Multivariate Statistics and Probability
Essays in Memory of Paruchuri R. Krishnaiah
- 1st Edition - October 28, 1989
- Imprint: Academic Press
- Editors: C. R. Rao, M. M. Rao
- Language: English
- Paperback ISBN:9 7 8 - 1 - 4 8 3 2 - 4 5 1 5 - 7
- eBook ISBN:9 7 8 - 1 - 4 8 3 2 - 6 3 8 3 - 0
Multivariate Statistics and Probability: Essays in Memory of Paruchuri R. Krishnaiah is a collection of essays on multivariate statistics and probability in memory of Paruchuri R.… Read more
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Request a sales quoteMultivariate Statistics and Probability: Essays in Memory of Paruchuri R. Krishnaiah is a collection of essays on multivariate statistics and probability in memory of Paruchuri R. Krishnaiah (1932-1987), who made significant contributions to the fields of multivariate statistical analysis and stochastic theory. The papers cover the main areas of multivariate statistical theory and its applications, as well as aspects of probability and stochastic analysis. Topics range from finite sampling and asymptotic results, including aspects of decision theory, Bayesian analysis, classical estimation, regression, and time-series problems. Comprised of 35 chapters, this book begins with a discussion on the joint asymptotic distribution of marginal quantiles and quantile functions in samples from a multivariate population. The reader is then introduced to kernel estimators of density function of directional data; moment conditions for valid formal edgeworth expansions; and ergodicity and central limit theorems for a class of Markov processes. Subsequent chapters focus on minimal complete classes of invariant tests for equality of normal covariance matrices and sphericity; normed likelihood as saddlepoint approximation; generalized Gaussian random fields; and smoothness properties of the conditional expectation in finitely additive white noise filtering. This monograph should be of considerable interest to researchers as well as to graduate students working in theoretical and applied statistics, multivariate analysis, and random processes.
Preface
Contributors
In Memoriam
Joint Asymptotic Distribution of Marginal Quantiles and Quantile Functions in Samples from a Multivariate Population
Kernel Estimators of Density Function of Directional Data
On Determination of the Order of an Autoregressive Model
Admissible Linear Estimation in a General Gauss-Markov Model with an Incorrectly Specified Dispersion Matrix
On Moment Conditions for Valid Formal Edgeworth Expansions
Ergodicity and Central Limit Theorems for a Class of Markov Processes
Conditionally Ordered Distributions
A Discounted Cost Relationship
Strong Consistency of M-Estimates in Linear Models
Minimal Complete Classes of Invariant Tests for Equality of Normal Covariance Matrices and Sphericity
Invariance Principles for Changepoint Problems
On the Area of the Circles Covered by a Random Walk
Normed Likelihood as Saddlepoint Approximation
Non-uniform Error Bounds for Asymptotic Expansions of Scale Mixtures of Distributions
Empirical and Hierarchical Bayes Competitors of Preliminary Test Estimators in Two Sample Problems
On Confidence Bands in Nonparametric Density Estimation and Regression
A Note on Generalized Gaussian Random Fields
Smoothness Properties of the Conditional Expectation in Finitely Additive White Noise Filtering
Equivariant Estimation of a Mean Vector μ of N(μ,Σ) with 'Σ-1=1 or Σ-1/2μ=c or Σ = σ2μ'μ1
A Generalized Cauchy—Binet Formula and Applications to Total Positivity and Majorization
Isotonic M-Estimation of Location: Union-Intersection Principle and Preliminary Test Versions
Some Asymptotic Inferential Problems Connected with Elliptical Distributions
Stochastic Integrals of Empirical-Type Processes with Applications to Censored Regression
Nonminimum Phase Non-Gaussian Deconvolution
Inference in a Model with at Most One Slope-Change Point
Maximum Likelihood Principle and Model Selection when the True Model is Unspecified
An Asymptotic Minimax Theorem of Order n-1/2
An Improved Estimation Method for Univariate Autoregressive Models
Paradoxes in Conditional Probability
Inference Properties of a One-Parameter Curved Exponential Family of Distributions with Given Marginals
Asymptotically Precise Estimate of the Accuracy of Gaussian Approximation in Hubert Space
The Estimation of the Bispectral Density Function and the Detection of Periodicities in a Signal
Analysis of Odds Ratios in 2xn Ordinal Contingency Tables
Asymptotic Expansions of the Distributions of Some Test Statistics for Gaussian ARMA Processes
Estimating Multiple Rater Agreement for a Rare Diagnosis
Author Index
Subject Index
- Edition: 1
- Published: October 28, 1989
- No. of pages (eBook): 582
- Imprint: Academic Press
- Language: English
- Paperback ISBN: 9781483245157
- eBook ISBN: 9781483263830
CR
C. R. Rao
Professor C. R. Rao, born in India, is one of this century's foremost statisticians, and received his education in statistics at the Indian Statistical Institute (ISI), Calcutta. He is Emeritus Holder of the Eberly Family Chair in Statistics at Penn State and Director of the Center for Multivariate Analysis. He has long been recognized as one of the world's top statisticians, and has been awarded 34 honorary doctorates from universities in 19 countries spanning 6 continents. His research has influenced not only statistics, but also the physical, social and natural sciences and engineering. In 2011 he was recipient of the Royal Statistical Society's Guy Medal in Gold which is awarded triennially to those "who are judged to have merited a signal mark of distinction by reason of their innovative contributions to the theory or application of statistics". It can be awarded both to fellows (members) of the Society and to non-fellows. Since its inception 120 years ago the Gold Medal has been awarded to 34 distinguished statisticians. The first medal was awarded to Charles Booth in 1892. Only two statisticians, H. Cramer (Norwegian) and J. Neyman (Polish), outside Great Britain were awarded the Gold medal and C. R. Rao is the first non-European and non-American to receive the award.
Other awards he has received are the Gold Medal of Calcutta University, Wilks Medal of the American Statistical Association, Wilks Army Medal, Guy Medal in Silver of the Royal Statistical Society (UK), Megnadh Saha Medal and Srinivasa Ramanujan Medal of the Indian National Science Academy, J.C.Bose Gold Medal of Bose Institute and Mahalanobis Centenary Gold Medal of the Indian Science Congress, the Bhatnagar award of the Council of Scientific and Industrial Research, India and the Government of India honored him with the second highest civilian award, Padma Vibhushan, for “outstanding contributions to Science and Engineering / Statistics, and also instituted a cash award in honor of C R Rao, “to be given once in two years to a young statistician for work done during the preceding 3 years in any field of statistics”.
For his outstanding achievements Rao has been honored with the establishment of an institute named after him, C.R.Rao Advanced Institute for Mathematics, Statistics and Computer Science, in the campus of the University of Hyderabad, India. C.R. Rao won International Statistics Prize in 2023. He passed away in 2023 two weeks before his 103rd birthday.
Affiliations and expertise
Center for multivariate Analysis, Department of statistics, The Pennsylvania State University.Read Multivariate Statistics and Probability on ScienceDirect