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The limiting distribution of the maximum rank correlation estimator. (English) Zbl 0773.62011
Summary: {\it 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.

62E20Asymptotic distribution theory in statistics
62P20Applications of statistics to economics
62F12Asymptotic properties of parametric estimators
62J99Linear statistical inference
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