共查询到20条相似文献,搜索用时 0 毫秒
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AbstractWe give here an almost sure central limit theorem for self-normalized partial sums of a strictly stationary φ-mixing sequences which is in the domain of attraction of the normal law with mean zero and possibly infinite variance. Our result substantially extend a result on the almost sure central limit theorem previously obtained by Huang and Pang (2010). 相似文献
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Yong Zhang 《统计学通讯:理论与方法》2013,42(22):6625-6640
ABSTRACTLet X, X1, X2, … be a sequence of strictly stationary φ-mixing random variables with EX = μ > 0. In this paper, we show that a self-normalized version of almost sure central limit theorem (ASCLT) holds under the assumptions that the mixing coefficients satisfy ∑∞n = 1φ1/2(2n) < ∞ and the weight sequence {dk} satisfies a mild growth condition similar to Kolmogorov’s condition for the LIL. This shows that logarithmic averages, used traditionally in ASCLT for products of sums, can be replaced by other averages, leading to considerably sharper results. 相似文献
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Qing-Pei Zang 《Statistics》2013,47(5):965-970
In this note, we investigate, under some mild conditions, the almost sure central limit theorem for random fields with general weight sequences. 相似文献
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We present an almost sure central limit theorem for the product of the partial sums of m-dependent random variables. In order to obtain the main result, we prove a corresponding almost sure central limit theorem for a triangular array. 相似文献
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Qunying Wu 《统计学通讯:理论与方法》2017,46(8):3667-3675
Let X1, X2, … be a sequence of stationary standardized Gaussian random fields. The almost sure limit theorem for the maxima of stationary Gaussian random fields is established. Our results extend and improve the results in Csáki and Gonchigdanzan (2002) and Choi (2010). 相似文献
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In this work we discuss almost sure convergence for sums of arbitrarily dependent stochastic sequence under different conditions of Chung’s type. Our approach is based on the stopping time technique and the theorem of convergence for martingale difference sequence. Meanwhile, the results here include some relevant classical conclusions. 相似文献
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Jigao Yan 《统计学通讯:理论与方法》2018,47(16):3893-3909
In this article, some results on almost sure convergence for weighted sums of widely negative orthant dependent (WNOD) random variables are presented. The results obtained in the article generalize and improve the corresponding one of J. Lita Da Silva. [(2015), “Almost sure convergence for weighted sums of extended negatively dependent random variables.” Acta Math. Hungar. 146 (1), 56–70]. As applications, the strong convergence for the estimator of non parametric regression model are established. 相似文献
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A number of score statistics are derived for a heterogeneous spatial Poisson process which has a composite intensity. The intensity consists of a 'background' process which is estimated from a control point process by kernel density estimation. The parametric form of the composite intensity yields score tests for particular spatial effects. A numerical example concerning respiratory cancer mortality is given. 相似文献
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AbstractThis paper develops almost sure convergence for sums of negatively superadditive dependent random vectors in Hilbert spaces, we obtain Chung type SLLN and the Jaite type SLLN for sequences of negatively superadditive dependent random vectors in Hilbert spaces. Rate of convergence is studied through considering almost sure convergence to 0 of tail series. As an application, the almost sure convergence of degenerate von Mises-statistics is investigated. 相似文献
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We use the martingale approach to study large deviations and laws of the iterated logarithm for certain multidimensional diffusion processes. The criteria for the validity of these properties are expressed in terms of averaging properties of the coefficients of the infinitesimal generator. In particular we apply our results to diffusion processes with random coefficients. 相似文献
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Kunpeng Wang 《统计学通讯:理论与方法》2020,49(22):5578-5586
AbstractIn this paper, we investigate the almost sure convergence for partial sums of asymptotically negatively associated (ANA, for short) random vectors in Hilbert spaces. The Khintchine-Kolmogorov type convergence theorem, three series theorem and the Kolmogorov type strong law of large numbers for partial sums of ANA random vectors in Hilbert spaces are obtained. The results obtained in the paper generalize some corresponding ones for independent random vectors and negatively associated random vectors in Hilbert spaces. 相似文献
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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
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AbstractWe study the almost sure convergence of weighted sums of ratios of independent random variables satisfying some general, mild conditions. The obtained results are applied to exact laws for order statistics. An exact law for independent random variables which are nonidentically distributed is also proved and applied to ratios of adjacent order statistics for a sample of uniformly distributed random variables. 相似文献
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Under missing at random, we estimate the unknown link function and the direction parameter in a single index model. The central limit theory and the convergence rate of the law of the iterated logarithm for the estimator of the direction parameter are derived, the optimal convergence rate for the estimator of the link function is obtained and simulation results support the theoretical results of the paper. 相似文献
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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
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In this paper, we obtain complete convergence results for Stout type weighted sums of i.i.d. random variables. A strong law for weighted sums of i.i.d. random variables is also obtained. As the applications of the strong law, the strong consistency and rate of the nonparametric regression estimations and the rates of the strong consistency of LS estimators for the unknown parameters of the simple linear errors in variables (EV) model are given. 相似文献