In this thesis we study the problem of estimation of parametric covariance and variogram functions for spatial and spatio- temporal random processes. It has the following principal parts. Variogram Estimation: We consider the "weighted" least squares criterion of fitting a parametric variogram function to second order stationary geo-statistical processes. Two new weight functions are investigated as alternative to the commonly used weight function proposed by Cressie (1985). We discuss asymptotic convergence properties of the sample variogram estimator and estimators of unknown parameters of parametric variogram functions, under a "mixed increasing domain" sampling design as proposed by Lahiriet al. While empirical results of Mean Square Errors, for parameter estimation, obtained using both the proposed functions are found to be comparatively better, we also theoretically establish that under general conditions one of the proposed weight functions give estimates with better asymptotic effciency. Spatio-Temporal Covariance Estimation: Over the past decade, there have been some important advances in methods for constructing valid spatiotemporal covariance functions; but not much attention has been given - so far - on methods of parameter estimation. In this thesis we propose a new frequency domain approach to estimating parameters of spatio-temporal covariance functions. We derive asymptotic strong consistency properties of the estimators using the concept of stochastic equicontinuity. The theory is illustrated with a simulation. Non-Linearity of Geostatistical Data: Linear prediction theory for spatial data is well established and substantial literature is available on the subject. Relatively less is known about non-linearity. In our final and ongoing, research problem we propose a non-linear predictor for geostatistical data. We demonstrate that the predictor is a function of higher order moments. This leads us to construct spatial bispectra for parametric third order moments.
| Identifer | oai:union.ndltd.org:bl.uk/oai:ethos.bl.uk:542750 |
| Date | January 2011 |
| Creators | Das, Sourav |
| Contributors | Boshnakov, Georgi |
| Publisher | University of Manchester |
| Source Sets | Ethos UK |
| Detected Language | English |
| Type | Electronic Thesis or Dissertation |
| Source | https://www.research.manchester.ac.uk/portal/en/theses/statistical-estimation-ofvariogram-and-covarianceparameters-of-spatial-andspatiotemporal-randomproceses(0b296a39-a6c4-4e72-8d13-6c6e0862111d).html |
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