上实现、易于推广等特点.     

Visualization of generalized mean estimators using auxiliary information in survey sampling

Abstract

The mean estimators with ratio depend on multiple auxiliary variables and unknown parameters in a finite population setting. We propose a new generalized approach with matrices for modeling the mutivariate mean estimators with two auxiliary variables. Our approach brings naturally a graphical analysis for comparing mean estimators.     

政府减排目标、产业结构与污染减排

政府是污染减排的重要主体,了解其行为对污染减排的作用对提升污染减排效果及实现中国绿色发展具有重要意义。创造性地将政府减排目标纳入研究框架,构建面板门槛模型,从工业污染排放总量的角度分析政府减排目标、产业结构、经济规模等因素对地方污染减排的影响,并用工业污染物强度进行稳健性检验。结果显示,政府减排目标对污染减排的作用存在阶段性不同:经济发展初级阶段,政府减排目标对污染排放总量的作用方向为正; 经济发展水平较高时,作用方向为负; 两者之间存在适应性调整阶段,作用方向具有不确定性,但总体由正向作用向负向作用转变。产业结构对工业污染排放总量的作用方向因污染物种类而异,经济规模对工业污染排放总量作用方向为正。     

上证30指数股市盈率实证分析

通过对2000年上证30指数股市盈率水平及其影响因素进行实证分析,可以发现,其中股息支付率、每股收益增长率、行业平均市盈率对股票P/E值起主要的解释作用,而股本规模因素,解释力却有限,除每股收益增长率外,各变量的相关性与理论分析基本一致.     

Subjective utility with upper and lower probabilities on finite states

This article is concerned with thresholds of discrimination of preference judgments under uncertainty. We establish an axiomatic characterization for a threshold representation, where thresholds are represented by inexact measurement of subjective probabilities, i.e., upper and lower probabilities. Since upper and lower probabilities need not be additive, the representational form adopts the Choquet integration.     

On the Convergence of the Monte Carlo Maximum Likelihood Method for Latent Variable Models

While much used in practice, latent variable models raise challenging estimation problems due to the intractability of their likelihood. Monte Carlo maximum likelihood (MCML), as proposed by Geyer & Thompson (1992 ), is a simulation-based approach to maximum likelihood approximation applicable to general latent variable models. MCML can be described as an importance sampling method in which the likelihood ratio is approximated by Monte Carlo averages of importance ratios simulated from the complete data model corresponding to an arbitrary value of the unknown parameter. This paper studies the asymptotic (in the number of observations) performance of the MCML method in the case of latent variable models with independent observations. This is in contrast with previous works on the same topic which only considered conditional convergence to the maximum likelihood estimator, for a fixed set of observations. A first important result is that when is fixed, the MCML method can only be consistent if the number of simulations grows exponentially fast with the number of observations. If on the other hand, is obtained from a consistent sequence of estimates of the unknown parameter, then the requirements on the number of simulations are shown to be much weaker.     

钢纤维混凝土基本性能试验研究

通过对30个立方体试块抗压强度试验,分析了钢纤维对普通混凝土的增强作用;通过对30个小梁试件三分点加载抗折试验,研究了体积率对钢纤维混凝土(SFRC)荷载-挠度关系及荷载-极限应变关系的影响.在脆性基体中掺入钢纤维,有效地提高了复合材料承受荷载时阻止裂缝引发与扩展的能力,达到对混凝土的增强效果,尤其是对于抗折强度的增强作用,使混凝土的破坏形式由脆性破坏变为塑性破坏.     

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.