Tensor Methods in Statistics - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Tensor Methods in Statistics write by P. McCullagh. This book was released on 2018-01-18. Tensor Methods in Statistics available in PDF, EPUB and Kindle. 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 and suitable tables of complementary set partitions are provided. Subsequent chapters deal with asymptotic approximations based on Edgeworth expansion and saddlepoint expansion. The saddlepoint expansion is introduced via the Legendre transformation of the cumulant generating function, also known as the conjugate function of the cumulant generating function. A recurring them is that, with suitably chosen notation, multivariate calculations are often simpler and more transparent than the corresponding univariate calculations. The final two chapters deal with likelihood ratio statistics, maximum likelihood estimation and the effect on inferences of conditioning on ancillary or approximately ancillary statistics. The Bartlett adjustment factor is derived in the general case and simplified for certain types of generalized linear models. Finally, Barndorff-Nielsen's formula for the conditional distribution of the maximum liklelihood estimator is derived and discussed. More than 200 Exercises are provided to illustrate the uses of tensor methodology.
Tensor Methods in Statistics
Tensor Methods in Statistics - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Tensor Methods in Statistics write by Peter McCullagh. This book was released on 2018-07-18. Tensor Methods in Statistics available in PDF, EPUB and Kindle. A pioneering monograph on tensor methods applied to distributional problems arising in statistics, this work begins with the study of multivariate moments and cumulants. An invaluable reference for graduate students and professional statisticians. 1987 edition.
Tensor Methods in Statistics
Tensor Methods in Statistics - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Tensor Methods in Statistics write by Peter McCullagh. This book was released on 1987. Tensor Methods in Statistics available in PDF, EPUB and Kindle.
Tensor Methods in Statistics
Tensor Methods in Statistics - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Tensor Methods in Statistics write by Peter McCullagh. This book was released on 2018-07-18. Tensor Methods in Statistics available in PDF, EPUB and Kindle. A pioneering monograph on tensor methods applied to distributional problems arising in statistics, this work begins with the study of multivariate moments and cumulants. An invaluable reference for graduate students and professional statisticians. 1987 edition.
Tensor Methods in Statistics
Tensor Methods in Statistics - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Tensor Methods in Statistics write by P. McCullagh. This book was released on 2018-01-18. Tensor Methods in Statistics available in PDF, EPUB and Kindle. 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 and suitable tables of complementary set partitions are provided. Subsequent chapters deal with asymptotic approximations based on Edgeworth expansion and saddlepoint expansion. The saddlepoint expansion is introduced via the Legendre transformation of the cumulant generating function, also known as the conjugate function of the cumulant generating function. A recurring them is that, with suitably chosen notation, multivariate calculations are often simpler and more transparent than the corresponding univariate calculations. The final two chapters deal with likelihood ratio statistics, maximum likelihood estimation and the effect on inferences of conditioning on ancillary or approximately ancillary statistics. The Bartlett adjustment factor is derived in the general case and simplified for certain types of generalized linear models. Finally, Barndorff-Nielsen's formula for the conditional distribution of the maximum liklelihood estimator is derived and discussed. More than 200 Exercises are provided to illustrate the uses of tensor methodology.
