The Limiting Distribution of the Maximum Rank Correlation Estimator

Abstract

Han's maximum rank correlation (MRC) estimator is shown to be √ 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.

Partial rank estimation of duration models with general forms of censoring

“…The arguments are analogous to those used in Sherman (1993) for establishing the asymptotic distribution of the MRC. Our results are based on a set of similar assumptions and we deliberately choose notation to match his as closely as possible.…”

“…Then we have the following representation of the variance covariance matrix which can be easily shown using arguments similar to ones given in Theorem 4 in Sherman (1993). Specifically, if SðÁ; Á; ÁÞ is differentiable with respect to its third argument, g 0 ðÁÞ is differentiable, and E½kx i k 2 o1, then…”

“…The asymptotic variance matrix can be estimated in a similar fashion to the estimator in Sherman (1993). As is the case with that estimator, the selection of smoothing parameters will be required.…”

Estimation of a Transformation Model with Truncation, Interval Observation and Time-Varying Covariates

“…Again this estimator has the same structure as Han (1987)'s maximum rank correlation estimator and the asymptotic distribution is therefore the one given in Sherman (1993) under the regularity conditions stated there.…”

Feature Screening for Ultrahigh Dimensional Categorical Data with Applications

“…One can also evaluate AUC according to (4.1) but based on the whole sample and then optimize it with respect to an arbitrary regression coefficient β. This leads to the Maximum Rank Correlation (MRC) estimator, which has been well studied by Han (1987), Sherman (1993), andBaker (2003).…”