Local asymptotic normality for regression models with long-memory disturbance

The local asymptotic normality property is established fur a regression mod el with fractional ARIMA(p, d, q) errors. This result allows for solving, i n an asymptotically optimal way, a variety of inference problems In the lon g-memory context: hypothesis testing, discriminant analysis, rank-based tes ting, locally asymptotically minimax and adaptive estimation, etc. The prob lem of testing linear constraints on the parameters, the discriminant analy sis problem, and the construction of locally asymptotically minimax adaptiv e estimators are treated in some detail.