MINIMUM DISTANCE REGRESSION-TYPE ESTIMATES WITH RATES UNDER WEAK DEPENDENCE

GEORGE G. ROUSSAS^{1} AND YANNIS G. YATRACOS^{2}

1Division of Statistics, University of California, Davis, CA 95616-8705, U.S.A.

2Departement de mathematiques et de statistique, Université Montréal, C.P. 6128, succursale A, Montreal, Quebec, Canada H3C 3J7 and University of California, Santa Barbara

(Received June 1, 1992; revised June 5, 1995)

Abstract. Under weak dependence, a minimum distance estimate is obtained for a smooth function and its derivatives in a regression-type framework. The upper bound of the risk depends on the Kolmogorov entropy of the underlying space and the mixing coefficient. It is shown that the proposed estimates have the same rate of convergence, in the L_{1}-norm sense, as in the independent case.

Key words and phrases: Kolmogorov’s entropy, minimum distance estimation, nonparametric regression, φ-mixing, rate of convergence.