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Simple estimators for monotone index models

07/2004;

ABSTRACT In this paper, estimation of the coe¢ cients in a "single-index" regression model is considered under the assumption that the regression function is a smooth and strictly monotonic function of the index. The estimation method follows a "two-step" approach, where the …rst step uses a nonparametric regression estimator for the dependent variable, and the second step estimates the unknown index coe¢ cients (up to scale) by an eigenvector of a matrix de…ned in terms of this …rst-step estimator. The paper gives conditions under which the proposed estimator is root-n-consistent and asymptotically normal.

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    ABSTRACT: This paper considers estimation and inference for the multinomial response model in the case where endogenous variables are arguments of the unknown link function. Semiparametric estimators are proposed that avoid the parametric assumptions underlying the likelihood approach as well as the loss of precision when using nonparametric estimation. A data based shrinkage estimator that seeks an optimal combination of estimators and results in superior risk performance under quadratic loss is also developed.
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    ABSTRACT: This paper considers estimation and inference for the multinomial response model in the case where endogenous variables are included as arguments of the unknown link function. Semiparametric estimators are proposed that avoid the parametric assumptions underlying the likelihood approach as well as the loss of precision when using nonparametric estimation. The large sample properties of the estimators are also developed in the context of a quasi-likelihood modeling framework.
    SSRN Electronic Journal 11/2003; DOI:10.2139/ssrn.468101
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    ABSTRACT: This paper considers estimation of the coe¢ cients in a semiparametric multinomial choice model with linear indirect utility functions (with common coe¢ cients but diering regressors) and errors that are assumed to be independent of the regressors. This implies that the conditional mean of the vector of dependent indicator variables is a smooth and invertible function of a corresponding vector of linear indices. The estimation method is an extension of an approach proposed by Ahn, Ichimura, and Powell (2004) for monotone single-index regression models to a multi-index setting, estimating the unknown index coe¢ cients (up to scale) by an eigenvector of a matrix de…ned in terms of a …rst- step nonparametric estimator of the conditional choice probabilities. Under suitable conditions, the proposed estimator is root-n-consistent and asymptotically normal.

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