137 research outputs found
Simpson's Paradox and Collapsibility
Simpson's paradox and collapsibility are two closely related concepts in the
context of data analysis. While the knowledge about the occurrence of Simpson's
paradox helps a statistician to draw correct and meaningful conclusions, the
concept of collapsibility deals with dimension-reduction aspects, when
Simpson's paradox does not occur. We discuss in this paper in some detail the
nature and the genesis of Simpson's paradox with respect to well-known examples
and also various concepts of collapsiblity. The main aim is to bring out the
close connections between these two phenomena, especially with regard to the
analysis of contingency tables, regression models and a certain measure of
association or a dependence function. There is a vast literature on these
topics and so we focus only on certain aspects, recent developments and some
important results in the above-mentioned areas.Comment: 19 page
Compound Poisson and signed compound Poisson approximations to the Markov binomial law
Compound Poisson distributions and signed compound Poisson measures are used
for approximation of the Markov binomial distribution. The upper and lower
bound estimates are obtained for the total variation, local and Wasserstein
norms. In a special case, asymptotically sharp constants are calculated. For
the upper bounds, the smoothing properties of compound Poisson distributions
are applied. For the lower bound estimates, the characteristic function method
is used.Comment: Published in at http://dx.doi.org/10.3150/09-BEJ246 the Bernoulli
(http://isi.cbs.nl/bernoulli/) by the International Statistical
Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm
On the Long-range Dependence of Fractional Poisson and Negative Binomial Processes
We study the long-range dependence (LRD) of the increments of the fractional
Poisson process (FPP), the fractional negative binomial process (FNBP) and the
increments of the FNBP. We first point out an error in the proof of Theorem 1
of Biard and Saussereau (2014) and prove that the increments of the FPP has
indeed the short-range dependence (SRD) property, when the fractional index
satisfies . We also establish that the FNBP has
the LRD property, while the increments of the FNBP possesses the SRD property.Comment: 17 page
- …