Dynamics of statistical experiments / Dmitri Koroliouk.

Format:

Book

Author/Creator:

Koroliouk, Dmitri.

Contributor:

Wiley InterScience (Online service)

Dr. D. Sergeant Pepper Memorial Fund.

Series:

Oregon State monographs. Mathematics and statistics series

MATHEMATICS AND STATISTICS SERIES.

Language:

English

Subjects (All):

Mathematical statistics.

Physical Description:

1 online resource (229 pages).

Place of Publication:

London : ISTE, Ltd. ; Hoboken : Wiley, 2020.

System Details:

text file

Contents:

Cover

Half-Title Page

Title Page

Copyright Page

Contents

Preface

List of Abbreviations

Introduction

1. Statistical Experiments

1.1. Statistical experiments with linear regression

1.1.1. Basic definitions

1.1.2. Difference evolution equations

1.1.3. The equilibrium state

1.1.4. Stochastic difference equations

1.1.5. Convergence to the equilibrium state

1.1.6. Normal approximation of the stochastic component

1.2. Binary SEs with nonlinear regression

1.2.1. Basic assumptions

1.2.2. Equilibrium

1.2.3. Stochastic difference equations

1.2.4. Convergence to the equilibrium state

1.2.5. Normal approximation of the stochastic component

1.3. Multivariate statistical experiments

1.3.1. Regression function of increments

1.3.2. The equilibrium state of multivariate EPs

1.3.3. Stochastic difference equations

1.3.4. Convergence to the equilibrium state

1.3.5. Normal approximation of the stochastic component

1.4. SEs with Wright-Fisher normalization

1.4.1. Binary RFs

1.4.2. Multivariate RFIs

1.5. Exponential statistical experiments

1.5.1. Binary ESEs

1.5.2. Steady regime of ESEs

1.5.3. Approximation of ESEs by geometric Brownian motion

2. Diffusion Approximation of Statistical Experiments in Discrete-Continuous Time

2.1. Binary DMPs

2.1.1. DMPs in discrete-continuous time

2.1.2. Justification of diffusion approximation

2.2. Multivariate DMPs in discrete-continuous time

2.2.1. Evolutionary DMPs in discrete-continuous time

2.2.2. SDEs for the DMP in discrete-continuous time

2.2.3. Diffusion approximation of DMPs in discrete-continuous time

2.3. A DMP in an MRE

2.3.1. Discrete and continuous MRE

2.3.2. Proof of limit theorems 2.3.1 and 2.3.2

2.4. The DMPs in a balanced MRE

2.4.1. Basic assumptions

2.4.2. Proof of limit theorem 2.4.1

2.5. Adapted SEs

2.5.1. Bernoulli approximation of the SE stochastic component

2.5.2. Adapted SEs

2.5.3. Adapted SEs in a series scheme

2.6. DMPs in an asymptotical diffusion environment

2.6.1. Asymptotic diffusion perturbation

2.7. A DMP with ASD

2.7.1. Asymptotically small diffusion

2.7.2. EGs of DMP

2.7.3. AF of DMPs

3. Statistics of Statistical Experiments

3.1. Parameter estimation of one-dimensional stationary SEs

3.1.1. Stationarity

3.1.2. Covariance statistics

3.1.3. A priori statistics

3.1.4. Optimal estimating function

3.1.5. Stationary Gaussian SEs

3.2. Parameter estimators for multivariate stationary SEs

3.2.1. Vector difference SDEs and stationarity conditions

3.2.2. Optimal estimating function

3.2.3. Stationary Gaussian Markov SEs

3.3. Estimates of continuous process parameters

3.3.1. Diffusion-type processes

3.3.2. Estimation of a continuous parameter

3.4. Classification of EPs

3.4.1. Basic assumption

3.4.2. Classification of EPs

Notes:

Electronic reproduction. Hoboken, N.J. Available via World Wide Web.

Print version record.

3.4.3. Justification of EP models classification

Includes bibliographical references and index.

Local Notes:

Acquired for the Penn Libraries with assistance from the Dr. D. Sergeant Pepper Memorial Fund.

Other Format:

Print version: Koroliouk, Dmitri. Dynamics of Statistical Experiments.

ISBN:

9781119720461

111972046X

9781119720447

1119720443

Publisher Number:

99986444056

Access Restriction:

Restricted for use by site license.