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AuthorIvanov, A. V. author
TitleStatistical Analysis of Random Fields [electronic resource] / by A. V. Ivanov, N. N. Leonenko
ImprintDordrecht : Springer Netherlands, 1989
Connect tohttp://dx.doi.org/10.1007/978-94-009-1183-3
Descript X, 244 p. online resource

CONTENT

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 case of a homogeneous isotropic field -- 4.5 Estimation by means of several independent sample functions -- 4.6 Confidence intervals -- References -- Comments


Mathematics Probabilities Mechanics Statistics Mathematics Probability Theory and Stochastic Processes Statistics for Business/Economics/Mathematical Finance/Insurance Mechanics



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