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.     

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.     

Statistical and Combinatorial Aspects of Comparative Genomics*

Abstract. This document presents a survey of the statistical and combinatorial aspects of four areas of comparative genomics: gene order based measures of evolutionary distances between species, construction of phylogenetic trees, detection of horizontal transfer of genes, and detection of ancient whole genome duplications.     

Kurtosis modelling by means of the J-transformation

Summary: The H–family of distributions or H–distributions, introduced by Tukey (1960; 1977), are generated by a single transformation of the standard normal distribution and allow for leptokurtosis represented by the parameter h. Alternatively, Haynes et al. (1997) generated leptokurtic distributions by applying the K–transformation to the normal distribution. In this study we propose a third transformation, the so–called J–transformation, and derive some properties of this transformation. Moreover, so-called elongation generating functions (EGFs) are introduced. By means of EGFs we are able to visualize the strength of tail elongation and to construct new transformations. Finally, we compare the three transformations towards their goodness–of–fit in the context of financial return data.     

变质量任意阶非线性非完整系统的相对论性广义Mac-Millan型方程

提出了变质量系统的相对论性万有D’Alembert原理,构造了相对论性广义动能函数,建立了变质量任意阶非线性非完整系统在准坐标下和广义坐标下的相对论性广义Mar-Millan型方程,并得到厂相应的型方程     

The analysis of incomplete data using stochastic covariates

In the development of many diseases there are often associated random variables which continuously reflect the progress of a subject towards the final expression of the disease (failure). At any given time these processes, which we call stochastic covariates, may provide information about the current hazard and the remaining time to failure. Likewise, in situations when the specific times of key prior events are not known, such as the time of onset of an occult tumour or the time of infection with HIV-1, it may be possible to identify a stochastic covariate which reveals, indirectly, when the event of interest occurred. The analysis of carcinogenicity trials which involve occult tumours is usually based on the time of death or sacrifice and an indicator of tumour presence for each animal in the experiment. However, the size of an occult tumour observed at the endpoint represents data concerning tumour development which may convey additional information concerning both the tumour incidence rate and the rate of death to which tumour-bearing animals are subject. We develop a stochastic model for tumour growth and suggest different ways in which the effect of this growth on the hazard of failure might be modelled. Using a combined model for tumour growth and additive competing risks of death, we show that if this tumour size information is used, assumptions concerning tumour lethality, the context of observation or multiple sacrifice times are no longer necessary in order to estimate the tumour incidence rate. Parametric estimation based on the method of maximum likelihood is outlined and is applied to simulated data from the combined model. The results of this limited study confirm that use of the stochastic covariate tumour size results in more precise estimation of the incidence rate for occult tumours.     

随机型细胞神经网络的稳定性

借助于李雅谱洛夫理论、矩阵分析方法和It?公式,结合不等式分析技巧,研究了随机细胞神经网络系统的均方指数稳定性,给出了系统的解的二阶矩Liapunov指数估计式和均方指数稳定的充分条件。     

WEIGHTED SUMS OF NEGATIVELY ASSOCIATED RANDOM VARIABLES

In this paper, we establish strong laws for weighted sums of negatively associated (NA) random variables which have a higher‐order moment condition. Some results of Bai Z.D. & Cheng P.E. (2000) [Marcinkiewicz strong laws for linear statistics. Statist. and Probab. Lett. 43, 105–112,] and Sung S.K. (2001) [Strong laws for weighted sums of i.i.d. random variables, Statist. and Probab. Lett. 52, 413–419] are sharpened and extended from the independent identically distributed case to the NA setting. Also, one of the results of Li D.L. et al. (1995) [Complete convergence and almost sure convergence of weighted sums of random variables. J. Theoret. Probab. 8, 49–76,] is complemented and extended.     

误码率与随机共振

用Maltab语言的Simulink软件，构成一面向结构，而且可以定量分析非线性双稳系统随机共振现象的计算机仿真实验系统，并对输入字符串信息的符号误码率随噪声振幅变化的实验数据进行了拟合，验证了非线性系统特有的随机共振现象的存在。