Statistical Analysis of Random Fields

Ivanov, A. V.; Leonenko, Nikolai

doi:10.1007/978-94-009-1183-3

Cited by 197 publications

(235 citation statements)

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“…The case of a Gaussian random field with non-integrable covariance function was considered by Ivanov and Leonenko in [7]. It is interesting to note that the central limit theorem they obtained features the sequence {u n , n ∈ N} growing rapidly enough for Var S n to converge to 0 as n → ∞.…”

Section: Gaussian Random Fieldsmentioning

confidence: 99%

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A Central Limit Theorem for the Volumes of High Excursions of Stationary Associated Random Fields

Demichev

Olszewski

2015

Stat., optim. inf. comput.

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Section: Gaussian Random Fieldsmentioning

confidence: 99%

“…Note that a similar model was studied in the monograph of Ivanov and Leonenko [7] for the case of a Gaussian random field. For associated random fields on lattices the asymptotic behaviour of excursion sets cardinalities corresponding to a growing excursion level was examined in [8].…”

Section: Introductionmentioning

confidence: 98%

A Central Limit Theorem for the Volumes of High Excursions of Stationary Associated Random Fields

Demichev

Olszewski

2015

Stat., optim. inf. comput.

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“…The correlation function (4) is widely used in statistical applications (see, for example, [9,10]). Properties of stochastic processes with the correlation function (5) are studied in [11].…”

Section: (5)mentioning

confidence: 99%

“…When proving the consistency of the estimator θ T (see the theorem below) we face the problem of studying the behavior as T → ∞ of the ratios (9) sin…”

Section: We Arrange the Frequenciesmentioning

confidence: 99%

Consistency of the least squares estimator of the amplitudes and angular frequencies of a sum of harmonic oscillations in models with long-range dependence

Ivanov¹

2010

Theor. Probability and Math. Statist.

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Abstract. The strong consistency of least squares estimators of unknown amplitudes and angular frequencies of the sum of harmonic oscillations observed in a strongly dependent Gaussian stationary noise is proved in the paper. Let a stochastic process(1)be observed, where, is a stochastic process defined on a complete probability space (Ω, , P) and satisfying the following condition.A1. ε(t), t ∈ R 1 , is a real, measurable, mean square continuous, stationary, Gaussian, zero-mean stochastic process. We also assume that at least one of the following two conditions holds. A2. The correlation function of the process ε(t), t ∈ R1 , is such thatwhere L(t) is a function slowly varying at infinity and B(0) = 1. A3.The statistical estimation of unknown amplitudes and angular frequencies (3) of a sum of harmonic oscillations (2) observed in a random noise ε(t) is a probabilistic setting of the problem of detection of hidden periodicities. Investigations of this problem as well as of its deterministic counterpart (ε(t) ≡ 0) are initiated by Lagrange. Many applications of this problem in numerous scientific fields are also known (see [1]).2000 Mathematics Subject Classification. Primary 62J02; Secondary 62J99. Key words and phrases. The detection of hidden periodicities, least squares estimator, consistency, long range dependence.

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“…Asymptotic properties of least squares estimators and least modules estimators of parameters of nonlinear regression models are studied by many authors. We only mention the monographs by Ivanov and Leonenko [9] and Ivanov [23], where a rather complete bibliography concerning this question can be found.…”

Section: Introductionmentioning

confidence: 99%

Asymptotic normality of $L_p$-estimators in nonlinear regression models with weak dependence

Ivanov

Orlovskii

2009

Theor. Probability and Math. Statist.

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Statistical Analysis of Random Fields

Cited by 197 publications

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A Central Limit Theorem for the Volumes of High Excursions of Stationary Associated Random Fields

A Central Limit Theorem for the Volumes of High Excursions of Stationary Associated Random Fields

Consistency of the least squares estimator of the amplitudes and angular frequencies of a sum of harmonic oscillations in models with long-range dependence

Asymptotic normality of $L_p$-estimators in nonlinear regression models with weak dependence

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