雍正《广东通志·澳门图》研究

雍正《广东通志·澳门图》是中国古地图中第一幅以描绘画形式详细绘澳门地理及建筑的澳门地图,具有极高的史料价值,该文对图中出现的澳门地名及澳门建筑进行了系统的研究,对澳门城市建设发展及军事设施的建置均提出了自己的看法,特别是关于图中涉及的澳门华人庙宇的起源问题,更提出了自己独到的观点。     

Nested coordinate descent algorithms for empirical likelihood

Empirical likelihood (EL) as a nonparametric approach has been demonstrated to have many desirable merits. While it has intensive development in methodological research, its practical application is less explored due to the requirements of intensive optimizations. Effective and stable algorithms therefore are highly desired for practical implementation of EL. This paper bears the effort to narrow the gap between methodological research and practical application of EL. We try to tackle the computation problems, which are considered difficult by practitioners, by introducing a nested coordinate descent algorithm and one modified version to EL. Coordinate descent as a class of convenient and robust algorithms has been shown in the existing literature to be effective in optimizations. We show that the nested coordinate descent algorithms can be conveniently and stably applied in general EL problems. The combination of nested coordinate descent with the MM algorithm further simplifies the computation. The nested coordinate descent algorithms are a natural and perfect match with inferences based on profile estimation and variable selection in high-dimensional data. Extensive examples are conducted to demonstrate the performance of the nested coordinate descent algorithms in the context of EL.     

High-dimensional covariance matrix estimation using a low-rank and diagonal decomposition

We study high-dimensional covariance/precision matrix estimation under the assumption that the covariance/precision matrix can be decomposed into a low-rank component $L$ and a diagonal component $D$. The rank of $L$ can either be chosen to be small or controlled by a penalty function. Under moderate conditions on the population covariance/precision matrix itself and on the penalty function, we prove some consistency results for our estimators. A block-wise coordinate descent algorithm, which iteratively updates $L$ and $D$, is then proposed to obtain the estimator in practice. Finally, various numerical experiments are presented; using simulated data, we show that our estimator performs quite well in terms of the Kullback–Leibler loss; using stock return data, we show that our method can be applied to obtain enhanced solutions to the Markowitz portfolio selection problem. The Canadian Journal of Statistics 48: 308–337; 2020 © 2019 Statistical Society of Canada     

The universal validity of the possible triangle constraint for affected sib pairs

The authors consider affected‐sib‐pair analysis, in which genetic marker data are collected from families with at least two sibs affected by a disease under investigation. At any locus not linked to the disease gene, a sib pair shares 0, 1 and 2 alleles identical by descent (IBD) with probabilities of 1/4, 1/2 and 1/4, respectively. With linkage, the IBD value increases stochastically. Louis, Payami & Thomson (1987) and Holmans (1993) were the first ones who discovered that the IBD distribution satisfies the “possible triangle constraint” in some situations. Consequently, more powerful statistical procedures can be designed in detecting linkage. It is of statistical and genetical importance to investigate whether the possible triangle constraint remains true under general genetic models. In this paper, the authors introduce a new technique to prove the possible triangle constraint. Their proof is particularly simple for the single disease locus case. The general case is proved by linking IBD distributions between marker loci through a transition probability matrix.     

Case study in data analysis: The genetic analysis of inflammatory bowel disease

Four teams of analysts try to determine the existence of an association between inflammatory bowel disease and certain genetic markers on human chromosome number 6. Their investigation involves data on several control populations and on 110 familles with two or more affected individuals. The problem is introduced by Mirea, Bull, Silverberg and Siminovitch; they and three other groups (Chen, Kalbfleisch and Romero‐Hidalgo; Darlington and Paterson; Roslin, Loredo‐Osti, Greenwood and Morgan) present analyses. Their approaches are discussed by Field and Smith.     

Steepest descent algorithms in a space of measures

The paper describes descent type algorithms suitable for solving optimisation problems for functionals that depend on measures. We mention several examples of such problems that appear in optimal design, cluster analysis and optimisation of spatial distribution of coverage processes.     

A note on an approximation to neyman type a distributions

This note outlines a steepest descent approximation to the tail probability of the Neyman type A distribution.     

A Note on Application of Nesterov’s Method in Solving Lasso-Type Problems

Many different algorithms have been proposed to solve penalized variable selection problems, in particular lasso and its variants, including group lasso and fused lasso. Loss functions other than quadratic loss also pose significant challenges for finding efficient solvers. Here, we note that Nesterov’s method can be used to transform an optimization problem with general smooth convex loss to quadratic loss with identity covariate matrix in each iteration. After such reduction, the problem becomes much easier to solve or even can be solved in closed form in some cases. We perform some simulations and apply our implementation to phoneme discrimination.     

浅谈卡诺图化简过程的精简

本文从卡诺图的填写、化简结果的形式及卡诺图化简法的灵活运用三个方面阐述了卡诺图化简过程的精简 处理。     

Varstab: a procedure for determining homoscedastic transformations of multivariate normal populations

Gnanadesikan 1977 illustrates the utility of the power transformations considered by Moore and Tukey (1954) Box and Cox (1964), and Andrews, Gnanadesikan, and Warner (1971). These transformations have been used to obtain and assess both the marginal and joint normality of the underlying distributions. This paper investigates the utility of this procedure in defining homoscedastic transformations in multivariate populations.