This paper addresses much needed asymptotic and nonparametric bootstrap methodology for two-sample tests for means on Riemannian manifolds with a simply transitive group of isometries. In particular, we develop a two-sample procedure for testing the equality of the generalized Frobenius means of...

We derive some general results on the Fisher information (FI) contained in the data obtained from the ranked set sampling (RSS) design relative to its counterpart under the simple random sampling (SRS) for a finite mixture model. We propose different variations of RSS data and show how to...

Multivariate panel count data arise in event history studies on recurrent events if there exist several related events and study subjects can be examined or observed only at discrete time points instead of over continuous periods. In these situations, a complicated issue that may arise is that...

The asymptotic cumulants of ability estimators using fallible or estimated item parameters in an ability test based on item response theory are given up to the fourth order with higher-order asymptotic variance. The ability estimators cover those obtained by maximum likelihood, Bayes, and pseudo...

This paper deals with the problem of estimating the tail of a bivariate distribution function. To this end we develop a general extension of the POT (peaks-over-threshold) method, mainly based on a two-dimensional version of the Pickands–Balkema–de Haan Theorem. We introduce a new parameter...

We are concerned with kernel density estimation on the rotation group SO(3). We prove asymptotically optimal convergence rates for the minimax risk of the mean integrated squared error for different function classes including bandlimited functions, functions with bounded Sobolev norm and...

In this paper, the high-dimensional sparse linear regression model is considered, where the overall number of variables is larger than the number of observations. We investigate the L1 penalized least absolute deviation method. Different from most of the other methods, the L1 penalized LAD...

The c-characteristic function has been shown to have properties similar to those of the Fourier transformation. We now give a new property of the c-characteristic function of the spherically symmetric distribution. With this property, we can easily determine whether a distribution is spherically...

We provide a closed-form estimator based on the VARMA representation for the unrestricted multivariate GARCH(1,1) model. We show that the GARCH parameters can be derived analytically, using the autocovariances of the observed data, applying simple linear algebra tools. The resulting estimator is...

In financial practice, it is important to understand the dependence structure between the returns of individual assets and the market index. This is particularly true under extreme situations. Theoretically, this amounts to regressing the dependence relationship against a set of pre-specified...