Statistical Analysis of Random Fields
Springer (Verlag)
978-94-010-7027-0 (ISBN)
1. Elements of the Theory of Random Fields.- 1.1 Basic concepts and notation.- 1.2 Homogeneous and isotropic random fields.- 1.3 Spectral properties of higher order moments of random fields.- 1.4 Some properties of the uniform distribution.- 1.5 Variances of integrals of random fields.- 1.6 Weak dependence conditions for random fields.- 1.7 A central limit theorem.- 1.8 Moment inequalities.- 1.9 Invariance principle.- 2. Limit Theorems for Functionals of Gaussian Fields.- 2.1 Variances of integrals of local Gaussian functionals.- 2.2 Reduction conditions for strongly dependent random fields.- 2.3 Central limit theorem for non-linear transformations of Gaussian fields.- 2.4 Approximation for distribution of geometric functional of Gaussian fields.- 2.5 Reduction conditions for weighted functionals.- 2.6 Reduction conditions for functionals depending on a parameter.- 2.7 Reduction conditions for measures of excess over a moving level.- 2.8 Reduction conditions for characteristics of the excess over a radial surface.- 2.9 Multiple stochastic integrals.- 2.10 Conditions for attraction of functionals of homogeneous isotropic Gaussian fields to semi-stable processes.- 3. Estimation of Mathematical Expectation.- 3.1 Asymptotic properties of the least squares estimators for linear regression coefficients.- 3.2 Consistency of the least squares estimate under non-linear parametrization.- 3.3 Asymptotic expansion of least squares estimators.- 3.4 Asymptotic normality and convergence of moments for least squares estimators.- 3.5 Consistency of the least moduli estimators.- 3.6 Asymptotic normality of the least moduli estimators.- 4. Estimation of the Correlation Function.- 4.1 Definition of estimators.- 4.2 Consistency.- 4.3 Asymptotic normality.- 4.4 Asymptotic normality. The caseof a homogeneous isotropic field.- 4.5 Estimation by means of several independent sample functions.- 4.6 Confidence intervals.- References.- Comments.
Reihe/Serie | Mathematics and its Applications ; 28 | Mathematics and its Applications ; 28 |
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Zusatzinfo | X, 244 p. |
Verlagsort | Dordrecht |
Sprache | englisch |
Maße | 155 x 235 mm |
Themenwelt | Sachbuch/Ratgeber ► Natur / Technik ► Garten |
Mathematik / Informatik ► Mathematik ► Statistik | |
Mathematik / Informatik ► Mathematik ► Wahrscheinlichkeit / Kombinatorik | |
Naturwissenschaften ► Physik / Astronomie ► Mechanik | |
Wirtschaft ► Volkswirtschaftslehre ► Ökonometrie | |
ISBN-10 | 94-010-7027-X / 940107027X |
ISBN-13 | 978-94-010-7027-0 / 9789401070270 |
Zustand | Neuware |
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