Suchergebnisse

We consider Grenander‐type estimators for a monotone function
, obtained as the slope of a concave (convex) estimate of the primitive of λ. Our main result is a central limit theorem for the Hellinger loss, which applies to estimation of a probability density, a regression function or a failure rate. In the case of density estimation, the limiting variance of the Hellinger loss turns out to be independent of λ.

We consider kernel smoothed Grenander‐type estimators for a monotone hazard rate and a monotone density in the presence of randomly right censored data. We show that they converge at rate n2/5 and that the limit distribution at a fixed point is Gaussian with explicitly given mean and variance. It is well known that standard kernel smoothing leads to inconsistency problems at the boundary points. It turns out that, also by using a boundary correction, we can only establish uniform consistency on intervals that stay away from the end point of the support (although we can go arbitrarily close to the right boundary).

Space–time autoregressive (STAR) models, introduced by Cliff and Ord [Spatial autocorrelation (1973) Pioneer, London] are successfully applied in many areas of science, particularly when there is prior information about spatial dependence. These models have significantly fewer parameters than vector autoregressive models, where all information about spatial and time dependence is deduced from the data. A more flexible class of models, generalized STAR models, has been introduced in Borovkovaet al. [Proc. 17th Int. Workshop Stat. Model. (2002), Chania, Greece] where the model parameters are allowed to vary per location. This paper establishes strong consistency and asymptotic normality of the least squares estimator in generalized STAR models. These results are obtained under minimal conditions on the sequence of innovations, which are assumed to form a martingale difference array. We investigate the quality of the normal approximation for finite samples by means of a numerical simulation study, and apply a generalized STAR model to a multivariate time series of monthly tea production in west Java, Indonesia.

To ensure the safety of plasma‐derived medicinal products, the Dutch Blood Supply Foundation (Sanquin) performs virus validation experiments. Data from these experiments are based on serial dilution assays. Regression analysis on assay data faces several problems: only a small number of data points are available, data contain censoring and are subject to sampling error. Furthermore, the process variability inherent to the experiments is not evident. In this paper we address these problems by introducing a regression model for serial dilution data and by analyzing how validation experiments and simulation techniques can help elucidate various sources of variability the experiments are subject to. These are then incorporated into the regression model.