The limiting distribution of the maximum rank correlation estimator. (English) Zbl 0773.62011

Sherman, Robert P.

Econometrica 61, No. 1, 123-137 (1993).

Summary: A. K. Han’s [J. Econ. 35, 303-316 (1987; Zbl 0638.62063)] maximum rank correlation (MRC) estimator is shown to be \(\sqrt n\)-consistent and asymptotically normal. The proof rests on a general method for determining the asymptotic distribution of a maximization estimator, a simple \(U\)-statistic decomposition, and a uniform bound for degenerate \(U\)-processes. A consistent estimator of the asymptotic covariance matrix is provided, along with a result giving the explicit form of this matrix for any model within the scope of the MRC estimator. The latter result is applied to the binary choice model, and it is found that the MRC estimator does not achieve the semiparametric efficiency bound.

MSC:

62E20	Asymptotic distribution theory in statistics
62P20	Applications of statistics to economics
62F12	Asymptotic properties of parametric estimators
62J99	Linear inference, regression

Keywords:

generalized regression model; maximum rank correlation estimator; discontinuous criterion function; general method; empirical process; VC class; Euclidean class; numerical derivatives; semiparametric efficiency bound; asymptotic normality; consistency; maximization estimator; \(U\)- statistic decomposition; uniform bound for degenerate \(U\)-processes; asymptotic covariance matrix; binary choice model