On the Consistent Separation of Scale and Variance for Gaussian Random Fields
نویسنده
چکیده
We present fixed domain asymptotic results that establish consistent estimates of the variance and scale parameters for a Gaussian random field with a geometric anisotropic Matérn autocovariance in dimension d > 4. When d < 4 this is impossible due to the mutual absolute continuity of Matérn Gaussian random fields with different scale and variance (see Zhang [33]). Informally, when d > 4, we show that one can estimate the coefficient on the principle irregular term accurately enough to get a consistent estimate of the coefficient on the second irregular term. These two coefficients can then be used to separate the scale and variance. We extend our results to the general problem of estimating a variance and geometric anisotropy for more general autocovariance functions. Our results illustrate the interaction between the accuracy of estimation, the smoothness of the random field, the dimension of the observation space, and the number of increments used for estimation. As a corollary, our results establish the orthogonality of Matérn Gaussian random fields with different parameters when d > 4. The case d = 4 is still open.
منابع مشابه
On the Consistent Separation of Scale and Variance for Gaussian Random Fields by Ethan Anderes
We present fixed domain asymptotic results that establish consistent estimates of the variance and scale parameters for a Gaussian random field with a geometric anisotropic Matérn autocovariance in dimension d > 4. When d < 4 this is impossible due to the mutual absolute continuity of Matérn Gaussian random fields with different scale and variance (see Zhang [J. Amer. Statist. Assoc. 99 (2004) ...
متن کاملNumerical solution of second-order stochastic differential equations with Gaussian random parameters
In this paper, we present the numerical solution of ordinary differential equations (or SDEs), from each order especially second-order with time-varying and Gaussian random coefficients. We indicate a complete analysis for second-order equations in special case of scalar linear second-order equations (damped harmonic oscillators with additive or multiplicative noises). Making stochastic differe...
متن کاملExtremes of a Class of Non-homogeneous Gaussian Random Fields
This contribution establishes exact tail asymptotics of sup(s,t)∈E X(s, t) for a large class of non-homogeneous Gaussian random fields X on a bounded convex set E ⊂ R, with variance function that attains its maximum on a segment on E. These findings extend the classical results for homogeneous Gaussian random fields and Gaussian random fields with unique maximum point of the variance. Applicati...
متن کاملAsymptotic Behaviors of the Lorenz Curve for Left Truncated and Dependent Data
The purpose of this paper is to provide some asymptotic results for nonparametric estimator of the Lorenz curve and Lorenz process for the case in which data are assumed to be strong mixing subject to random left truncation. First, we show that nonparametric estimator of the Lorenz curve is uniformly strongly consistent for the associated Lorenz curve. Also, a strong Gaussian approximation for ...
متن کاملPredicting separation anxiety in primary school children based on mothers' personality structure and thematic relationships
The purpose of this research was to predict the separation anxiety of primary school children based on the personality structure and thematic relationships of mothers. The descriptive research method was correlation type. The statistical population included all primary school children of schools in the 2nd district of Tehran in 2019, and 384 of them were selected using available sampling. The i...
متن کامل