The empirical process for bivariate sequences with long memory

被引：0

作者：

Marinucci D. ^{[1
]}

机构：

[1] Department of Mathematics, University di Rome 'Tor Vergata', 00133 Roma

来源：

Statistical Inference for Stochastic Processes | 2005年 / 8卷 / 2期

关键词：

Empirical process; Functional central limit theorem; Long range dependence;

D O I：

10.1007/s11203-004-2790-9

中图分类号：

学科分类号：

摘要：

We establish a functional central limit theorem for the empirical process of bivariate stationary long range dependent sequences under Gaussian subordination conditions. The proof is based upon a convergence result for cross-products of Hermite polynomials and a multivariate uniform reduction principle, as in Dehling and Taqqu [Ann. Statist. 17 (1989), 1767-1783] for the univariate case. The effect of estimated parameters is also discussed.

引用

页码：205 / 223

页数：18

共 20 条

[1]

Arcones M.A., Limit theorems for nonlinear functionals of a stationary Gaussian sequence of vectors, Ann. Prob., 22, pp. 2242-2274, (1994)

[2]

Bingham N.H., Goldie C.M., Teugels J.L., Regular Variation, (1987)

[3]

Dahlhaus R., Efficient parameter estimation for self-similar processes, Ann. Stat., 17, pp. 1749-1766, (1989)

[4]

Dehling H., Taqqu M.S., The Empirical process of some long-range dependent sequences with an application to U-statistics, Ann. Stat., 17, pp. 1767-1783, (1989)

[5]

Dobrushin R.L., Major P., Non-central limit theorems for non-linear functionals of Gaussian fields, Zeitschrift fur Wahrscheinlichkeitstheorie Verwandte Gebiete, 50, pp. 53-83, (1979)

[6]

Dudley R.M., Uniform Central Limit Theorems, (1999)

[7]

Durbin J., Weak convergence of the sample distribution function when parameters are estimated, Ann. Stat., 1, pp. 279-290, (1973)

[8]

Fox R., Taqqu M.S., Large sample properties of parameter estimates for strongly dependent stationary Gaussian time series, Ann. Stat., 14, pp. 517-532, (1986)

[9]

Giraitis L., Surgailis D., A central limit theorem for quadratic forms in strongly dependent linear variables and its application to asymptotic normality of whittle's estimate, Prob. Theory Related Fields, 86, pp. 87-104, (1990)

[10]

Giraitis L., Taqqu M.S., Whittle estimator for finite variance non-Gaussian time series with long memory, Ann. Stat., 27, pp. 178-203, (1999)

← 1 2 →