%40تخفیف

HILBERTIAN SPATIAL PERIODICALLY CORRELATED PROCESSES

Name: HILBERTIAN SPATIAL PERIODICALLY CORRELATED PROCESSES
SKU: 14873
Price: 210000 IRR
Availability: InStock

تعداد62 صفحه در فایل word

Ph.D. DISSERTATION IN

MATHEMATICAL STATISTICS

HILBERTIAN SPATIAL PERIODICALLY

CORRELATED PROCESSES

This thesis includes three parts‎. ‎In the first part, ‎we consider Hilbertian spatial periodically‎ ‎correlated autoregressive models‎. ‎Our studies on these models include model‎ ‎building‎, ‎existence‎, ‎time domain moving average representation‎, ‎least square parameter estimation and prediction based on the‎ ‎autoregressive structured past data‎. ‎We also fit a model of this‎ ‎type to a real data of invisible infrared satellite images‎.

‎In the second part, ‎ Hilbertian spatial periodically‎ ‎correlated models will be studied in spectral domain‎. ‎The harmonizability of this process will be discussed‎ and the spectral distribution operator will be characterized‎. ‎Evolutionary random spectra on Hilbert spaces‎ ‎ will be introduced and a space-dependent spectral density for a periodically correlated random field will be given‎.‎ ‎‎

The third part, concerns Hilbertian spatial stationary autoregressive of order p models‎. We established some sufficient conditions to obtain causality and moving average representation. The model coefficients are estimated using a method of least square error. A simulation study is carried out to investigate the mean square error of derived estimators.

دسته: زبان خارجه, زبان خارجه برچسب: HILBERTIAN SPATIAL PERIODICALLY CORRELATED PROCESSES

توضیحات

Content						Page
List of Figures						……………….………………………….…………….…			viii
Chapter 1: Introduction……….…………………….…………………….….									2
	1.1	Aims………………………………….………………….……….…..							2
	1.2	Preliminaries …………………………………….……………….…..							3
		1.2.1		Notations…………………………………….……………….					3
		1.2.2		H-valued Random Variables……….…………………….…..					4
		1.2.3		Expectation……….…………………….…………………….					4
		1.2.4		Covariance and Cross-covariance Operators………….……..					5
		1.2.5		Functional Principal Component Analysis…………….……..					6
	1.3	H-valued Random Fields…….………………….……..……….…….							7
		1.3.1		Hilbertian Stationary Spatial Processes……….……………..					7
		1.3.2		Hilbertian Periodically Correlated Spatial Processes………..					8
		1.3.3		Hilbertian Spatial Autoregressive Processes…………….…..					9
				1.3.3.1			Hilbertian Spatial Stationary Autoregressive Processes……………..……….……………………		9
				1.3.3.2			Hilbertian Spatial Periodically Correlated Autoregressive Processes…..……….………………		11
	1.4	Literature Review….………………….……….……………….…….							11
	1.5	Thesis Summary and Future Work ………………………………….							12
Chapter 2: Hilbertian Spatial Periodically Correlated Autoregressive Models……….…………………….…………………….………..									15
	2.1	Introduction……….…………………….…………………….……..							15
	2.2	Preliminaries……….…………………….….………………….……							16
	2.3	Stationary Representation of HSPC Models…………….……………							17
	2.4	Parameters Estimation……….………………………….……………							25
	2.5	Simulation Study……….……………………………….……………							28
	2.6	Real-Data example……….……………………….…….……………							32
	2.7	Discussion……….…………………..………………….……………							34
Chapter 3‎: Spectral Theory of Hilbertian Spatial Periodically Correlated Processes……….…….……….…………………….……………									38
	3.1	Introduction……….……………………….…………………….……							38
	3.2	Preliminary Definitions……….……..………………….……………							39
	3.3	Harmonizability of HSPC Process……….…………………….…….							41
	3.4	Spectral Distribution Operator……….…………………….…………							48
	3.5	Evolutionary Random Spectra……….…………………….…………							52
Chapter 4‎: Hilbertian Spatial Stationary Autoregressive‎ ‎Models of Order p									60
	4.1	Introduction……….…………………….…………………….……..							60
	4.2	Preliminaries and Notations……….…………………….……………							62
	4.3	Moving Average Representation of HSS-AR(p) Processes……….…							63
	4.4	Parameter Estimation of HSS-AR(p) Processes……….………….…							66
	4.5	Simulation Study……….…………………….………………………							67
Appendix A: Hilbert Spaces and Operators……….…………………….….									75
	A.1		Metric Spaces……….…………………….…………………….…..						75
	A.2		Vector Spaces……….…………………….…………………………						76
			A.2.1		Normed Spaces……….…………………….………………				77
					A.2.1.1			Inner Product Spaces……….……………………	78
			A.2.2		Orthonormal Sets……….…………………….……………				79
			A.2.3		Direct Sum of Hilbert Spaces……….………………………				80
			A.2.4		Operators……….…………………….………………….…				81
					A.2.4.1			Isomorphism and Isometry……….……………..	82
					A.2.4.2			Adjoint, Self-adjoint and Positive Operators……	83
					A.2.4.3			Unitary Operators……….………………………	83
					A.2.4.4			Hilbert-Schmidt Operators……….……………..	83
					A.2.4.5			Trace Class Operators……….…………..………	84
					A.2.4.6			Convergence of sequences of operators…………	85
					A.2.4.7			Close Graph Theorem…..………….……………	86
			A.2.5		Bounded Linear Functionals. ……….……………..………				86
			A.2.6		Measures on Hilbert Spaces……….…………….…………				87
					A.2.6.1			Vector-valued Measures…….……..……………	87
					A.2.6.2			Spectral Measures……………………………….	87
			A.2.7		Measurability……….………………………………………				89
			A.2.8		Integration on Hilbert Spaces……….………………………				89
	A.3		Fourier Transforms and Kernels……….……………………………						90
References……….…………………….…………………….………………									94

