Summary. Uniform confidence bands for densities f via non-parametric kernel estimates were first constructed by Bickel and Rosenblatt. In this paper this is extended to confidence bands in the deconvolution problem g D f * ψ for an ordinary smooth error density ψ. Under certain regularity conditions, we obtain asymptotic uniform confidence bands based on the asymptotic distribution of the maximal deviation (L 1 -distance) between a deconvolution kernel estimator f and f. Further consistency of the simple non-parametric bootstrap is proved. For our theoretical developments the bias is simply corrected by choosing an undersmoothing bandwidth. For practical purposes we propose a new data-driven bandwidth selector that is based on heuristic arguments, which aims at minimizing the L 1 -distance betweenf and f . Although not constructed explicitly to undersmooth the estimator, a simulation study reveals that the bandwidth selector suggested performs well in finite samples, in terms of both area and coverage probability of the resulting confidence bands. Finally the methodology is applied to measurements of the metallicity of local F and G dwarf stars. Our results confirm the 'G dwarf problem', i.e. the lack of metal poor G dwarfs relative to predictions from 'closed box models' of stellar formation.

We present general results on the identifiability of finite mixtures of elliptical distributions under conditions on the characteristic generators or density generators. Examples include the multivariate "t"-distribution, symmetric stable laws, exponential power and Kotz distributions. In each case, the shape parameter is allowed to vary in the mixture, in addition to the location vector and the scatter matrix. Furthermore, we discuss the identifiability of finite mixtures of elliptical densities with generators that correspond to scale mixtures of normal distributions. Copyright 2006 Board of the Foundation of the Scandinavian Journal of Statistics..

We introduce a new class of circular time series based on hidden Markov models. These are compared with existing models, their properties are outlined and issues relating to parameter estimation are discussed. The new models conveniently describe multi-modal circular time series as dependent mixtures of circular distributions. Two examples from biology and meteorology are used to illustrate the theory. Finally, we introduce a hidden Markov model for bivariate linear-circular time series and use it to describe larval movement of the fly Drosophila.

Bimodality, Convergence analysis, Cross-sectional income distribution, Likelihood ratio test, Finite mixture,

In this paper we study statistical inference for certain inverse problems. We go beyond mere estimation purposes and review and develop the construction of confidence intervals and confidence bands in some inverse problems, including deconvolution and the backward heat equation. Further, we discuss the construction of certain hypothesis tests, in particular concerning the number of local maxima of the unknown function. The methods are illustrated in a case study, where we analyze the distribution of heliocentric escape velocities of galaxies in the Centaurus galaxy cluster, and provide statistical evidence for its bimodality.