Under some mild regularity on the normalizing sequence, we obtain necessary and sufficient conditions for the Strong Law of Large Numbers for (symmetrized) U-statistics. We also obtain nasc’s for the a.s. convergence of series of an analogous form.

We attempted to determine the number of sperm cells required for genotyping of one microsatellite marker. The crude genomic DNA extracted from about 760 or more sperm cells gave sufficient quantity of PCR product using a 20 microl-scale PCR. We also studied the effects of non-ionic detergents on extraction of crude sperm genomic DNA. PCR products amplified with the crude sperm genomic DNA extra...

The idea of dimension-reduction without loss of information can be quite helpful for guiding the construction of summary plots in regression without requiring a pre-specified model. Focusing on the central subspace, we investigate such “sufficient” dimension-reduction in regressions with a binary response. Three existing methods, SIR and pHd and SAVE, and one new method DOC are studied for thei...

Chen et al. (2010) propose a unified method – coordinate-independent sparse estimation (CISE) – that is able to simultaneously achieve sparse sufficient dimension reduction and screen out irrelevant and redundant variables efficiently. However, its attractive features depend on appropriate choice of the tuning parameter. In this note, we re-examine the Bayesian information criterion (BIC) in su...

1 Theoretical foundation 2 1.1 Statistical models and parameter spaces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.2 Limit theorems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.3 Estimation theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.4 Likelihood-based estimation . . . . . . . ....

Explicit formulas for the non-centrality parameters of the limiting chi-square distribution of proposed multisample rank based test statistics, aimed at testing the hypothesis of the simultaneous equality of location and scale parameters of underlying populations, are obtained by means of a general assertion concerning the location-scale test statistics. The finite sample behaviour of the propo...

Selecting between different dependency structures of hidden Markov random field can be very challenging, due to the intractable normalizing constant in the likelihood. We answer this question with approximate Bayesian computation (ABC) which provides a model choice method in the Bayesian paradigm. This comes after the work of Grelaud et al. (2009) who exhibited sufficient statistics on directly...