HILBERTIAN SPATIAL PERIODICALLY CORRELATED PROCESSES

تعداد62 صفحه در فایل word

Ph.D. DISSERTATION IN

MATHEMATICAL STATISTICS

HILBERTIAN SPATIAL PERIODICALLY

CORRELATED PROCESSES

Table of Contents

Content

Page

List of Figures

……………….………………………….…………….…

viii

Chapter 1: Introduction……….…………………….…………………….….

2

1.1

Aims………………………………….………………….……….…..

2

1.2

Preliminaries …………………………………….……………….…..

3

1.2.1

Notations…………………………………….……………….

3

1.2.2

H-valued Random Variables……….…………………….…..

4

1.2.3

Expectation……….…………………….…………………….

4

1.2.4

Covariance and Cross-covariance Operators………….……..

5

1.2.5

Functional Principal Component Analysis…………….……..

6

1.3

H-valued Random Fields…….………………….……..……….…….

7

1.3.1

Hilbertian Stationary Spatial Processes……….……………..

7

1.3.2

Hilbertian Periodically Correlated Spatial Processes………..

8

1.3.3

Hilbertian Spatial Autoregressive Processes…………….…..

9

1.3.3.1

Hilbertian Spatial Stationary Autoregressive Processes……………..……….……………………

9

1.3.3.2

Hilbertian Spatial Periodically Correlated Autoregressive Processes…..……….………………

11

1.4

Literature Review….………………….……….……………….…….

11

1.5

Thesis Summary and Future Work ………………………………….

12

Chapter 2: Hilbertian Spatial Periodically Correlated Autoregressive Models……….…………………….…………………….………..

15

2.1

Introduction……….…………………….…………………….……..

15

2.2

Preliminaries……….…………………….….………………….……

16

2.3

Stationary Representation of HSPC Models…………….……………

17

2.4

Parameters Estimation……….………………………….……………

25

2.5

Simulation Study……….……………………………….……………

28

2.6

Real-Data example……….……………………….…….……………

32

2.7