The multivariate linear model, in which the matrix of the first order parameters is divided into two matrices: to the matrix of the useful parameters and to the matrix of the nuisance parameters, is considered. We examine eliminating transformations which eliminate the nuisance parameters without loss of information on the useful parameters and on the variance components.
In this paper, we analyze the celebrated EM algorithm from the point of view of proximal point algorithms. More precisely, we study a new type of generalization of the EM procedure introduced in [Chretien and Hero (1998)] and called Kullback-proximal algorithms. The proximal framework allows us to prove new results concerning the cluster points. An essential contribution is a detailed analysis of the case where some cluster points lie on the boundary of the parameter space.
We prove the complete convergence of Shannon’s, paired, genetic and α-entropy for random partitions of the unit segment. We also derive exact expressions for expectations and variances of the above entropies using special functions.
Equivalence testing is the natural approach to many statistical problems. First, its main application, bioequivalence testing, is reviewed. The basic concepts of bioequivalence testing (2×2 crossover designs, TOST, interval inclusion principle, etc.) and its problems (TOST biased character, the carryover problem, etc.) are considered. Next, equivalence testing is discussed more generally. Some applications and methods are reviewed and the relation of equivalence testing and distance-based inference...
There exist many different ways of determining the best linear unbiased estimation of regression coefficients in general regression model. In Part I of this article it is shown that all these ways are numerically equivalent almost everyvhere. In Part II conditions are considered under which all the unbiased estimations of the unknown covariance matrix scalar factor are numerically equivalent almost everywhere.
There exist many different ways of determining the best linear unbiased estimation of regression coefficients in general regression model. In Part I of this article it is shown that all these ways are numerically equivalent almost everyvhere. In Part II conditions are considered under which all the unbiased estimations of the unknown covariance matrix scalar factor are numerically equivalent almost everywhere.