Local Whittle estimator for anisotropic random fields

Abstract

a b s t r a c tA local Whittle estimator is developed to simultaneously estimate the long memory parameters for stationary anisotropic scalar random fields. It is shown that these estimators are consistent and asymptotically normal, under some weak technical conditions. A brief simulation study illustrates a practical application of the estimator.

On a class of minimum contrast estimators for Gegenbauer random fields

“…A burgeoning literature on spatio-temporal estimation has emerged in recent decades (see Beran et al (2009), Chan andTsai (2012), Giraitis et al (2001), Guo et al (2009), Li and McLeod (1986), Reisen et al (2006), among others). One of the most popular estimation tools applied was the maximum likelihood estimation method (MLE).…”

“…Leonenko and Sakhno (2006) gave a continuous version of the Whittle contrast functional supplied with a specific weight function for the estimation of continuous-parameter stochastic processes, deriving the consistency and asymptotic normality of such estimators. Guo et al (2009) demonstrated that the Whittle maximum likelihood estimator is consistent and asymptotically normal for stationary seasonal autoregressive fractionally integrated movingaverage (SARFIMA) processes.…”

Asymptotic properties of parameter estimates for random fields with tapered data

“…For instance, [43] applied the minimum contrast parameter estimation to approximate the drift parameter of the Ornstein-Uhlenbeck process, when the corresponding stochastic differential equation is driven by the fractional Brownian motion. Consistency and asymptotic normality of the Whittle maximum likelihood estimator for stationary seasonal autoregressive fractionally integrated moving-average (SARFIMA) processes was proved in [26]. Maximization of the Whittle likelihood has also been considered in the papers [17,16,32].…”

A goodness-of-fit test for marginal distribution of linear random fields with long memory

“…The other papers that discuss the estimation of the long memory intensity d for some fully observable random field models include Boissy et al (2005), Leonenko and Sakhno (2006), Frias et al (2008), and Guo et al (2009). However, most of these results do not apply to the model in (1.1) -(1.2).…”