1. CMB 2011 (vol 54 pp. 464)
||A Characterization of the Compound-Exponential Type Distributions|
In this paper, a fixed point equation of the
compound-exponential type distributions is derived, and under some
both the existence and uniqueness of
this fixed point equation are investigated.
A question posed by Pitman and Yor
can be partially answered by using our approach.
Keywords:fixed point equation, compound-exponential type distributions
2. CMB 2011 (vol 54 pp. 566)
||Non-uniform Randomized Sampling for Multivariate Approximation by High Order Parzen Windows|
We consider approximation of multivariate functions in Sobolev
spaces by high order Parzen windows in a non-uniform sampling
setting. Sampling points are neither i.i.d. nor regular, but are
noised from regular grids by non-uniform shifts of a probability
density function. Sample function values at sampling points are
drawn according to probability measures with expected values being
values of the approximated function. The approximation orders are
estimated by means of regularity of the approximated function, the
density function, and the order of the Parzen windows, under
suitable choices of the scaling parameter.
Keywords:multivariate approximation, Sobolev spaces, non-uniform randomized sampling, high order Parzen windows, convergence rates
3. CMB 2009 (vol 40 pp. 231)
||Asymptotic theory and the foundations of statistics |
Statistics in the 20th century
has been enlivened by a passionate, occasionally bitter, and still vibrant
debate on the foundations of statistics and in particular on
Bayesian vs. frequentist approaches to inference.
In 1975 D.~V.~Lindley predicted a Bayesian 21st century for statistics.
This prediction has often been discussed since,
but there is still no consensus on the probability
of its correctness.
Recent developments in the asymptotic theory of statistics are,
surprisingly, shedding new light on this debate, and may have the
potential to provide a common middle ground.
Categories:62-02, 62A10, 62A15
4. CMB 1998 (vol 41 pp. 33)
||Asymptotic existence of tight orthogonal main effect plans |
Our main result is showing the asymptotic existence of tight
$\OMEP$s. More precisely, for each fixed number $k$ of rows, and with the
exception of $\OMEP$s of the form $2 \times 2 \times \cdots 2 \times 2s\specdiv 4s$
with $s$ odd and with more than three rows, there are only a finite number
of tight $\OMEP$ parameters for which the tight $\OMEP$ does not exist.