265,323 research outputs found
Efficient semiparametric estimation of a partially linear quantile regression model
This paper is concerned with estimating a conditional quantile function that is assumed to be partially linear. The paper develops a simple estimator of the parametric component of the conditional quantile. The semiparametric efficiency bound for the parametric component is derived, and two types of efficient estimators are considered. Asymptotic properties of the proposed estimators are established under regularity conditions. Some Monte Carlo experiments indicate that the proposed estimators perform well in small samples
Maximal uniform convergence rates in parametric estimation problems
This paper considers parametric estimation problems with independent, identically nonregularly distributed data. It focuses on rate efficiency, in the sense of maximal possible convergence rates of stochastically bounded estimators, as an optimality criterion, largely unexplored in parametric estimation. Under mild conditions, the Hellinger metric, defined on the space of parametric probability measures, is shown to be an essentially universally applicable tool to determine maximal possible convergence rates. These rates are shown to be attainable in general classes of parametric estimation problems
Inference in Additively Separable Models With a High-Dimensional Set of Conditioning Variables
This paper studies nonparametric series estimation and inference for the
effect of a single variable of interest x on an outcome y in the presence of
potentially high-dimensional conditioning variables z. The context is an
additively separable model E[y|x, z] = g0(x) + h0(z). The model is
high-dimensional in the sense that the series of approximating functions for
h0(z) can have more terms than the sample size, thereby allowing z to have
potentially very many measured characteristics. The model is required to be
approximately sparse: h0(z) can be approximated using only a small subset of
series terms whose identities are unknown. This paper proposes an estimation
and inference method for g0(x) called Post-Nonparametric Double Selection which
is a generalization of Post-Double Selection. Standard rates of convergence and
asymptotic normality for the estimator are shown to hold uniformly over a large
class of sparse data generating processes. A simulation study illustrates
finite sample estimation properties of the proposed estimator and coverage
properties of the corresponding confidence intervals. Finally, an empirical
application to college admissions policy demonstrates the practical
implementation of the proposed method
- …