Asymptotic expansions for the moments of serial correlation coefficients

This work is concerned with evaluating the moments of a number of serial correlation coefficients which arise in various ways and where the observations are from the first order autoregressive Gaussian process with known zero mean. The forms considered have biases whose main parts (of order 0(n^-1) , where n is the sample size) are substantially different. They are the intra-class correlation,the maximum likelihood estimators and an estimator whose main part of the bias is sere. The moments are obtained as asymptotic expansions in terms of the parameter of the process and to terms of order 0(n^-3). It is found that removing certain end terms in the denominator of a serial correlation has the effect of reducing the magnitude of the main part of its bias considerably and in one case completely eliminating it. This work extends the results of various authors,e.g.Kandall(1954), Marriott and pope(1954) and white (1961) in the special cases of the first order autogressive process.     

关于正定复矩阵的若干结论

本文讨论了正定复矩阵Schur补的性质,应用子(矩阵)结构讨论了正定复矩阵,给出了一类正定复矩阵判别法,以及两个正定矩阵的Kronecker积与Hadamard积的复正定性。     

Nonlinear Censored Regression Using Synthetic Data

Abstract.  The problem of estimating a nonlinear regression model, when the dependent variable is randomly censored, is considered. The parameter of the model is estimated by least squares using synthetic data. Consistency and asymptotic normality of the least squares estimators are derived. The proofs are based on a novel approach that uses i.i.d. representations of synthetic data through Kaplan–Meier integrals. The asymptotic results are supported by a small simulation study.     

The computation of average run length and average time to signal: an overview

Control charts are widely used in industries to monitor a process for quality improvement. Evaluation of the average run length (ARL) or average time to signal (ATS) plays an important role in the design of control charts and performance comparison. In this paper, we review several basic and popular procedures, including the Markov chain and integral equation methods for computing ARL, ATS and associated run length distributions for cumulative sum charts, exponentially weighted moving average charts and combined control charts, respectively. Some important references and key formulations are provided for practitioners.     

Statistical Corrections of Invalid Correlation Matrices

Suppose estimates are available for correlations between pairs of variables but that the matrix of correlation estimates is not positive definite. In various applications, having a valid correlation matrix is important in connection with follow‐up analyses that might, for example, involve sampling from a valid distribution. We present new methods for adjusting the initial estimates to form a proper, that is, nonnegative definite, correlation matrix. These are based on constructing certain pseudo‐likelihood functions, formed by multiplying together exact or approximate likelihood contributions associated with the individual correlations. Such pseudo‐likelihoods may then be maximized over the range of proper correlation matrices. They may also be utilized to form pseudo‐posterior distributions for the unknown correlation matrix, by factoring in relevant prior information for the separate correlations. We illustrate our methods on two examples from a financial time series and genomic pathway analysis.     

Complete integral convergence for arrays of row-wise extended independent random variables under Sub-linear expectations

Abstract

In this paper, we establish the complete convergence and complete integral convergence for arrays of row-wise extended independent random variables under sub-linear expectation space with some conditions. At the same time we extend some complete convergence and complete integral convergence theorems from the classical probability space to the sub-linear expectation space. The results generalize corresponding results obtained by Wu et al. (2017 Zhang, L. X. 2016b. Exponential inequalities under the sub-linear expectations with applications to laws of the iterated logarithm. Science China Mathematics 59 (12):2503–26. doi: 10.1007/s11425-016-0079-1.[Crossref], [Web of Science ®] , [Google Scholar]).     

CVX‐based algorithms for constructing various optimal regression designs

CVX‐based numerical algorithms are widely and freely available for solving convex optimization problems but their applications to solve optimal design problems are limited. Using the CVX programs in MATLAB, we demonstrate their utility and flexibility over traditional algorithms in statistics for finding different types of optimal approximate designs under a convex criterion for nonlinear models. They are generally fast and easy to implement for any model and any convex optimality criterion. We derive theoretical properties of the algorithms and use them to generate new A‐, c‐, D‐ and E‐optimal designs for various nonlinear models, including multi‐stage and multi‐objective optimal designs. We report properties of the optimal designs and provide sample CVX program codes for some of our examples that users can amend to find tailored optimal designs for their problems. The Canadian Journal of Statistics 47: 374–391; 2019 © 2019 Statistical Society of Canada     

The new unified representation of multivariate skewed distributions

There are so many proposals in construction skewed distributions, and it is worth finding an overall class which covers all of these proposals. We introduce a new unified representation of multivariate skewed distributions. We will show that this new unified multivariate form of skewed distributions includes all of the continuous multivariate skewed distributions in the literature. This new unified representation is based on the multivariate probability integral transformation and can be decomposed into one factor that is original multivariate symmetric probability density function (pdf) f on ? ^k and skewed factor defined by a pdf p on [0, 1] ^k . This decomposition leads us to prove some useful properties of this new unified form. Stochastic representations and basic properties of this new form are also investigated in this article. Our work is motivated by considering the different skewing mechanisms which lead to different skewed distributions and show that all of these common-used distributions can be viewed as a new unified form.     

现代汉语领属结构被领者上“一/这/那”的语用属性考察

汉语领属结构＂他的一张嘴＂中的＂一张＂以及＂他的这/那位父亲＂中的＂这/那位＂都不是结构的必有成分,都不表数量和指别等基本意义。通过与光杆被领者前后成分匹配情况的对比,文章发现此类领属结构被领者上的＂一/这/那＂并不是定指/不定指用法,而是主观评价性用法,同时指出了其中有定和无定标记词用法上的差别。