In this selective review, we first provide some empirical examples that motivate the usefulness of semi-nonparametric techniques in modelling economic and financial time series. We describe popular classes of semi-nonparametric dynamic models and some temporal dependence properties. We then...

This paper studies nonparametric estimation of conditional moment models in which the residual functions could be nonsmooth with respect to the unknown functions of endogenous variables. It is a problem of nonparametric nonlinear instrumental variables (IV) estimation, and a difficult nonlinear...

We study the problem of nonparametric regression when the regressor is endogenous, which is an important nonparametric instrumental variables (NPIV) regression in econometrics and a difficult ill-posed inverse problem with unknown operator in statistics. We first establish a general upper bound...

This paper makes several important contributions to the literature about nonparametric instrumental variables (NPIV) estimation and inference on a structural function h0 and its functionals. First, we derive sup-norm convergence rates for computationally simple sieve NPIV (series 2SLS)...

We establish the consistency and asymptotic normality for a class of estimators that are linear combinations of a set of √ n-consistent estimators whose cardinality increases with sample size. A special case of our framework corresponds to the conditional moment restriction and the implied...

For semi/nonparametric conditional moment models containing unknown parametric components θ and unknown functions of endogenous variables (h), Newey and Powell (2003) and Ai and Chen (2003) propose sieve minimum distance (SMD) estimation of (θ, h) and derive the large sample properties. This...

In this paper, we clarify the relations between the existing sets of regularity conditions for convergence rates of nonparametric indirect regression (NPIR) and nonparametric instrumental variables (NPIV) regression models. We establish minimax risk lower bounds in mean integrated squared error...

The goal of this paper is to develop techniques to simplify semiparametric inference. We do this by deriving a number of numerical equivalence results. These illustrate that in many cases, one can obtain estimates of semiparametric variances using standard formulas derived in the...

This paper computes the semiparametric efficiency bound for finite dimensional parameters identified by models of sequential moment restrictions containing unknown functions. Our results extend those of Chamberlain (1992b) and Ai and Chen (2003) for semiparametric conditional moment restriction...

This paper considers semiparametric efficient estimation of conditional moment models with possibly nonsmooth residuals in unknown parametric components (θ) and unknown functions (h) of endogenous variables. We show that: (1) the penalized sieve minimum distance(PSMD) estimator (ˆθ,ˆh) can...