The general class of complex elliptical shape distributions on a complex sphere provides a natural framework for modeling shapes in two dimensions. Such class includes many distributions, e.g., complex Normal, Watson, Bingham, angular central Gaussian and several others. We employ this class of...

Recent results on quasi-maximum likelihood histogram sieve estimators in inverse problems for Poisson processes are generalized to B-spline sieves. The impact of discretization effects on strong L2 consistency and convergence rates are studied in detail. In particular, a "rates saturation...

A class of affine-invariant test statistics, including a sign test and a related family of signed-rank tests, is proposed for randomized complete block designs with one observation per treatment. This class is obtained by using the transformation-retransformation approach of Chakraborty,...

In this note we consider von Mises-Fisher families of probability densities on spheres and more generally on Stiefel manifolds, which include the orthogonal groups. It addresses the estimation of the mean direction or the mean location by empirical mean location, which for the von Mises-Fisher...

Correlated multivariate processes have a dependence structure which must be taken into account when estimating the covariance matrix. The natural estimator of the covariance matrix is introduced and is shown that to be biased under the dependence structure. This bias is studied under two...

We consider wavelet block thresholding method for density estimation. A block-thresholded density estimator is proposed and is shown to achieve optimal global rate of convergence over Besov spaces and simultaneously attain the optimal adaptive pointwise convergence rate as well. These results...

The conjugate prior for the exponential family, referred to also as the natural conjugate prior, is represented in terms of the Kullback-Leibler separator. This representation permits us to extend the conjugate prior to that for a general family of sampling distributions. Further, by replacing...

A distance for mixed nominal, ordinal and continuous data is developed by applying the Kullback-Leibler divergence to the general mixed-data model, an extension of the general location model that allows for ordinal variables to be incorporated in the model. The distance obtained can be...

We provide the rate of convergence of the Bayes action derived from non smooth loss functions involved in Bayesian robustness. Such loss functions are typically not twice differentiable but admit right and left second derivatives. The asymptotic limit of three measures of global robustness is...

This paper considers the implementation of prior stochastic information on unknown outcomes of the response variables into estimation and forecasting of systems of linear regression equations in the context of time series, cross sections, pooled and longitudinal data models. The established...