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We develop a new method for selecting the penalty parameter for ℓ1-penalized M-estimators in high dimensions, which we refer to as bootstrapping after cross validation. We derive rates of convergence for the corresponding ℓ1-penalized M-estimator and also for the post-ℓ1-penalized M-estimator, which refits the nonzero entries of the former estimator without penalty in the criterion function. We demonstrate via simulations that our methods are not dominated by cross…

利用级数方法检验一类半参数或非参数条件矩限制模型AI 解读

This paper proposes a new test for a class of conditional moment restrictions (CMRs) whose parameterization involves unknown, unrestricted conditional expectation functions. Motivating examples of such CMRs arise from models of discrete choice under uncertainty including certain static games of incomplete information. The proposed test may be viewed as a semi-/nonparametric extension of the Bierens (1982, Journal of Econometrics 20, 105–134) goodness-of-fit test of a…