共查询到14条相似文献,搜索用时 0 毫秒
1.
We consider partial sums Sn of a general class of stationary sequences of integer-valued random variables, and we provide sufficient conditions for Sn to satisfy a local limit theorem. To prove this result, we introduce a concept called the Bernoulli part. The amount of Bernoulli part in Sn determines the extent to which the density of Sn is relatively flat. If in addition Sn satisfies a global central limit theorem, the local limit theorem follows. 相似文献
2.
R.J. Tomkins 《Revue canadienne de statistique》1978,6(2):169-177
Certain convergence theorems, akin to results of Lévy and Lebesgue for conditional expectations, are established for conditional medians. An explicit representation of a conditional median is given. 相似文献
3.
The strong laws of large numbers for weighted sums of extended negatively dependent random variables
Guohui Zhang 《统计学通讯:理论与方法》2017,46(20):9881-9891
In this paper, the strong laws of large numbers for maximum value of weighted sums of extended negatively dependent random variables are obtained, which improve and extend the corresponding ones for independent random variables and some dependent random variables. 相似文献
4.
Luc P. Devroye 《Revue canadienne de statistique》1978,6(2):179-191
If (X1,Y1), …, (Xn,Yn) is a sequence of independent identically distributed Rd × R-valued random vectors then Nadaraya (1964) and Watson (1964) proposed to estimate the regression function m(x) = ? {Y1|X1 = x{ by where K is a known density and {hn} is a sequence of positive numbers satisfying certain properties. In this paper a variety of conditions are given for the strong convergence to 0 of essXsup|mn (X)-m(X)| (here X is independent of the data and distributed as X1). The theorems are valid for all distributions of X1 and for all sequences {hn} satisfying hn → 0 and nh/log n→0. 相似文献
5.
AbstractLet {Xn, n ? 1} be a sequence of negatively superadditive dependent (NSD, in short) random variables and {bni, 1 ? i ? n, n ? 1} be an array of real numbers. In this article, we study the strong law of large numbers for the weighted sums ∑ni = 1bniXi without identical distribution. We present some sufficient conditions to prove the strong law of large numbers. As an application, the Marcinkiewicz-Zygmund strong law of large numbers for NSD random variables is obtained. In addition, the complete convergence for the weighted sums of NSD random variables is established. Our results generalize and improve some corresponding ones for independent random variables and negatively associated random variables. 相似文献
6.
We establish a strong invariance principle for triangular arrays of a broad class of weakly dependent real random variables. We approximate the original array of dependent random variables by an array of rowwise independent standard normal variables. We demonstrate the functional central limit theorem and law of the iterated logarithm for the approximating array and thereby extend these results to the original array. Among several examples, we look at arrays used in describing the rate of convergence of estimators in regression analysis. 相似文献
7.
In this paper, we proved an almost sure central limit theorem for the maxima (after centered at the sample mean) and the partial sums of standardized stationary Gaussian sequences under some conditions related to the convergence rate of covariance functions, which extended the existing results. 相似文献
8.
AbstractIn this paper, we will study the strong law of large numbers of the delayed sums for Markov chains indexed by a Cayley tree with countable state spaces. Firstly, we prove a strong limit theorem for the delayed sums of the bivariate functions for Markov chains indexed by a Cayley tree. Secondly, the strong law of large numbers for the frequencies of occurrence of states of the delayed sums is obtained. As a corollary, we obtain the strong law of large numbers for the frequencies of occurrence of states for countable Markov chains indexed by a Cayley tree. 相似文献
9.
ABSTRACTIn the article, the complete convergence and complete moment convergence for weighted sums of sequences of random variables satisfying a maximal Rosenthal type inequality are studied. As an application, the Marcinkiewicz–Zygmund type strong law of large numbers is obtained. Our partial results generalize and improve the corresponding ones of Shen (2013). 相似文献
10.
Jean Vaillancourt 《Revue canadienne de statistique》1995,23(2):171-184
Consider a family of square-integrable Rd-valued statistics Sk = Sk(X1,k1; X2,k2;…; Xm,km), where the independent samples Xi,kj respectively have ki i.i.d. components valued in some separable metric space Xi. We prove a strong law of large numbers, a central limit theorem and a law of the iterated logarithm for the sequence {Sk}, including both the situations where the sample sizes tend to infinity while m is fixed and those where the sample sizes remain small while m tends to infinity. We also obtain two almost sure convergence results in both these contexts, under the additional assumption that Sk is symmetric in the coordinates of each sample Xi,kj. Some extensions to row-exchangeable and conditionally independent observations are provided. Applications to an estimator of the dimension of a data set and to the Henze-Schilling test statistic for equality of two densities are also presented. 相似文献
11.
Herold Dehling 《Revue canadienne de statistique》2009,37(3):307-326
André Robert Dabrowski, Professor of Mathematics and Dean of the Faculty of Sciences at the University of Ottawa, died October 7, 2006, after a short battle with cancer. The author of the present paper, a long‐term friend and collaborator of André Dabrowski, gives a survey of André's work on weak dependence and limit theorems in probability theory. The Canadian Journal of Statistics 37: 307–326; 2009 © 2009 Statistical Society of Canada 相似文献
12.
Olman and Shmundak proved 1985 that in estimating a bounded normal mean under squared error loss the Bayes estimator with
respect to the uniform distribution on the parameter interval is gamma-minimax when the parameter interval is sufficiently
small and the class of priors consists of all symmetric and unimodal distributions. Recently, one of the authors showed that
this result remains valid for quite general families of distributions which satisfy some regularity conditions. In the present
paper a generalization to the class of unimodal priors with fixed mode is derived. It is proved that the Bayes estimator with
respect to a suitable mixture of two uniform distributions is gamma-minimax for sufficiently small parameter intervals. To
that end appropriate characterizations of a saddle point in the corresponding statistical games are established. Some results
of a numerical study are presented. 相似文献
13.
James H. Albert 《Revue canadienne de statistique》1996,24(3):327-347
A general methodology is presented for finding suitable Poisson log-linear models with applications to multiway contingency tables. Mixtures of multivariate normal distributions are used to model prior opinion when a subset of the regression vector is believed to be nonzero. This prior distribution is studied for two- and three-way contingency tables, in which the regression coefficients are interpretable in terms of odds ratios in the table. Efficient and accurate schemes are proposed for calculating the posterior model probabilities. The methods are illustrated for a large number of two-way simulated tables and for two three-way tables. These methods appear to be useful in selecting the best log-linear model and in estimating parameters of interest that reflect uncertainty in the true model. 相似文献
14.
Krishna B. Athreya Malay Ghosh Leone Y. Low Pranab K. Sen 《Journal of statistical planning and inference》1984,9(2):185-194
For the bootstrapped mean, a strong law of large numbers is obtained under the assumption of finiteness of the rth moment, for some r>1, and a weak law of large numbers is obtained under the finiteness of the first moment. The results are then extended to bootstrapped U-statistics under parallel conditions. Stochastic convergence of the jackknifed estimator of the variance of a bootstrapped U-statistic is proved. The asymptotic normality of the bootstrapped pivot and the bias of the bootstrapped U-statistic are indicated. 相似文献