浅议实变函数与数学分析间的联系

从两个不同的角度浅议实变函数与数学分析间的联系一、数学分析的内容与方法是研究实变函数的重要手段;二、用实变函数理论可以透视数学分析.     

Approach to normality of mean and M-estimators of location

The approach to normality of an estimate is displayed graphically by the nonlinearity in the derivative of the log density, and this nonlinearity is related to the accuracy of the normal approximation for the tail area. Using techniques from small-sample asymptotics, an alternate proof of the central limit theorem is given and same indices of tail behavior are examined.     

稳态光散射法测粒下限及其影响因素的讨论

在经典Ｍｉｅ散射理论基础上，讨论全方位稳态光散射法激光测粒仪测量粒径的下限及其影响因素，认为通过减小激光测粒仪的系统误差和增大探测的散射角范围，可降低测粒仪的测量下降。     

A Continuous Representation of the Family of Stable Law Distributions

Conventional parametric representations of stable law distributions do not allow all members of the family to be obtained as continuous limits of the parameters. Model building (or simulation) using such representations will be numerically unstable near such limits in consequence. Existing tables are not satisfactory near such limits as interpolation cannot be carried out. We show that these difficulties are overcome by using a new shifted Cartesian representation which characterizes the entire stable law family in a completely continuous way. Standardization is still possible with this representation so that tabulation, using just two bounded parameters, can be carried out. Its use is illustrated in a non-regular threshold estimation problem involving stable distributions which are discontinuous limits in conventional representations.     

Profile upper Confidence Limits from Discrete Data

When the data are discrete, standard approximate confidence limits often have coverage well below nominal for some parameter values. While ad hoc adjustments may largely solve this problem for particular cases, Kabaila & Lloyd (1997) gave a more systematic method of adjustment which leads to tight upper limits, which have coverage which is never below nominal and are as small as possible within a particular class. However, their computation for all but the simplest models is infeasible. This paper suggests modifying tight upper limits by an initial replacement of the unknown nuisance parameter vector by its profile maximum likelihood estimator. While the resulting limits no longer possess the optimal properties of tight limits exactly, the paper presents both numerical and theoretical evidence that the resulting coverage function is close to optimal. Moreover these profile upper limits are much (possibly many orders of magnitude) easier to compute than tight upper limits.     

二次型与(半)稳定矩阵的判定

对二次型与（半）稳定矩阵之间的相互关系进行了讨论，得到了二者之间的相互判定方法，且利用二次型的不同配方法得到判定（半）稳定矩阵的一些条件     

On Robust Analysis of a Normal Location Parameter

Pericchi and Smith considered a normal location parameter problem with double-exponential and Student t prior distributions. These two prior distributions both belong to the class of scale mixtures of normal distributions and are useful in providing a robust analysis of the normal location parameter problem. In this paper we extend the analysis to other scale mixtures of normal distributions, such as the exponential power and the symmetric stable distributions.     

利用稳定分布构建开放式基金业绩评价体系

经典的基金业绩评价方法是在收益率服从正态分布假设下构建风险指标，该指标或者高估风险，或者低估风险。可引入稳定分布来描述收益率，并利用稳定分布，构建风险调整的基金业绩评价体系，并利用该体系对我国开放式基金的业绩进行评价。     

Random regression models for human immunodeficiency virus ribonucleic acid data subject to left censoring and informative drop-outs

Objectives in many longitudinal studies of individuals infected with the human immunodeficiency virus (HIV) include the estimation of population average trajectories of HIV ribonucleic acid (RNA) over time and tests for differences in trajectory across subgroups. Special features that are often inherent in the underlying data include a tendency for some HIV RNA levels to be below an assay detection limit, and for individuals with high initial levels or high ranges of change to drop out of the study early because of illness or death. We develop a likelihood for the observed data that incorporates both of these features. Informative drop-outs are handled by means of an approach previously published by Schluchter. Using data from the HIV Epidemiology Research Study, we implement a maximum likelihood procedure to estimate initial HIV RNA levels and slopes within a population, compare these parameters across subgroups of HIV-infected women and illustrate the importance of appropriate treatment of left censoring and informative drop-outs. We also assess model assumptions and consider the prediction of random intercepts and slopes in this setting. The results suggest that marked bias in estimates of fixed effects, variance components and standard errors in the analysis of HIV RNA data might be avoided by the use of methods like those illustrated.     

The number of records within a random interval of the current record value

LetX ₁,X ₂, … be a sequence of i.i.d. random variables with some continuous distribution functionF. LetX(n) be then-th record value associated with this sequence and μ _n ⁻ , μ _n ⁺ be the variables that count the number of record values belonging to the random intervals(f−(X(n)), X(n)), (X(n), f+(X(n))), wheref−, f+ are two continuous functions satisfyingf−(x)<x, f+(x)>x. Properties of μ _n ⁻ , μ _n ⁺ are studied in the present paper. Some statistical applications connected with these variables are also provided.