Mathematics and Its Applications

By: A. V. Ivanov, Alexander V. Ivanov

Write A Review

Hardcover | 30 November 1996

At a Glance

Hardcover
340 Pages

Dimensions(cm)
25.4 x 17.15 x 2.54

Hardcover

$169.75

or 4 interest-free payments of $42.44 with

or

Ships in 5 to 7 business days

Let us assume that an observation Xi is a random variable (r.v.) with values in 1 1 (1R1 , 8 ) and distribution Pi (1R1 is the real line, and 8 is the cr-algebra of its Borel subsets). Let us also assume that the unknown distribution Pi belongs to a 1 certain parametric family {Pi() , () E e}. We call the triple £i = {1R1 , 8 , Pi(), () E e} a statistical experiment generated by the observation Xi. n We shall say that a statistical experiment £n = {lRn, 8 , P; ,() E e} is the product of the statistical experiments £i, i = 1, ... ,n if PO' = P () X ... X P () (IRn 1 n n is the n-dimensional Euclidean space, and 8 is the cr-algebra of its Borel subsets). In this manner the experiment £n is generated by n independent observations X = (X1, ... ,Xn). In this book we study the statistical experiments £n generated by observations of the form j = 1, ... ,n. (0.1) Xj = g(j, (}) + cj, c c In (0.1) g(j, (}) is a non-random function defined on e , where e is the closure in IRq of the open set e ~ IRq, and C j are independent r. v .-s with common distribution function (dJ.) P not depending on ().

Shipping

	Standard Shipping	Express Shipping
Metro postcodes:	$9.99	$14.95
Regional postcodes:	$9.99	$14.95
Rural postcodes:	$9.99	$14.95

Orders over $89.00 qualify for free shipping.

How to return your order

At Booktopia, we offer hassle-free returns in accordance with our returns policy. If you wish to return an item, please get in touch with Booktopia Customer Care.

Additional postage charges may be applicable.

Defective items

If there is a problem with any of the items received for your order then the Booktopia Customer Care team is ready to assist you.

For more info please visit our Help Centre.

More in Cybernetics & Systems Theory

The Laws of Thought

The Quest for a Mathematical Theory of the Mind

Paperback

RRP $34.99

$28.75

18%
OFF

Psycho-Cybernetics 365

Thrive and Grow Every Day of the Year

Paperback

RRP $34.99

$28.75

18%
OFF

Psycho-Cybernetics (Updated and Expanded)

Psycho-cybernetics

Paperback

RRP $26.99

$22.99

15%
OFF

Thinking in Systems

A Primer

Paperback

RRP $55.00

$30.75

44%
OFF

Handbook of Intelligent Robots : Theory, Methods and Applications - Humberto Sossa-Azuela

$110.75

17%
OFF

Handbook of Systems Thinking Methods

Paperback

RRP $105.00

$88.75

15%
OFF

Data and Model Centric Artificial Intelligence for Industry 5.0

Hardcover

RRP $315.00

$271.99

14%
OFF

Intelligent Manufacturing Systems

Digitalization of Industrial Production

Hardcover

RRP $315.00

$271.99

14%
OFF

Introduction	p. 1
Consistency	p. 5
Introductory Remarks	p. 5
Large Deviations of the Least Squares Estimator in the Case of Errors Having an Exponential Moment	p. 9
Large Deviations of the Least Squares Estimator in the Case of Errors with a Moment of Finite Order	p. 25
The Differentiability of Regression Functions and the Consistency of the Least Squares Estimator	p. 45
Strong Consistency	p. 58
Taking the Logarithm of Non-Linear Models	p. 73
Approximation by a Normal Distribution	p. 79
Stochastic Asymptotic Expansion of Least Squares Estimators	p. 79
Asymptotic Normality of Least Squares Estimators: First Results	p. 92
Asymptotic Normality of Least Moduli Estimators	p. 108
Asymptotic Expansion of the Distribution of Least Squares Estimators	p. 119
Calculation of First Polynomials of an Asymptotic Expansion of the Distribution of a Least Squares Estimator	p. 144
Asymptotic Expansions Related to the Least Squares Estimator	p. 155
Asymptotic Expansion of Least Squares Estimator Moments	p. 155
Asymptotic Expansions Related to the Estimator of the Variance of Errors of Observation	p. 168
Asymptotic Expansion of the Distribution of the Variance Estimator of Observational Error in Gaussian Regression	p. 188
Jack Knife and Cross-Validation Methods of Estimation of the Variance of Errors of Observation	p. 196
Asymptotic Expansions of Distributions of Quadratic Functionals of the Least Squares Estimator	p. 207
Comparison of Powers of a Class of Tests of Hypotheses on a Non-Linear Regression Parameter	p. 229
Geometric Properties of Asymptotic Expansions	p. 251
Certain Aspects of the Differential Geometry of Models of Non-Linear Regression	p. 251
The Geometric Interpretation of Asymptotic Expansions	p. 276
Subsidiary Facts	p. 289
List of Principal Notations	p. 298
Commentary	p. 303
Bibliography	p. 309
Index	p. 325
Table of Contents provided by Blackwell. All Rights Reserved.

Mathematics and Its Applications

At a Glance

Hardcover

Shipping

How to return your order

Defective items

You Can Find This Book In

More in Cybernetics & Systems Theory

The Laws of Thought

The Quest for a Mathematical Theory of the Mind

Psycho-Cybernetics 365

Thrive and Grow Every Day of the Year

Psycho-Cybernetics (Updated and Expanded)

Psycho-cybernetics

Thinking in Systems

A Primer

Handbook of Intelligent Robots

Theory, Methods and Applications

An Introduction to Systems Biology

Design Principles of Biological Circuits

Handbook of Systems Thinking Methods

Data and Model Centric Artificial Intelligence for Industry 5.0

Intelligent Manufacturing Systems

Digitalization of Industrial Production

Leveraging Computer Vision to Biometric Applications

Chapman & Hall/Distributed Computing and Intelligent Data Analytics Series

Advanced Techniques and Applications of Cybersecurity and Forensics

Emerging Technologies

Computational Intelligence Applications in Cyber Security

The Law of Complex Earth and Outer Space Systems

The Cosmolegal Proposal

Multimodal Biometric Identification System

Case Study of Real-Time Implementation

Nature Inspired Robotics

Markov Decision Processes and Reinforcement Learning

Fundamentals of Polar, LDPC and Turbo Codes

Including MATLAB , Mathcad and Python Simulations with Desktop Video Lectures

Proper Time and Mass as Dynamical Variables

Why it's Possible and Some Consequences

Handbook of Dynamic Data Driven Applications Systems

Volume 3

Smart Systems and Wireless Communication

Proceedings of SSWC 2025

Complexity in Universal Evolution

A Big History Perspective

Complex Systems and Their Applications

Sixth International Conference (EDIESCA 2025)

Integrable Peakon Systems

Applied Mathematical Sciences

Digital Twins for Distributed IoT Applications

Synthesis Lectures on Engineering, Science, and Technology

This product is categorised by