Strong approximation of empirical kac processes

Summary A strong approximation result is derived for the Poisson sample size empirical characteristic process. Work done while the author was on leave from Szeged University and a Visiting Scientist at Carleton University, supported by Canadian N.R.C. operating grants of D. A. Dawson and J. N. K. Rao.     

Testing for linearity

A nonparametric large sample test is proposed for testing the linearity of a regression model with independent and identically distributed errors satisfying only a very mild tail condition. The statistic is based on the functional least squares estimator of the slope vector. The test is applied to the stack loss data.     

Completeness properties of perturbed sequences

If S is an arbitrary sequence of positive integers, let P(S) be the set of all integers which are representable as a sum of distinct terms of S. Call S complete if P(S) contains all large integers, and subcomplete if P(S) contains an infinite arithmetic progression. It is shown that any sequence can be perturbed in a rather moderate way into a sequence which is not subcomplete. On the other hand, it is shown that if S is any sequence satisfying a mild growth condition, then a surprisingly gentle perturbation suffices to make S complete in a strong sense. Various related questions are also considered.     

Strong approximations of the Hoeffding,Blum, Kiefer,Rosenblatt multivariate empirical process

Hoeffding (Ann. Math. Statist. 1948) and Blum, Kiefer and Rosenblatt (Ann. Math. Statist. 1961) constructed distribution free tests of independence based on a multivariate empirical process. We establish strong invariance principles for the latter and also for appropriate functionals of it.     

Strangeness correlation: A clue to hadron modification in dense matter?

We discuss the possibility to observe hadron modification in hot matter via the correlation of identical particles. We find that the hadron modification causes a new type of correlation, back-to-back correlation.