Test for homogeneity in Hardy–Weinberg normal mixture model

The phenotype of a quantitative trait locus (QTL) is often modeled by a finite mixture of normal distributions. If the QTL effect depends on the number of copies of a specific allele one carries, then the mixture model has three components. In this case, the mixing proportions have a binomial structure according to the Hardy–Weinberg equilibrium. In the search for QTL, a significance test of homogeneity against the Hardy–Weinberg normal mixture model alternative is an important first step. The LOD score method, a likelihood ratio test used in genetics, is a favored choice. However, there is not yet a general theory for the limiting distribution of the likelihood ratio statistic in the presence of unknown variance. This paper derives the limiting distribution of the likelihood ratio statistic, which can be described by the supremum of a quadratic form of a Gaussian process. Further, the result implies that the distribution of the modified likelihood ratio statistic is well approximated by a chi-squared distribution. Simulation results show that the approximation has satisfactory precision for the cases considered. We also give a real-data example.     

Generalized quasi-likelihood

The quasi-score function, as defined by Wedderburn (1974) and McCullagh (1983) and so on, is a linear function of observations. The generalized quasi-score function introduced in this paper is a linear function of some unbiased basis functions, where the unbiased basis functions may be some linear functions of the observations or not, and can be easily constructed by the meaning of the parameters such as mean and median and so on. The generalized quasi-likelihood estimate obtained by such a generalized quasi-score function is consistent and has an asymptotically normal distribution. As a result, the optimum generalized quasi-score is obtained and a method to construct the optimum unbiased basis function is introduced. In order to construct the potential function, a conservative generalized estimating function is defined. By conservative, a potential function for the projected score has many properties of a log-likelihood function. Finally, some examples are given to illustrate the theoretical results. This paper is supported by NNSF project (10371059) of China and Youth Teacher Foundation of Nankai University.     

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.     

20世纪中国文学在韩国的研究回眸

回眸20世纪中国文学在韩国的研究轨迹,对韩中两国的学术界都有重要意义。20世纪韩国的中国现当代 文学研究与中国的研究方向差别不大,中国当代文学及港台文学研究方面较落后,研究对象集中。21世纪的研究倾 向是:韩国的中国当代文学研究更多起来,并脱离中国研究的既定道路,韩中比较文学研究相对活跃。     

20世纪中国文学思潮的演变及其反思--兼论中国现当代文学史分期问题

20世纪中国文学已经走完了它的全程 ,并完整地展现在我们的记忆与案头。纵览 2 0世纪中国社会思潮的发展进程 ,可以看出 :从“人文主义精神”到“社会主义思潮” ,再到世纪末“现代主义理念”的“生、住、异、灭”的嬗变演进 ,这些决定了 2 0世纪中国文学的整体走向 ,也使传统“现当代文学史”分期理论与编史叙述的本质缺陷清晰地暴露出来 ,从而有力地支撑着“2 0世纪中国文学”编史叙述的基本构想。     

马克思与后现代主义"颠覆主体性"之比较

马克思与后现代主义都对传统主体概念进行了颠覆。在马克思那里 ,主体不再指自我意识或自我 ,而是渗透了历史性原则 ,是创造和规定人及产物的历史过程 ;其客观上表现为一定的社会关系和社会形态 ,主观上表现为人的社会历史存在。而后现代主义则反对主客二分 ,反对人类中心主义 ,反对寻求同一性 ,反对普遍主义 ,把以认识主体为核心的反映论作为批判的目标。这是两种不同的颠覆方式 ,但都宣判了传统主体概念的死亡。     

政府法令与民间惯行:以国民政府颁行"年利20%"为中心

南京国民政府实行年利率不得超过 2 0 %的法令 ,但这一法令仅在个别地区有些微作用 ,总体来说始终处于“表达”层面 ,而无“实践”意义 ,乡村借贷在很大程度上仍受着传统惯行而非国家法律的支配 ,高利贷横行的格局一直未曾根本改变。也就是说 ,在离开高利贷农村社会经济就无法运转的历史条件下 ,仅靠一纸行政命令是不可能消灭高利贷的 ,在现代农村金融建立和健全以前 ,高利贷仍有生存和发展的空间 ,甚至与现代农村金融是相辅相成的     

20世纪中国文学思潮进程现象反观(一)

每一个时代都有自己时代所需要的历史叙述与文学观念 ,成为了学术的基本权力。 2 0世纪中国文学已经走完了它的全程 ,并完整地展现在我们的记忆与案头。纵览 2 0世纪中国社会思潮的史学进程 :从“人文主义精神”到“社会主义思潮” ,再向世纪末“现代主义理念”的嬗变演进 ,决定 2 0世纪中国文学思潮的整体走向 ,传统的“现、当代文学史”的分期理论与编史叙述的本质缺陷 ,清晰地暴露出来 ,从而有力地支撑着“2 0世纪中国文学”编史叙述的基本构想。     

On the asymptotic normality of the L1- and L2-errors in histogram density estimation

The L₁ and L₂-errors of the histogram estimate of a density f from a sample X₁,X₂,…,Xn using a cubic partition are shown to be asymptotically normal without any unnecessary conditions imposed on the density f. The asymptotic variances are shown to depend on f only through the corresponding norm of f. From this follows the asymptotic null distribution of a goodness-of-fit test based on the total variation distance, introduced by Györfi and van der Meulen (1991). This note uses the idea of partial inversion for obtaining characteristic functions of conditional distributions, which goes back at least to Bartlett (1938).     

Generalized partially linear varying-coefficient models

Generalized varying-coefficient models are useful extensions of generalized linear models. They arise naturally when investigating how regression coefficients change over different groups characterized by certain covariates such as age. In this paper, we extend these models to generalized partially linear varying-coefficient models, in which some coefficients are constants and the others are functions of certain covariates. Procedures for estimating the linear and non-parametric parts are developed and their associated statistical properties are studied. The methods proposed are illustrated using some simulations and real data analysis.