共查询到20条相似文献,搜索用时 0 毫秒
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Ming Le Guo 《统计学通讯:理论与方法》2014,43(10-12):2527-2539
In this article, the complete moment convergence of weighted sums for ?-mixing sequence of random variables is investigated. By applying moment inequality and truncation methods, the equivalent conditions of complete moment convergence of weighted sums for ?-mixing sequence of random variables are established. These results promote and improve the corresponding results obtained by Li et al. (1995) and Gut (1993) from i.i.d. to ?-mixing setting. Moreover, we obtain the complete moment convergence of moving average processes based on ?-mixing random variables, which extends the result of Kim et al. (2008) in the sense that it does not require a specific mixing rate. 相似文献
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Consider a finite sequence of independent binary (zero-one) random variables ordered on a line or on a circle. The number of the ?-overlapping runs of ones of a fixed length k is studied for both types of the concerned ordering. Recurrences for the exact probability mass functions for these numbers are obtained via simple probabilistic arguments. Exact closed formulae, for the mean and variance of the studied numbers are obtained via their representations through properly defined indicators. Two application case studies, concerning record sequences and reliability of consecutive systems, clarify further the theoretical results. 相似文献
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Han-Ying Liang 《统计学通讯:理论与方法》2013,42(11):1999-2021
In this article we establish pointwise asymptotic normality of nonparametric kernel estimator of regression function for a left truncation model. It is assumed that the lifetime observations with multivariate covariates form a stationary α-mixing sequence. Also, the asymptotic normality of the estimation of the covariable's density is considered. As a by-product, we obtain a uniform weak convergence rate for the product-limit estimator of the lifetime and truncated distributions under dependence, which is interesting independently. Finite sample behavior of the estimator of the regression function is investigated as well. 相似文献
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Lichun Wang 《统计学通讯:理论与方法》2013,42(12):2209-2220
ABSTRACT This article considers the empirical Bayes estimation problem in the uniform distribution U(0, θ) with censored data. For the parameter θ, using the empirical Bayes (EB) approach, we propose an EB estimation of θ which possesses a rate of convergence can be arbitrarily close to O(n ?1/2) when the historical samples are randomly censored from the right, where n is the number of historical sample. A sample and some simulation results are also presented. 相似文献
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《Journal of Statistical Computation and Simulation》2012,82(5):946-963
Measures of divergence or discrepancy are used extensively in statistics in various fields. In this article, we are focusing on divergence measures that are based on a class of measures known as Csiszar's divergence measures. In particular, we propose a class of goodness-of-fit tests based on Csiszar's class of measures designed for censored survival or reliability data. Further, we derive the asymptotic distribution of the test statistic under simple and composite null hypotheses as well as under contiguous alternative hypotheses. Simulations are furnished and real data are analysed to show the performance of the proposed tests for different ?-divergence measures. 相似文献
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In this article, we investigate the strong consistency of conditional value-at-risk estimate for ? ?mixing samples under mild conditions. Moreover, the corresponding strong consistency rate is also obtained. 相似文献
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In this article, we investigate the nonparametric estimation of the conditional density of a scalar response variable Y, given the explanatory variable X taking value in a Hilbert space when the observations are linked with a single index structure. The goal of this article is to present the asymptotic results such as pointwise almost complete consistency and the uniform almost complete convergence of the kernel estimation with rate for the conditional density in the setting of the α-mixing functional data, which extend the i.i.d case in Attaoui et al. (2011) to the dependence setting. As an application, the convergence rate of the kernel estimation for the conditional mode is also obtained. 相似文献
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《Journal of statistical planning and inference》1996,53(3):285-295
Let Xn, n ⩾ 1 be a sequence of ϕ-mixing random variables having a smooth common distribution function F. The smoothed empirical distribution function is obtained by integrating a kernel type density estimator. In this paper we provide necessary and sufficient conditions for the central limit theorem to hold for smoothed empirical distribution functions and smoothed sample quantiles. Also, necessary and sufficient conditions are given for weak convergence of the smoothed empirical process and the smoothed uniform quantile process. 相似文献
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Wellner JA 《Lifetime data analysis》2007,13(4):481-496
We review limit theory and inequalities for the Kaplan–Meier Kaplan and Meier (J Am Stat Assoc 53:457–481, 1958) product limit
estimator of a survival function on the whole line . Along the way we provide bounds for the constant in an interesting inequality due to Biotouzé et al. (Ann Inst H Poincaré
Probab Stat 35:735–763, 1999), and provide some numerical evidence in support of one of their conjectures.
Supported in part by NSF grant DMS-0503822 and by NI-AID grant 2R01 AI291968-04. 相似文献
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We reconsider the derivation of Blest’s (2003) skewness adjusted version of the classical moment-based coefficient of kurtosis and propose an adaptation of it which generally eliminates the effects of asymmetry a little more successfully. Lower bounds are provided for the two skewness adjusted kurtosis moment measures as functions of the classical coefficient of skewness. The results from a Monte Carlo experiment designed to investigate the sampling properties of numerous moment-based estimators of the two skewness adjusted kurtosis measures are used to identify those estimators with lowest mean squared error for small to medium sized samples drawn from distributions with varying levels of asymmetry and tailweight. 相似文献
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In this paper, by relaxing the mixing coefficients to α(n) = O(n ?β), β > 3, we investigate the Bahadur representation of sample quantiles under α-mixing sequence and obtain the rate as ${O(n^{-\frac{1}{2}}(\log\log n\cdot\log n)^{\frac{1}{2}})}$ . Meanwhile, for any δ > 0, by strengthening the mixing coefficients to α(n) = O(n ?β ), ${\beta > \max\{3+\frac{5}{1+\delta},1+\frac{2}{\delta}\}}$ , we have the rate as ${O(n^{-\frac{3}{4}+\frac{\delta}{4(2+\delta)}}(\log\log n\cdot \log n)^{\frac{1}{2}})}$ . Specifically, if ${\delta=\frac{\sqrt{41}-5}{4}}$ and ${\beta > \frac{\sqrt{41}+7}{2}}$ , then the rate is presented as ${O(n^{-\frac{\sqrt{41}+5}{16}}(\log\log n\cdot \log n)^{\frac{1}{2}})}$ . 相似文献
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This paper discusses characteristics of standard conjugate priors and their induced posteriors in Bayesian inference for von Mises–Fisher distributions, using either the canonical natural exponential family or the more commonly employed polar coordinate parameterizations. We analyze when standard conjugate priors as well as posteriors are proper, and investigate the Jeffreys prior for the von Mises–Fisher family. Finally, we characterize the proper distributions in the standard conjugate family of the (matrix-valued) von Mises–Fisher distributions on Stiefel manifolds. 相似文献
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The problem of testing for a parameter change has been a core issue in time series analysis. It is well known that the estimates-based CUSUM test often suffers from severe size distortions in general GARCH type models. The residual-based CUSUM test has been used as an alternative, which, however, has a defect not to detect the ARMA parameter changes in ARMA–GARCH models. As a remedy, one can employ the score vector-based CUSUM test in ARMA–GARCH models as in Oh and Lee (0000). However, it shows some size distortions for relatively small samples. Hence, we consider the bootstrap counterpart for obtaining a more stable test. Focus is made on the verification of the weak consistency of the proposed test. An empirical study is illustrated for its evaluation. 相似文献
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《Journal of Statistical Computation and Simulation》2012,82(4):177-194
Formulating the model first in continuous time, we have developed a state space approach to the problem of testing for threshold-type nonlinearity when the data are irregularly spaced. 相似文献