Tensor Methods in Statistics

Name: Tensor Methods in Statistics
Brand: CRC Press

CRC Press

This book provides a systematic development of tensor methods in statistics, beginning with the study of multivariate moments and cumulants. The effect on moment arrays and on cumulant arrays of making linear or affine transformations of the variables is studied. > This book provides a systematic development of tensor methods in statistics, beginning with the study of multivariate moments and cumulants. The effect on moment arrays and on cumulant arrays of making linear or affine transformations of the variables is studied. Because of their importance in statistical theory, invariant functions of the cumulants are studied in some detail. This is followed by an examination of the effect of making a polynomial transformation of the original variables. The fundamental operation of summing over complementary set partitions is introduced at this stage. This operation shapes the notation and pervades much of the remainder of the book. The necessary lattice-theory is discussed s