Ursula U. Müller

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For nonparametric regression models with fixed and random design, two classes of estimators for the error variance have been introduced: second sample moments based on residuals from a nonparametric fit, and difference-based estimators. The former are asymptotically optimal but require estimating the regression function; the latter are simple but have(More)
We consider nonparametric regression models with multivariate covariates and estimate the regression curve by an undersmoothed local polynomial smoother. The resulting residual-based empirical distribution function is shown to differ from the errorbased empirical distribution function by the density times the average of the errors, up to a uniformly(More)
Primary analysis of case-control studies focuses on the relationship between disease D and a set of covariates of interest (Y, X). A secondary application of the case-control study, which is often invoked in modern genetic epidemiologic association studies, is to investigate the interrelationship between the covariates themselves. The task is complicated(More)
Soft thresholds are ubiquitous in living organisms, in particular in mechanisms of neurons and of neural networks such as sensory systems. Which soft threshold functions produce (threshold) stochastic resonance remains a question. The answer may depend on the information measure used. We argue that Fisher information about signal parameters is an attractive(More)
This paper addresses estimation of linear functionals of the error distribution in nonparametric regression models. It derives an i.i.d. representation for the empirical estimator based on residuals, using undersmoothed estimators for the regression curve. Asymptotic efficiency of the estimator is proved. Estimation of the error variance is discussed in(More)
Consider a detector which records the times at which the realizations of a nonparametric regression model exceed a certain threshold. If the error distribution is known, the regression function can still be identified from these threshold data. We construct estimators for the regression function. They are transformations of kernel estimators. We determine(More)
We consider semiparametric models of semi-Markov processes with arbitrary state space. Assuming that the process is geometrically ergodic, we characterize efficient estimators, in the sense of Hájek and Le Cam, for arbitrary real-valued smooth functionals of the distribution of the embedded Markov renewal process. We construct efficient estimators of the(More)
This article considers linear and nonlinear regression with a response variable that is allowed to be “missing at random”. The only structural assumptions on the distribution of the variables are that the errors have mean zero and are independent of the covariates. The independence assumption is important. It enables us to construct an estimator for the(More)