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Advances in Directional and Linear Statistics A Festschrift for Sreenivasa Rao Jammalamadaka

:	Martin T. Wells, Ashis SenGupta
:	Martin T. Wells, Ashis SenGupta
:	Advances in Directional and Linear Statistics A Festschrift for Sreenivasa Rao Jammalamadaka
:	Physica-Verlag
:	9783790826289
:	1
:	CHF 85.30
:

:	Wahrscheinlichkeitstheorie, Stochastik, Mathematische Statistik
:	English

:	321
:	Wasserzeichen/DRM
:	PC/MAC/eReader/Tablet
:	PDF

The present volume consists of papers written by students, colleagues and collaborators of Sreenivasa Rao Jammalamadaka from various countries, and covers a variety of research topics which he enjoys and contributed immensely to.

Professor Sreenivasa Rao Jammalamadaka, formerly known as J. S. Rao and affectionately known to most of us as JS, was born on December 7, 1944, at Munipalle, India. Being under-aged for engineering studies was a blessing in disguise, and he was among the first batch of students selected for the Bachelor of Statistics (B. Stat.) degree at the Indian Statistical Institute (ISI), Kolkata. He received his Masters and Ph.D. degrees also from the ISI, and has the distinction of being the first B.Stat.-M.Stat.-Ph.D. of the ISI. He received his education from such legendary figures as Professors P. C. Mahalanobis, J. B. S. Haldane, C. R. Rao, and D. Basu among others, and worked with Professor C.R. Rao for his Ph.D. (1969) on a then newly emerging area, Directional Data Analysis. JS moved to the USA in 1969 and was a faculty member at the Indiana University and then at the University of Wisconsin, Madison, before he moved to the University of California, Santa Barbara (UCSB) in 1976, where he has remained since then. At UCSB he played a leading role in creating the new Department of Statistics and Applied Probability and was its first Chairman. He has been a prodigious mentor to the graduate students in that department, having provided guidance to as many of 35 Ph.D. students, at the last count. Throughout his career, JS has been generous to his colleagues in India, inviting them to the U.S. and spending many of his sabbaticals helping Universities in India as well as in other countries. JS has published extensively in leading international journals. His research work spans a wide spectrum which includes: Goodness-of-Fit tests, Linear Models, Non-parametric and Semi-parametric inference, Bayesian analysis, Reliability, Spacings statistics, and most notably, Directional Data Analysis. He has written several books, both for undergraduate students as well as for advanced researchers. He has collaborated with a large number of researchers from around the world in general, and from India in particular. A Fellow of both the ASA and the IMS among other professional organizations, he has served the cause of statistics at many national and international levels, including that of the President of the International Indian Statistical Association.

