Toeplitz lemma,complete convergence,and complete moment convergence

In this paper, we study the Toeplitz lemma, the Cesàro mean convergence theorem, and the Kronecker lemma. At first, we study “complete convergence” versions of the Toeplitz lemma, the Cesàro mean convergence theorem, and the Kronecker lemma. Two counterexamples show that they can fail in general and some sufficient conditions for “complete convergence” version of the Cesàro mean convergence theorem are given. Second, we introduce two classes of complete moment convergence, which are stronger versions of mean convergence and consider the Toeplitz lemma, the Cesàro mean convergence theorem, and the Kronecker lemma under these two classes of complete moment convergence.     

积分第二中值定理中ξ的渐近性质

本文研究了积分第二中值定理中ξ的渐近性质，得到主要结果：     

Bayesian Semiparametric Modelling in Quantile Regression

Abstract. We propose a Bayesian semiparametric methodology for quantile regression modelling. In particular, working with parametric quantile regression functions, we develop Dirichlet process mixture models for the error distribution in an additive quantile regression formulation. The proposed non‐parametric prior probability models allow the shape of the error density to adapt to the data and thus provide more reliable predictive inference than models based on parametric error distributions. We consider extensions to quantile regression for data sets that include censored observations. Moreover, we employ dependent Dirichlet processes to develop quantile regression models that allow the error distribution to change non‐parametrically with the covariates. Posterior inference is implemented using Markov chain Monte Carlo methods. We assess and compare the performance of our models using both simulated and real data sets.     

Mean square prediction error for long-memory processes

ARFIMA (p, d, q) processes. In particular we obtain the (asymptotic) mean square prediction error when the parameters of the process are either known or estimated in the cases both of correct and misspecified model. Some Monte Carlo experiments confirm the validity of the asymptotic results. Received: August 6, 1999; revised version: June 26, 2000     

Estimation in linear models using gradient descent with early stopping

A new shrinkage estimator of the coefficients of a linear model is derived. The estimator is motivated by the gradient-descent algorithm used to minimize the sum of squared errors and results from early stopping of the algorithm. The statistical properties of the estimator are examined and compared with other well-established methods such as least squares and ridge regression, both analytically and through a simulation study. An important result is that the new estimator is shown to be comparable to other shrinkage estimators in terms of mean squared error of parameters and of predictions, and superior under certain circumstances.Supported by the Greek State Scholarships Foundation     

唯仁者能好人,能恶人——论儒家的“中庸”与“不”

儒家倡导“中庸之道”、“和为贵”,但在美与丑、善与恶、是与非等问题上,从来都是立场坚定、旗帜鲜明、态度明确的,从未要人只说“是”、不言“不”。勇于说“不”是儒家的思想传统。“不”是“中庸”的应有之意。     

修辞形式等同与功能等值在功能翻译理论中的体现

功能翻译理论强调修辞形式等同和功能等值的一致性,修辞是手段,是形式;功能是修辞产生的结果或达到的目的,是内容的总合。本文试从功能翻译理论的要点、方法论、理论基础和关联理论等方面对此进行分析。     

On upper bounds for the characteristic values of the covariance matrix for multinomial,dirichlet and multivariate hypergeometric distributions

For the characteristic values T1 of the matrix V:=Diag(p)-pp^T with p=(p1,...,pk), p1≥p2≥...≥pk≥pk+1>0 and p1+p2+...+pk+pk+1=1 the inequalities p1≥τ1≥p2≥τ2≥...≥pk≥τk>0 are given by RONNING (1982). These inequalities give, if p and pk+1 are unknown, the upper bound 1≥T1. However, in this note the bound 1/2≥T1 is derived. V is proportional to the covariance matrix for multinomial, Dirichlet and multivariate hypergeometric distributions. A statistical application for the multinomial distribution is given.     

Gaussian-based kernels

We derive a class of higher-order kernels for estimation of densities and their derivatives, which can be viewed as an extension of the second-order Gaussian kernel. These kernels have some attractive properties such as smoothness, manageable convolution formulae, and Fourier transforms. One important application is the higher-order extension of exact calculations of the mean integrated squared error. The proposed kernels also have the advantage of simplifying computations of common window-width selection algorithms such as least-squares cross-validation. Efficiency calculations indicate that the Gaussian-based kernels perform almost as well as the optimal polynomial kernels when die order of the derivative being estimated is low.     

Bayes factors for goodness of fit testing

We propose the use of the generalized fractional Bayes factor for testing fit in multinomial models. This is a non-asymptotic method that can be used to quantify the evidence for or against a sub-model. We give expressions for the generalized fractional Bayes factor and we study its properties. In particular, we show that the generalized fractional Bayes factor has better properties than the fractional Bayes factor.