Robust inference in deconvolution

Kotlarski's identity has been widely used in applied economic research based on repeated‐measurement or panel models with latent variables. However, how to conduct inference for these models has been an open question for two decades. This paper addresses this open problem by constructing a novel confidence band for the density function of a latent variable in repeated measurement error model. The confidence band builds on our finding that we can rewrite Kotlarski's identity as a system of linear moment restrictions. Our approach is robust in that we do not require the completeness. The confidence band controls the asymptotic size uniformly over a class of data generating processes, and it is consistent against all fixed alternatives. Simulation studies support our theoretical results.

Empirical Likelihood-Based Inference in Regressive Model with Moment Restrictions

In this paper, we consider the parameter estimation problem of linear regression model when the auxiliary information can be denoted by moment restrictions. We use the weighted least squares method to estimate the model parameters and to obtain the weights based on the auxiliary information by using the empirical likelihood method. The limiting distribution of the estimator is established, and the simulation studies are carried out to demonstrate the feasibility of our theoretical results.

Uniform nonparametric inference for time series using Stata

In this article, we introduce a command, tssreg, that conducts nonparametric series estimation and uniform inference for time-series data, including the case with independent data as a special case. This command can be used to nonparametrically estimate the conditional expectation function and the uniform confidence band at a user-specified confidence level, based on an econometric theory that accommodates general time-series dependence. The uniform inference tool can also be used to perform nonparametric specification tests for conditional moment restrictions commonly seen in dynamic equilibrium models.

On the Convergence Rate of the SCAD-Penalized Empirical Likelihood Estimator

This paper investigates the asymptotic properties of a penalized empirical likelihood estimator for moment restriction models when the number of parameters ( p n ) and/or the number of moment restrictions increases with the sample size. Our main result is that the SCAD-penalized empirical likelihood estimator is n / p n -consistent under a reasonable condition on the regularization parameter. Our consistency rate is better than the existing ones. This paper also provides sufficient conditions under which n / p n -consistency and an oracle property are satisfied simultaneously. As far as we know, this paper is the first to specify sufficient conditions for both n / p n -consistency and the oracle property of the penalized empirical likelihood estimator.