	Preface	223
	8	223
	Contents	223
	10	223
	Contributors	223
	12	223
	Chapter 1:	223
	15	223
	1.1 Introduction	15
	1.2 Some Well-Known Circular Models	16
	1.3 Introducing Asymmetry	17
	1.4 Axial Models	18
	1.5 Asymmetric Axial Models	21
	1.6 Bivariate Axial Distributions	22
	References	23
	Chapter 2:	23
	24	23
	2.1 Introduction	24
	2.2 Preliminaries	26
	2.3 Assumptions and Main Results	29
	2.4 Proof of Theorems and Corollary 2.1	32
	References	38
	Chapter 3:	38
	39	38
	3.1 Introduction	39
	3.2 Data	40
	3.3 Multivariate Regression Models with Space-Time ARMA Errors	42
	3.3.1 The Model	42
	3.3.2 Model Estimation and Model Selection	43
	3.4 Asymptotic Properties and Simulations	45
	3.5 Simulation Study	54
	3.5.1 Model 1	54
	3.5.2 Model 2	54
	3.5.3 Model 3	55
	3.6 Real Data Analysis	55
	3.7 Conclusion	61
	References	61
	Chapter 4:	61
	63	61
	4.1 Introduction	63
	4.2 Information Theoretic Results for Directional Distributions	65
	4.3 Other Properties	69
	References	79
	Chapter 5:	79
	81	79
	5.1 Introduction	81
	5.2 Theory	82
	5.2.1 Estimation of the Asymptotic Variance	85
	5.3 Simulation Studies	86
	5.4 An Example	89
	5.5 Conclusion	90
	References	93
	Chapter 6:	93
	96	93
	6.1 Introduction	96
	6.2 Model Description	97
	6.2.1 Heteroscedastic Model	97
	6.2.2 Homoscedastic Model	99
	6.3 Model Fitting and Estimation	99
	6.3.1 Heteroscedastic Model	100
	6.3.2 Homoscedastic Model	101
	6.4 A Simulation Study	102
	6.5 Application to Spellman Data	104
	6.6 Conclusion	106
	References	106
	Chapter 7:	106
	108	106
	7.1 Introduction	108
	7.2 Markov Chain Monte Carlo Stochastic Approximation Algorithms	109
	7.3 Simulations	111
	7.4 A Hybrid Algorithm	116
	7.5 Conclusions	121
	References	121
	Chapter 8:	121
	123	121
	8.1 Introduction	123
	8.2 Stochastic Orders	124
	8.3 Spacings	127
	8.3.1 One-Sample Problem	128
	8.3.2 Two-Samples Problem	129
	8.4 Sample Range	134
	8.5 Applications	135
	8.5.1 Type-II Censoring	135
	8.5.2 Reliability	136
	8.5.3 Dependence Orderings Among Order Statistics	137
	References	137
	Chapter 9:	137
	140	137
	9.1 Introduction	140
	9.2 Models with Deterministic Number of Terms	142
	9.2.1 Peak to Sum Ratio	142
	9.2.2 Peak to Average Ratio	144
	9.3 Models with Random Number of Terms	144
	9.3.1 Peak to Sum Ratio	144
	9.3.2 Peak to Average Ratio	145
	9.4 Geometric Example	146
	9.5 An Illustrative Data Example	148
	References	150
	Chapter 10:	150
	152	150
	10.1 Introduction	152
	10.2 Main Results	153
	10.3 Almost Sure Limits	156
	10.4 Asymptotic Normality	158
	10.5 Partial Loss of Association	160
	10.6 Conclusion	161
	References	163
	Chapter 11:	163
	164	163
	11.1 Introduction	164
	11.2 Main Result	170
	11.3 Large Deviation Results	174
	Appendix	178
	References	178
	Chapter 12:	178
	181	178
	12.1 Introduction	181
	12.2 Time Series Models	182
	12.3 Innovations	183
	12.4 Market Setting and Data	187
	12.5 SARIMA Model of Balancing Energy Demand	189
	12.6 Innovation Distribution	192
	12.7 Conclusion	193
	References	195
	Chapter 13:	195
	197	195
	13.1 Introduction	197
	13.2 Results	198
	13.3 Proofs	201
	References	207
	Chapter 14:	207
	208	207
	14.1 Introduction	208
	14.2 Classification	209
	14.2.1 Conventional Classification Methods	210
	14.2.1.1 Parametric Model	210
	14.2.1.2 Nonparametric Model	211
	14.2.2 Nonparametric Classification: New Developments	212
	14.2.3 Probabilistic Classifier	215
	14.2.4 Applications of the Probabilistic Classifier	217
	14.3 k-NN Estimation in Natural Resources	219
	14.4 Final Remarks	221
	References	222
	Chapter 15:	222
	224	222
	15.1 Introduction	224
	15.2 An Illustrative Example	226
	15.3 Dermal Patch Problem	226
	15.4 Patterns in Coin Tossing	228
	15.5 Chemical Bonding Problem	232
	15.6 Yell Game	234
	15.7 Noodles Problem	235
	15.7.1 Introduction	235
	15.7.2 Expected Value	236