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171.
It is well known that the standard independent, identically distributed (iid) bootstrap of the mean is inconsistent in a location model with infinite variance (α-stable) innovations. This occurs because the bootstrap distribution of a normalised sum of infinite variance random variables tends to a random distribution. Consistent bootstrap algorithms based on subsampling methods have been proposed but have the drawback that they deliver much wider confidence sets than those generated by the iid bootstrap owing to the fact that they eliminate the dependence of the bootstrap distribution on the sample extremes. In this paper we propose sufficient conditions that allow a simple modification of the bootstrap (Wu, 1986) to be consistent (in a conditional sense) yet to also reproduce the narrower confidence sets of the iid bootstrap. Numerical results demonstrate that our proposed bootstrap method works very well in practice delivering coverage rates very close to the nominal level and significantly narrower confidence sets than other consistent methods. 相似文献
172.
Tachen Liang 《统计学通讯:理论与方法》2013,42(3):565-577
We investigate an empirical Bayes testing problem in a positive exponential family having pdf f{x/θ)=c(θ)u(x) exp(?x/θ), x>0, θ>0. It is assumed that θ is in some known compact interval [C1, C2]. The value C1 is used in the construction of the proposed empirical Bayes test δ* n. The asymptotic optimality and rate of convergence of its associated Bayes risk is studied. It is shown that under the assumption that θ is in [C1, C2] δ* n is asymptotically optimal at a rate of convergence of order O(n?1/n n). Also, δ* n is robust in the sense that δ* n still possesses the asymptotic optimality even the assumption that "C1≦θ≦C2 may not hold. 相似文献
173.
Tachen Liang 《统计学通讯:理论与方法》2013,42(8):1543-1553
174.
《随机性模型》2013,29(1):77-99
Abstract In this paper, we present sufficient conditions, under which the stationary probability vector of a QBD process with both infinite levels and phases decays geometrically, characterized by the convergence norm η and the 1/η-left-invariant vector x of the rate matrix R. We also present a method to compute η and x based on spectral properties of the censored matrix of a matrix function constructed with the repeating blocks of the transition matrix of the QBD process. What makes this method attractive is its simplicity; finding η reduces to determining the zeros of a polynomial. We demonstrate the application of our method through a few interesting examples. 相似文献
175.
The estimation problem for varying coefficient models has been studied by many authors. We consider the problem in the case that the unknown functions admit different degrees of smoothness. In this paper we propose a reducing component local polynomial method to estimate the unknown functions. It is shown that all of our estimators achieve the optimal convergence rates. The asymptotic distributions of our estimators are also derived. The established asymptotic results and the simulation results show that our estimators outperform the the existing two-step estimators when the coefficient functions admit different degrees of smoothness. We also develop methods to speed up the estimation of the model and the selection of the bandwidths. 相似文献
176.
In this paper, the Rosenthal-type maximal inequalities and Kolmogorov-type exponential inequality for negatively superadditive-dependent (NSD) random variables are presented. By using these inequalities, we study the complete convergence for arrays of rowwise NSD random variables. As applications, the Baum–Katz-type result for arrays of rowwise NSD random variables and the complete consistency for the estimator of nonparametric regression model based on NSD errors are obtained. Our results extend and improve the corresponding ones of Chen et al. [On complete convergence for arrays of rowwise negatively associated random variables. Theory Probab Appl. 2007;52(2):393–397] for arrays of rowwise negatively associated random variables to the case of arrays of rowwise NSD random variables. 相似文献
177.
Vassili Blandin 《Statistics》2013,47(6):1202-1232
The purpose of this paper is to study the asymptotic behaviour of the weighted least-squares estimators of the unknown parameters of random coefficient bifurcating autoregressive processes. Under suitable assumptions on the immigration and the inheritance, we establish the almost sure convergence of our estimators, as well as a quadratic strong law and central limit theorems. Our study mostly relies on limit theorems for vector-valued martingales. 相似文献
178.
179.
In this paper, WILKS'type-B integral equation is solved in the general form of a series of beta functions and a series of weighted gamma functions as proposed by WALD and BROOKNER 1941. The coefficients in both representations can be obtained by explicit recurrence relartions, therefore the results solve many distributional problems and have the fewest computational difficulties of any representation that has surfaced to date. The radius of convergence of the second series representation is given, whereas the convergence property of the first series representation is given, whereas the convergence property of the first series representation was studied by WALD and Brookner. The exact null distributions of WILKS' statistic A for testing the independence of several groups of variables and of V = -log A are given. The coefficients in all the series representration can be computed recursilvely and hence can be obtained easily with the help of modern computatinal facilities 相似文献
180.
Sandra De Iaco 《Journal of applied statistics》2013,40(4):808-822
Nowadays, there is an increasing interest in multi-point models and their applications in Earth sciences. However, users not only ask for multi-point methods able to capture the uncertainties of complex structures and to reproduce the properties of a training image, but also they need quantitative tools for assessing whether a set of realizations have the properties required. Moreover, it is crucial to study the sensitivity of the realizations to the size of the data template and to analyze how fast realization-based statistics converge on average toward training-based statistics. In this paper, some similarity measures and convergence indexes, based on some physically measurable quantities and cumulants of high-order, are presented. In the case study, multi-point simulations of the spatial distribution of coarse-grained limestone and calcareous rock, generated by using three templates of different sizes, are compared and convergence toward training-based statistics is analyzed by taking into account increasing numbers of realizations. 相似文献