國立高雄大學圖資館 |

語系: 繁體中文

說明(常見問題)

圖資館首頁

登入

回首頁

切換: 標籤 | MARC模式 | ISBD

Asymptotic statistical inferencea ba...

Deshmukh, Shailaja.

Asymptotic statistical inferencea basic course using R /

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Asymptotic statistical inferenceby Shailaja Deshmukh, Madhuri Kulkarni.
其他題名:	a basic course using R /
作者:	Deshmukh, Shailaja.
其他作者:	Kulkarni, Madhuri.
出版者:	Singapore :Springer Singapore :2021.
面頁冊數:	xviii, 529 p. :ill., digital ;24 cm.
Contained By:	Springer Nature eBook
標題:	Mathematical statisticsAsymptotic theory.
電子資源:	https://doi.org/10.1007/978-981-15-9003-0
ISBN:	9789811590030$q(electronic bk.)

Asymptotic statistical inferencea basic course using R /
Deshmukh, Shailaja.

Asymptotic statistical inferencea basic course using R /[electronic resource] :by Shailaja Deshmukh, Madhuri Kulkarni. - Singapore :Springer Singapore :2021. - xviii, 529 p. :ill., digital ;24 cm.

Chapter 1: Introduction -- Chapter 2: Consistency of an Estimator -- Chapter 3: Consistent and Asymptotically Normal Estimators -- Chapter 4: CAN Estimators in Exponential and Cramer Families -- Chapter 5: Large Sample Test Procedures -- Chapter 6: Goodness of Fit Test and Tests for Contingency Tables -- Chapter 7: Solutions to Conceptual Exercises.

The book presents the fundamental concepts from asymptotic statistical inference theory, elaborating on some basic large sample optimality properties of estimators and some test procedures. The most desirable property of consistency of an estimator and its large sample distribution, with suitable normalization, are discussed, the focus being on the consistent and asymptotically normal (CAN) estimators. It is shown that for the probability models belonging to an exponential family and a Cramer family, the maximum likelihood estimators of the indexing parameters are CAN. The book describes some large sample test procedures, in particular, the most frequently used likelihood ratio test procedure. Various applications of the likelihood ratio test procedure are addressed, when the underlying probability model is a multinomial distribution. These include tests for the goodness of fit and tests for contingency tables. The book also discusses a score test and Wald's test, their relationship with the likelihood ratio test and Karl Pearson's chi-square test. An important finding is that, while testing any hypothesis about the parameters of a multinomial distribution, a score test statistic and Karl Pearson's chi-square test statistic are identical. Numerous illustrative examples of differing difficulty level are incorporated to clarify the concepts. For better assimilation of the notions, various exercises are included in each chapter. Solutions to almost all the exercises are given in the last chapter, to motivate students towards solving these exercises and to enable digestion of the underlying concepts. The concepts from asymptotic inference are crucial in modern statistics, but are difficult to grasp in view of their abstract nature. To overcome this difficulty, keeping up with the recent trend of using R software for statistical computations, the book uses it extensively, for illustrating the concepts, verifying the properties of estimators and carrying out various test procedures. The last section of the chapters presents R codes to reveal and visually demonstrate the hidden aspects of different concepts and procedures. Augmenting the theory with R software is a novel and a unique feature of the book. The book is designed primarily to serve as a text book for a one semester introductory course in asymptotic statistical inference, in a post-graduate program, such as Statistics, Bio-statistics or Econometrics. It will also provide sufficient background information for studying inference in stochastic processes. The book will cater to the need of a concise but clear and student-friendly book introducing, conceptually and computationally, basics of asymptotic inference.

ISBN: 9789811590030$q(electronic bk.)

