Related papers: Higher order semiparametric frequentist inference …

In this paper, inference for the parametric component of a semiparametric model based on sampling from the posterior profile distribution is thoroughly investigated from the frequentist viewpoint. The higher-order validity of the profile…

The penalized profile sampler for semiparametric inference is an extension of the profile sampler method (Lee, Kosorok and Fine, 2005) obtained by profiling a penalized log-likelihood. The idea is to base inference on the posterior…

The major goal of this paper is to study the second order frequentist properties of the marginal posterior distribution of the parametric component in semiparametric Bayesian models, in particular, a second order semiparametric…

Generalized Fiducial Inference (GFI) is motivated by R.A. Fisher's approach of obtaining posterior-like distributions when there is no prior information available for the unknown parameter. Without the use of Bayes' theorem GFI proposes a…

We consider the problem of estimation of a shift parameter of an unknown symmetric function in Gaussian white noise. We introduce a notion of semiparametric second-order efficiency and propose estimators that are semiparametrically…

Inference on the parametric part of a semiparametric model is no trivial task. If one approximates the infinite dimensional part of the semiparametric model by a parametric function, one obtains a parametric model that is in some sense…

This paper is concerned with the estimation of the period of an unknown periodic function in Gaussian white noise. A class of estimators of the period is constructed by means of a penalized maximum likelihood method. A second-order…

Bayesian inference requires specification of a single, precise prior distribution, whereas frequentist inference only accommodates a vacuous prior. Since virtually every real-world application falls somewhere in between these two extremes,…

We present a theory of point and interval estimation for nonlinear functionals in parametric, semi-, and non-parametric models based on higher order influence functions (Robins (2004), Section 9; Li et al. (2004), Tchetgen et al. (2006),…

We establish a general Bernstein--von Mises theorem for approximately linear semiparametric functionals of fractional posterior distributions based on nonparametric priors. This is illustrated in a number of nonparametric settings and for…

Robins et al. (2008, 2017) applied the theory of higher order influence functions (HOIFs) to derive an estimator of the mean $\psi$ of an outcome Y in a missing data model with Y missing at random conditional on a vector X of continuous…

We suggest an iterative approach to computing K-step maximum likelihood estimates (MLE) of the parametric components in semiparametric models based on their profile likelihoods. The higher order convergence rate of K-step MLE mainly depends…

This paper is concerned with estimation and inference for ultrahigh dimensional partially linear single-index models. The presence of high dimensional nuisance parameter and nuisance unknown function makes the estimation and inference…

We introduce a new method of estimation of parameters in semiparametric and nonparametric models. The method is based on estimating equations that are $U$-statistics in the observations. The $U$-statistics are based on higher order…

We consider estimating the parametric components of semi-parametric multiple index models in a high-dimensional and non-Gaussian setting. Such models form a rich class of non-linear models with applications to signal processing, machine…

The parametric complexity is the key quantity in the minimum description length (MDL) approach to statistical model selection. Rissanen and others have shown that the parametric complexity of a statistical model approaches a simple function…

Bayesian and frequentist methods differ in many aspects, but share some basic optimality properties. In practice, there are situations in which one of the methods is more preferred by some criteria. We consider the case of inference about a…

As a specific proportional hazard rates model, sequential order statistics can be used to describe the lifetimes of load-sharing systems. Inference for these systems needs to account for small sample sizes, which are prevalent in…

This paper investigates the accuracy of bootstrap-based inference in the case of long memory fractionally integrated processes. The re-sampling method is based on the semi-parametric sieve approach, whereby the dynamics in the process used…

We consider a class of semiparametric regression models which are one-parameter extensions of the Cox [J. Roy. Statist. Soc. Ser. B 34 (1972) 187-220] model for right-censored univariate failure times. These models assume that the hazard…