Discussion of “Simple Estimators for Invertible Index Models” by H. Ahn,H. Ichimura,J. Powell,and P. Ruud

This is an interesting article that considers the question of inference on unknown linear index coefficients in a general class of models where reduced form parameters are invertible function of one or more linear index. Interpretable sufficient conditions such as monotonicity and or smoothness for the invertibility condition are provided. The results generalize some work in the previous literature by allowing the number of reduced form parameters to exceed the number of indices. The identification and estimation expand on the approach taken in previous work by the authors. Examples include Ahn, Powell, and Ichimura (2004 Ahn, H., Powell, J., and Ichimura, H. (2004), “Simple Estimators for Monotone Index Models,” UC Berkeley Working Paper. [Google Scholar]) for monotone single-index regression models to a multi-index setting and extended by Blundell and Powell (2004 Blundell, R. W., and Powell, J. L. (2004), “Endogeneity in Semiparametric Binary Response Models,” The Review of Economic Studies, 71, 655–679.[Crossref], [Web of Science ®] , [Google Scholar]) and Powell and Ruud (2008 Powell, J., and Ruud, P. (2008), “Simple Estimators for Semiparametric Multinomial Choice Models,” UC Berkeley Working Paper. [Google Scholar]) to models with endogenous regressors and multinomial response, respectively. A key property of the inference approach taken is that the estimator of the unknown index coefficients (up to scale) is computationally simple to obtain (relative to other estimators in the literature) in that it is closed form. Specifically, unifying an approach for all models considered in this article, the authors propose an estimator, which is the eigenvector of a matrix (defined in terms of a preliminary estimator of the reduced form parameters) corresponding to its smallest eigenvalue. Under suitable conditions, the proposed estimator is shown to be root-n-consistent and asymptotically normal.     

Developing “A Framework for Planning U.S. Federal Statistics, 1978–1989”

The Statistical Policy Division of the Office of Management and Budget has the overall responsibility for the planning and coordination of U.S. government statistics. The present staff of the Statistical Policy Division is attempting, through an integrated publication entitled “A Framework for Planning U.S. Federal Statistics, 1978–1989,” to state its perspective on necessary developments in the coming years. This article illustrates the character of the Framework materials and outlines the process for public review and comment on this undertaking.     

Nadaraya–Watson estimator for I.I.D. paths of diffusion processes

This paper deals with a nonparametric Nadaraya–Watson (NW) estimator of the drift function computed from independent continuous observations of a diffusion process. Risk bounds on the estimator and its discrete-time approximation are established. The paper also deals with extensions of the PCO and leave-one-out cross-validation bandwidth selection methods for our NW estimator. Finally, some numerical experiments are provided.     

沁园春.统计

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