Standard No.: 10.1007/978-981-15-9003-0doiSubjects--Topical Terms:

182609
Mathematical statistics
--Asymptotic theory.

LC Class. No.: QA276 / .D474 2021

Dewey Class. No.: 519.5

Asymptotic statistical inferencea basic course using R /
LDR:04072nmm a2200325 a 4500 001 602525
003 DE-He213
005 20210705151529.0
006 m d
007 cr nn 008maaau
008 211112s2021 si s 0 eng d
020 $a 9789811590030$q(electronic bk.)
020 $a 9789811590023$q(paper)
024 7 $a 10.1007/978-981-15-9003-0 $2 doi
035 $a 978-981-15-9003-0
040 $a GP $c GP
041 0 $a eng
050 4 $a QA276 $b .D474 2021
072 7 $a PBT $2 bicssc
072 7 $a MAT029000 $2 bisacsh
072 7 $a PBT $2 thema
082 0 4 $a 519.5 $2 23
090 $a QA276 $b .D456 2021
100 1 $a Deshmukh, Shailaja. $3 569185
245 1 0 $a Asymptotic statistical inference $h [electronic resource] : $b a basic course using R / $c by Shailaja Deshmukh, Madhuri Kulkarni.
260 $a Singapore : $b Springer Singapore : $b Imprint: Springer, $c 2021.
300 $a xviii, 529 p. : $b ill., digital ; $c 24 cm.
505 0 $a Chapter 1: Introduction -- Chapter 2: Consistency of an Estimator -- Chapter 3: Consistent and Asymptotically Normal Estimators -- Chapter 4: CAN Estimators in Exponential and Cramer Families -- Chapter 5: Large Sample Test Procedures -- Chapter 6: Goodness of Fit Test and Tests for Contingency Tables -- Chapter 7: Solutions to Conceptual Exercises.
520 $a The book presents the fundamental concepts from asymptotic statistical inference theory, elaborating on some basic large sample optimality properties of estimators and some test procedures. The most desirable property of consistency of an estimator and its large sample distribution, with suitable normalization, are discussed, the focus being on the consistent and asymptotically normal (CAN) estimators. It is shown that for the probability models belonging to an exponential family and a Cramer family, the maximum likelihood estimators of the indexing parameters are CAN. The book describes some large sample test procedures, in particular, the most frequently used likelihood ratio test procedure. Various applications of the likelihood ratio test procedure are addressed, when the underlying probability model is a multinomial distribution. These include tests for the goodness of fit and tests for contingency tables. The book also discusses a score test and Wald's test, their relationship with the likelihood ratio test and Karl Pearson's chi-square test. An important finding is that, while testing any hypothesis about the parameters of a multinomial distribution, a score test statistic and Karl Pearson's chi-square test statistic are identical. Numerous illustrative examples of differing difficulty level are incorporated to clarify the concepts. For better assimilation of the notions, various exercises are included in each chapter. Solutions to almost all the exercises are given in the last chapter, to motivate students towards solving these exercises and to enable digestion of the underlying concepts. The concepts from asymptotic inference are crucial in modern statistics, but are difficult to grasp in view of their abstract nature. To overcome this difficulty, keeping up with the recent trend of using R software for statistical computations, the book uses it extensively, for illustrating the concepts, verifying the properties of estimators and carrying out various test procedures. The last section of the chapters presents R codes to reveal and visually demonstrate the hidden aspects of different concepts and procedures. Augmenting the theory with R software is a novel and a unique feature of the book. The book is designed primarily to serve as a text book for a one semester introductory course in asymptotic statistical inference, in a post-graduate program, such as Statistics, Bio-statistics or Econometrics. It will also provide sufficient background information for studying inference in stochastic processes. The book will cater to the need of a concise but clear and student-friendly book introducing, conceptually and computationally, basics of asymptotic inference.
650 0 $a Mathematical statistics $x Asymptotic theory. $3 182609
650 1 4 $a Statistical Theory and Methods. $3 274054
650 2 4 $a Statistics and Computing/Statistics Programs. $3 275710
700 1 $a Kulkarni, Madhuri. $3 898240
710 2 $a SpringerLink (Online service) $3 273601
773 0 $t Springer Nature eBook
856 4 0 $u https://doi.org/10.1007/978-981-15-9003-0
950 $a Mathematics and Statistics (SpringerNature-11649)