On rates of convergence to infinitely divisible laws for dependent random variables

Large O and small o approximations of the expected value of a class of functions (modified K-functional and Lipschitz class) of the normalized partial sums of dependent random variables by the expectation of the corresponding functions of infinitely divisible random variables have been established. As a special case, we have obtained rates of convergence to the Stable Limit Laws and to the Weak Laws of Large Numbers. The technique used is the conditional version of the operator method of Trotter and the Taylor expansion.     

Perfect simulation for correlated Poisson random variables conditioned to be positive

In this paper we present a perfect simulation method for obtaining perfect samples from collections of correlated Poisson random variables conditioned to be positive. We show how to use this method to produce a perfect sample from a Boolean model conditioned to cover a set of points: in W.S. Kendall and E. Thönnes (Pattern Recognition 32(9): 1569–1586, 1999), this special case was treated in a more complicated way. The method is applied to several simple examples where exact calculations can be made, so as to check correctness of the program using ²-tests, and some small-scale experiments are carried out to explore the behaviour of the conditioned Boolean model.     

Continuous outcomes stochastically mismeasured as discrete random variables: a maximum likelihood approach

In an economic model of retirement behavior, a continuous dependent variable was required; the variable could only be estimated discretely with error, however. Parameter estimates using this dependent variable and ordinary least squares regression are inefficient. In th is paper, we develop a maximum likelihood procedure which adjusts for this heteroscedasticity.     

试论在高师院校《实变函数》教学中引入现代数学思想的必要性及可能的途径

阐述了在高师院校实变函数教学中引入现代数学思想的必要性 ;指出目前在实变函数教学中较系统和全面地介绍分形的数学思想和应用是一个非常好的课题 ,并给出了具体的理由和可供操作的可能途径     

Monte carlo evidence on the robustness of conditional moment tests in tobit and probit models

This paper numerically examines the size robustness of various conditional moment tests in misspecified tobit and probit models. The misspecifications considered include the incorrect exclusion of regressors, ignored heteroskedasticity and false distributional assumptions. An important feature of the experimental design is that it is based on an existing empirical study and is more realistic than many simulation studies. The tests are seen to have mixed performance depending on both the original null hypothesis being tested and type of misspecification encountered.     

中国区域经济差异源于FDI？——析二次统计误差的形成

 摘　　要:本文比较分析了两项关于FDI与中国区域经济发展差异的研究成果，通过分析这两项成果间迥异的研究结论和相应的近乎对立的政策主张，剖析了实证研究中可能形成的二次统计误差，提请人们从变量选择、模型方法、数据运用等各个方面，全面关注实证研究的客观性和科学性。     

Robust models in probability sampling

In the estimation of a population mean or total from a random sample, certain methods based on linear models are known to be automatically design consistent, regardless of how well the underlying model describes the population. A sufficient condition is identified for this type of robustness to model failure; the condition, which we call 'internal bias calibration', relates to the combination of a model and the method used to fit it. Included among the internally bias-calibrated models, in addition to the aforementioned linear models, are certain canonical link generalized linear models and nonparametric regressions constructed from them by a particular style of local likelihood fitting. Other models can often be made robust by using a suboptimal fitting method. Thus the class of model-based, but design consistent, analyses is enlarged to include more realistic models for certain types of survey variable such as binary indicators and counts. Particular applications discussed are the estimation of the size of a population subdomain, as arises in tax auditing for example, and the estimation of a bootstrap tail probability.     

Prediction in Some Poisson Errors in Variables Models

Predictive distributions are developed and illustrated for prediction in some Poisson errors in variables models. Two different situations in which multiplicative treatment effects are appropriate are considered within the context of predicting counts of road accidents. Hierarchical prior structures are investigated, and numerical integration and Gibbs sampling routines are used to derive the predictive and posterior probabilities. Examples of analyses are provided with data from road accidents in Sweden.     

A new class of measurement-error models,with applications to dietary data

Measurement-error modelling occurs when one cannot observe a covariate, but instead has possibly replicated surrogate versions of this covariate measured with error. The vast majority of the literature in measurement-error modelling assumes (typically with good reason) that given the value of the true but unobserved (latent) covariate, the replicated surrogates are unbiased for latent covariate and conditionally independent. In the area of nutritional epidemiology, there is some evidence from biomarker studies that this simple conditional independence model may break down due to two causes: (a) systematic biases depending on a person's body mass index, and (b) an additional random component of bias, so that the error structure is the same as a one-way random-effects model. We investigate this problem in the context of (1) estimating distribution of usual nutrient intake, (2) estimating the correlation between a nutrient instrument and usual nutrient intake, and (3) estimating the true relative risk from an estimated relative risk using the error-prone covariate. While systematic bias due to body mass index appears to have little effect, the additional random effect in the variance structure is shown to have a potentially important effect on overall results, both on corrections for relative risk estimates and in estimating the distribution of usual nutrient intake. However, the effect of dietary measurement error on both factors is shown via examples to depend strongly on the data set being used. Indeed, one of our data sets suggests that dietary measurement error may be masking a strong risk of fat on breast cancer, while for a second data set this masking is not so clear. Until further understanding of dietary measurement is available, measurement-error corrections must be done on a study-specific basis, sensitivity analyses should be conducted, and even then results of nutritional epidemiology studies relating diet to disease risk should be interpreted cautiously.     

A Full Bayesian Non-parametric Analysis Involving a Neutral to the Right Process

Implementation of a full Bayesian non-parametric analysis involving neutral to the right processes (apart from the special case of the Dirichlet process) has been difficult for two reasons: first, the posterior distributions are complex and therefore only Bayes estimates (posterior expectations) have previously been presented; secondly, it is difficult to obtain an interpretation for the parameters of a neutral to the right process. In this paper we extend Ferguson & Phadia (1979) by presenting a general method for specifying the prior mean and variance of a neutral to the right process, providing the interpretation of the parameters. Additionally, we provide the basis for a full Bayesian analysis, via simulation, from the posterior process using a hybrid of new algorithms that is applicable to a large class of neutral to the right processes (Ferguson & Phadia only provide posterior means). The ideas are exemplified through illustrative analyses.