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无限方差过程的稳健因果性检验AI 解读

This paper develops a robust causality test for time series with infinite variance innovation processes. First, we introduce a measure of dependence for vector nonparametric linear processes, and derive the asymptotic distribution of the test statistic by Taniguchi et al. (1996) in the infinite variance case. Second, we construct a weighted version of the generalized empirical likelihood (GEL) test statistic, called the self-weighted GEL statistic in the time domain. The…

平稳过程的控制变量降方差方法AI 解读

The sample mean is one of the most natural estimators of the population mean based on independent identically distributed sample. However, if some control variate is available, it is known that the control variate method reduces the variance of the sample mean. The control variate method often assumes that the variable of interest and the control variable are i.i.d. Here we assume that these variables are stationary processes with spectral density matrices, i.e. dependent.…

短记忆与长记忆高斯过程的 Stein–James 估计量AI 解读

We investigate the mean squared error of the Stein–James estimator for the mean when the observations are generated from a Gaussian vector stationary process with dimension greater than two. First, assuming that the process is short-memory, we evaluate the mean squared error, and compare it with that for the sample mean. Then a sufficient condition for the Stein–James estimator to improve upon the sample mean is given in terms of the spectral density matrix around the…

平稳过程谱参数最小对比估计量的高阶渐近理论AI 解读

Let g(λ) be the spectral density of a stationary process and let fθ(λ), θ ∈ Θ, be a fitted spectral model for g(λ). A minimum contrast estimator of θ is defined that minimizes a distance between , where is a nonparametric spectral density estimator based on n observations. It is known that is asymptotically Gaussian efficient if g(λ) = fθ(λ). Because there are infinitely many candidates for the distance function , this paper discusses higher order asymptotic theory for in…

长记忆扰动回归模型的局部渐近正态性AI 解读

The local asymptotic normality property is established for a regression model with fractional ARIMA($p, d, q$) errors. This result allows for solving, in an asymptotically optimal way, a variety of inference problems in the long-memory context: hypothesis testing, discriminant analysis, rank-based testing, locally asymptotically minimax andadaptive estimation, etc. The problem of testing linear constraints on the parameters, the discriminant analysis problem, and the…

长记忆依赖下 Durbin–Watson 统计量的渐近理论AI 解读

In time series regression models with “short-memory” residual processes, the Durbin–Watson statistic ( DW ) has been used for the problem of testing for independence of the residuals. In this paper we elucidate the asymptotics of DW for “long-memory” residual processes. A standardized Durbin–Watson statistic ( SDW ) is proposed. Then we derive the asymptotic distributions of SDW under both the null and local alternative hypotheses. Based on this result we evaluate the local…

多元时间序列的判别与聚类AI 解读

Minimum discrimination information provides a useful generalization of likelihood methodology for classification and clustering of multivariate time series. Discrimination between different classes of multivariate time series that can be characterized by differing covariance or spectral structures is of importance in applications occurring in the analysis of geophysical and medical time series data. For discrimination between such multivariate series, Kullback-Leibler…

多元时间序列谱密度矩阵相关统计量的分布渐近展开及应用AI 解读

Let { X ( t )} be a multivariate Gaussian stationary process with the spectral density matrix f 0 (ω), where θ is an unknown parameter vector. Using a quasi-maximum likelihood estimator θ̂ of θ, we estimate the spectral density matrix f 0 (ω) by f θ̂ (ω). Then we derive asymptotic expansions of the distributions of functions of f θ̂ (ω). Also asymptotic expansions for the distributions of functions of the eigenvalues of f θ̂ (ω) are given. These results can be applied to…

平稳过程谱密度的最小对比估计AI 解读

SUMMARY Let {z(n)} be a stationary process with mean zero and true spectral density g(λ). In this paper we approximate g(λ) by a parametric family f θ(λ) and propose a minimum contrast estimator θ^ which minimizes D(fθ,g^N)=∫−ππK{fθ(λ)/g^N(λ)}dλ with respect to θ, where K(.) is an appropriate function and ĝ N(λ) is a nonparametric spectral estimator of g(λ). We give the asymptotic distribution of θ^ and sufficient conditions such that θ^ is asymptotically efficient. Also, we…

局部备择下高斯 ARMA 过程似然比统计量分布的渐近展开AI 解读

In this paper, we shall derive the asymptotic expansion for the distribution of the likelihood ratio criterion for a Gaussian autoregressive moving average process under a sequence of local alternative hypotheses converging to the null hypothesis with rate of convergence where n is the sample size. Explicit algebraic formulae are presented for certain special cases, including the ARMA(1,1).

高斯 ARMA 过程估计量的二阶渐近效率AI 解读

In this paper we investigate an optimal property of maximum likelihood and quasi-maximum likelihood estimators of Gaussian autoregressive moving average processes by the second order approximation of the sampling distribution. It is shown that appropriate modifications of these estimators for Gaussian ARMA processes are second order asymptotically efficient if efficiency is measured by the degree of concentration of the sampling distribution up to second order. This concept…

四阶累积量谱密度积分的估计AI 解读

It is known that the asymptotic variance of a quasimaximum likelihood estimate for a non-Gaussian process contains certain integrals of the fourth order cumulant spectral density. If we apply the asymptotic theory we are required to estimate these integrals. Here we shall propose some operational consistent estimates for them.

四阶累积量谱密度积分的估计AI 解读

It is known that the asymptotic variance of a quasimaximum likelihood estimate for a non-Gaussian process contains certain integrals of the fourth order cumulant spectral density. If we apply the asymptotic theory we are required to estimate these integrals. Here we shall propose some operational consistent estimates for them.

某类谱密度模型的参数估计程序AI 解读

Summary Let {X(t)} be a Gaussian stationary process with mean zero and true spectral density g(x). We shall fit a certain spectral model f θ (x) for this process, and propose an estimate of θ, say θ^n, by minimizing a criterion D{f θ , g), which measures the nearness of f θ (x) to g(x). Also we shall derive the asymptotic distribution of θ^n. For the case of some appropriate spectral parametrization of f θ (x) we show that θ^n can be expressed in an explicit form.…