The Annals of Statistics

Local asymptotic normality for regression models with long-memory disturbance

Kokyo Choy, Marc Hallin, Abdeslam Serroukh, and Masanobu Taniguchi

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Abstract

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 construction of locally asymptotically minimax adaptive estimators are treated in some detail.

Article information

Source
Ann. Statist., Volume 27, Number 6 (1999), 2054-2080.

Dates
First available in Project Euclid: 4 April 2002

Permanent link to this document
https://projecteuclid.org/euclid.aos/1017939250

Digital Object Identifier
doi:10.1214/aos/1017939250

Mathematical Reviews number (MathSciNet)
MR1765628

Zentralblatt MATH identifier
0957.62077

Subjects
Primary: 60G10: Stationary processes 62E20: Asymptotic distribution theory
Secondary: 62A10 62F05: Asymptotic properties of tests

Keywords
Long-memory process FARIMA model local asymptotic normality locally asymptotically optimal test adaptive estimation discriminant analysis

Citation

Hallin, Marc; Taniguchi, Masanobu; Serroukh, Abdeslam; Choy, Kokyo. Local asymptotic normality for regression models with long-memory disturbance. Ann. Statist. 27 (1999), no. 6, 2054--2080. doi:10.1214/aos/1017939250. https://projecteuclid.org/euclid.aos/1017939250


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