Daniel Wilhelm

Optimal bandwidth selection for robust generalized method of moments estimation

A two-step generalized method of moments estimation procedure can be made robust to heteroskedasticity and autocorrelation in the data by using a nonparametric estimator of the optimal weighting matrix. This paper addresses the issue of choosing the corresponding smoothing parameter (or bandwidth) so that the resulting point estimate is optimal in a certain sense. We derive an asymptotically optimal bandwidth that minimizes a higher-order approximation to the asymptotic mean-squared error of the estimator of interest. We show that the optimal bandwidth is of the same order as the one minimizing the mean-squared error of the nonparametric plugin estimator, but the constants of proportionality are signifi cantly di fferent. Finally, we develop a data-driven bandwidth selection rule and show, in a simulation experiment, that it may substantially reduce the estimators mean-squared error relative to existing bandwidth choices, especially when the number of moment conditions is large.

Data-Driven Bandwidth Selection for Nonparametric Nonstationary Regressions

We provide a solution to the open problem of bandwidth selection for the nonparametric estimation of potentially non-stationary regressions, a setting in which the popular method of cross-validation has not been justified theoretically. Our procedure is based on minimizing moment conditions involving nonparametric residuals and applies to β-recurrent Markov chains, stationary processes being a special case, as well as nonlinear functions of integrated processes. Local and uniform versions of the criterion are proposed. The selected bandwidths are rate-optimal up to a logarithmic factor, a typical cost of adaptation in other contexts. We further show that the bias induced by (near-) minimax optimality can be removed by virtue of a simple randomized procedure. In a Monte Carlo exercise, we find that our proposed bandwidth selection method, and its subsequent bias correction, fare favorably relative to cross-validation, even in stationary environments.

An adaptive test of stochastic monotonicity

We propose a new nonparametric test of stochastic monotonicity which adapts to the unknown smoothness of the conditional distribution of interest, possesses desirable asymptotic properties, is conceptually easy to implement, and computationally attractive. In particular, we show that the test asymptotically controls size at a polynomial rate, is non-conservative, and detects certain smooth local alternatives that converge to the null with the fastest possible rate. Our test is based on a data-driven bandwidth value and the critical value for the test takes this randomness into account. Monte Carlo simulations indicate that the test performs well in finite samples. In particular, the simulations show that the test controls size and, under some alternatives, is significantly more powerful than existing procedures. ∗This version: September 30, 2019. We thank Ivan Canay and Whitney Newey for useful comments. †Department of Economics, University of California at Los Angeles, 315 Portola Plaza, Bunche Hall 8369, Los Angeles, CA 90024, USA; E-Mail address: chetverikov@econ.ucla.edu. ‡Department of Economics, University College London, Gower Street, London WC1E 6BT, United Kingdom; E-Mail address: d.wilhelm@ucl.ac.uk. The author gratefully acknowledges financial support from the ESRC Centre for Microdata Methods and Practice at IFS (RES-589-28-0001) and the European Research Council (ERC-2014-CoG-646917-ROMIA and ERC-2015-CoG-682349). §Department of Economics, Simon Fraser University, 8888 University Drive, Burnaby, BC, V5A 16S, Canada; E-Mail address: dongwook@sfu.ca.