A survey of statistical methods on remote sensing in russian literature from 1976 to 1985

In this article we review the major areas of remote sensing in the Russian literature for the period 1976 to 1985 that use statistical methods to analyze the observed data. For each of the areas, the problems that have been studied and the statistical techniques that have been used are briefly described     

Relation of modified power series distributions to lagrangian probability distributions

The class of Lagrangian probability distributions ‘LPD’, given by the expansion of a probability generating function gt;fgt;‘gt;tgt;’ under the transformation gt;ugt; = gt;tgt;/gt;ggt;‘gt;tgt;’ where gt;ggt; ‘gt;tgt;’ is also a p.g.f., has been substantially widened by removing the restriction that the defining functions gt;ggt; ‘gt;tgt;’ and gt;fgt;‘gt;tgt;’ be probability generating functions. The class of modified power series distributions defined by Gupta ‘1974’ has been shown to be a sub-class of the wider class of LPDs     

Estimation of p{x > y} based on progressively truncated versions of the wilcqxon-mann-whitney statistics

Stochastic processes related to some generalized U-statistics (with especial emphasis on the Wilcoxon-Mann-Whitney (WMW-) statistic), under progressive right censoring, are considered for prediction purposes. Their weak convergence results are incorporated in the study of the asymptotic properties of the predictors. The form of the estimable parameter as a function of the truncation point is studied for the WMW case for some typical distributions and the theoretical results are supplemented by simulated ones.     

Parameter inference for time series with regular and seasonal unit roots

It is common to have both regular and seasonal roots present in many time series data. It may occur that one or both of the roots are just close but not equal to unity. Parameter inference for this situation is considered both when the time series has a finite or an infinite variance. Asymptotic char-acterizations of the test statistics were obtained via functionals of Ornstein-Uhlenbeck processes and Lévy processes. Tabulations for the large sample distributions are obtained. The results will be useful in applications deciding whether both regular and seasonal differencing are needed in fitting a time series model.     

Identities and inequalities for the expected values of random matrices and loewner's theory

We consider the identity associated with the expected values of the matrix-valued quadratic forms of two random matrices. As a special case the identity yields the matrix-valued inequality of the Schwarz type. The most important application is for Loewner's theory in the context of the operator-monotone function, and the inequalities based on the concavityconvexity of the matrix-valued functions are derived.