Kim and Pollard (Annals of Statistics, 18 (1990) 191-219) showed that a general class of M-estimatorsconverge at rate n rather than at the standard rate n . Many times, this situation arises when the objective function is non-smooth. The limiting distribution is the (almost surely unique) random vector that maximizes a certain Gaussian process and is difficult to analyze analytically. In this paper, we propose the use of the subsampling method for inferential purposes. The general method is then applied to Manski's maximum score estimator and its small sample performance is highlighted via a simulation study.

SummaryIn this paper we propose a new method to estimate nonparametrically a time varying parameter model when some qualitative information from outside data (e.g. seasonality) is available. In this framework we make two main contributions. First, the resulting estimator is shown to belong to the class of generalized ridge estimators and under some conditions its rate of convergence is optimal within its smoothness class. Furthermore, if the outside data information is full lled by the underlying model, the estimator shows e ciency gains in small sample sizes. Second, for the implementation process, since the estimation procedure envolves the computation of the inverse of a high order matrix we provide an algorithm that avoids this computation and, also, a data-driven method is derived to select the control parameters. The practical performance of the method is demonstrated in a simulation study and in an application to the demand of soft drinks in Canada.

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