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针对周期自回归的局部最优检验：参数与非参数方法AI 解读

Locally asymptotically optimal tests are derived for the null hypothesis of traditional AR dependence, with unspecified AR coefficients and unspecified innovation densities, against an alternative of periodically correlated AR dependence. Parametric and nonparametric rank-based versions are proposed. Local powers and asymptotic relative efficiencies (with respect, e.g., to the corresponding Gaussian Lagrange multiplier tests proposed in Ghysels and Hall [1992, “Lagrange…

有界随机变量线性组合的改进Eaton界及统计应用AI 解读

The problem of evaluating tail probabilities for linear combinations of independent, possibly nonidentically distributed, bounded random variables arises in various statistical contexts, mainly connected with nonparametric inference. A remarkable inequality on such tail probabilities has been established by Eaton. The significance of Eaton's inequality is substantiated by a recent result of Pinelis showing that the minimum B EP of Eaton's bound B E and a traditional…

改进的 Berry–Esseen–Chebyshev 界及统计应用AI 解读

A Sharpening Of Nonuniform bounds of the Berry-Esseen type initially obtained by Esseen and later generalized by Kolodjažnyĭ–who also proved that they are, in some sense, optimal–is proposed. Further, the corresponding inequalities are shown to provide uniformly improved Chebyshev bounds for the tail probabilities of the distribution functions to be approximated. In contrast with most results on Berry–Esseen bounds, which emphasize rates of convergence to normality, the…

自相关系数的置换极值与检验序列依赖的 Pitman 检验AI 解读

Normal approximations, as provided by permutational central limit theorems, conditionally can be arbitrarily bad. Such approximations therefore are poorly suited to the construction of critical values for Pitman (permutation) tests. A classical remedy consists in substituting a beta approximation (over the appropriate conditional interval range) for the normal one. Whereas deriving permutational extreme values for usual, nonserial statistics is generally straightforward, the…

非参数 t 检验的非一致界AI 解读

This paper gives simple nonuniform bounds on the tail areas of the permutation distribution of the usual Student's t -statistic when the observations are independent with symmetric distributions. As opposed to uniform bounds, nonuniform bounds depend on the observed sample. It is shown that the nonuniform bounds proposed are always tighter than uniform exponential bounds previously suggested. The use of the bounds to perform nonparametric t -tests is discussed and numerical…

针对一阶序列依赖的随机性秩检验AI 解读

Optimal rank-based procedures were derived in Hallin, Ingenbleek, and Puri (1985, 1987) and Hallin and Puri (1988) for some fundamental testing problems arising in time series analysis. The optimality properties of these procedures are of an asymptotic nature, however, whereas much of the attractiveness of rank-based methods lies in their small-sample applicability and robustness features. Accordingly, the objective of this article is twofold: (a) a study of the…

针对一阶序列依赖的基于秩的随机性检验AI 解读

Optimal rank-based procedures were derived in Hallin, Ingenbleek, and Puri (1985, 1987) and Hallin and Puri (1988) for some fundamental testing problems arising in time series analysis. The optimality properties of these procedures are of an asymptotic nature, however, whereas much of the attractiveness of rank-based methods lies in their small-sample applicability and robustness features. Accordingly, the objective of this article is twofold: (a) a study of the…

时间序列分析的最优秩方法：检验 ARMA 模型AI 解读

The problem of testing a given ARMA model (in which the density of the generating white noise is unspecified) against other ARMA models is considered. A distribution-free asymptotically most powerful test, based on a generalized linear serial rank statistic, is provided against contiguous ARMA alternatives with specified coefficients. In the case when the ARMA model in the alternative has unspecified coefficients, the asymptotic sufficiency (in the sense of Le Cam) of a…

非高斯平稳时间序列的时间可逆性与移动平均表示唯一性AI 解读

A recent result by Findley (1986) on the uniqueness of moving average representations for non-Gaussian time series is shown to establish a conjecture by Weiss (1975) on the time-reversibility of general linear processes.

非高斯平稳时间序列的时间可逆性与移动平均表示唯一性AI 解读

A recent result by Findley (1986) on the uniqueness of moving average representations for non-Gaussian time series is shown to establish a conjecture by Weiss (1975) on the time-reversibility of general linear processes.

针对 ARMA 备择的随机性线性序列秩检验AI 解读

In this paper we introduce a class of linear serial rank statistics for the problem of testing white noise against alternatives of ARMA serial dependence. The asymptotic normality of the proposed statistics is established, both under the null as well as alternative hypotheses, using LeCam's notion of contiguity. The efficiency properties of the proposed statistics are investigated, and an explicit formulation of the asymptotically most efficient score-generating functions is…

非平稳移动平均过程的谱分解AI 解读

We solve here the general nonstationary multivariate MA spectral factorization problem, i.e. the problem of obtaining all the possible MA models (with time-dependent coefficients) corresponding to a given (time-dependent) autocovariance function. Our result (Theorem 8) relies on a symbolic generalization (Theorem 1) of the classical factorization property of the characteristic polynomial associated with stationary autocovariance functions, and is obtained by means of a…

时间序列模型的可逆性与广义可逆性AI 解读

Summary A new invertibility concept was recently introduced by Granger and Andersen (1978), generalizing the classical one for time-independent models; we show that, in the case of time-dependent models, it cannot be considered any more as a generalization. We also give a modified definition, which provides a strict generalization and still preserves Granger and Andersen's results.