## The Annals of Statistics

### Local asymptotic normality for regression models with long-memory disturbance

#### 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

https://projecteuclid.org/euclid.aos/1017939250

Digital Object Identifier
doi:10.1214/aos/1017939250

Mathematical Reviews number (MathSciNet)
MR1765628

Zentralblatt MATH identifier
0957.62077

#### 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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