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 study an optimal nonparametric regression model for a threshold detector exposed to a noisy, subthreshold signal. The problem of recovering the signal is similar to that faced by neurons in nervous systems, although our model is intended to be normative rather than realistic. In our approach, the time-integrating activity of the neuron is modeled by(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)
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 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 error-based empirical distribution function by the density times the average of the errors, up to a uniformly(More)
We consider regression models with parametric (linear or nonlin-ear) regression function and allow responses to be " missing at random. " We assume that the errors have mean zero and are independent of the covariates. In order to estimate expectations of functions of covariate and response we use a fully imputed estimator, namely an empirical estimator(More)
Suppose we observe a discrete-time Markov chain at certain periodic or random time points only. Which observation patterns allow us to identify the transition distribution? In case we can identify it, how can we construct (good) estimators? We discuss these questions both for nonparametric models and for linear autoregression. 1.1 Introduction For Markov(More)
Goodness-of-fit tests for discrete data and models with parameters to be estimated are usually based on Pearson's χ 2 or the Likelihood Ratio Statistic. Both are included in the family of Power-Divergence Statistics SD λ which are asymptotically χ 2 distributed for the usual sampling schemes. We derive a limiting standard normal distribution for a(More)
This paper addresses estimation of linear functionals of the error distribution in non-parametric 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)
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)