<p>KIM, HYON-JUNG. Variance Estimation in Spatial Regression Using a NonparametricSemivariogram Based on Residuals. (Under the direction of Professor Dennis D. Boos.)The empirical semivariogram of residuals from a regression model withstationary errors may be used to estimate the covariance structure of the underlyingprocess.For prediction (Kriging) the bias of the semivariogram estimate induced byusing residuals instead of errors has only a minor effect because thebias is small for small lags. However, for estimating the variance of estimatedregression coefficients and of predictions,the bias due to using residuals can be quite substantial. Thus wepropose a method for reducing the bias in empirical semivariogram estimatesbased on residuals. The adjusted empirical semivariogram is then isotonizedand made positive definite and used to estimate the variance of estimatedregression coefficients in a general estimating equations setup.Simulation results for least squares and robust regression show that theproposed method works well in linear models withstationary correlated errors. Spectral Analysis with Spatial Periodogram and Data Tapers.(Under the direction of Professor Montserrat Fuentes.)The spatial periodogram is a nonparametric estimate of the spectral density, which is the Fourier Transform of the covariance function. The periodogram is a useful tool to explain the dependence structure of aspatial process.Tapering (data filtering) is an effective technique to remove the edge effects even inhigh dimensional problemsand can be applied to the spatial data in order to reduce the bias of the periodogram.However, the variance of the periodogram increases as the bias is reduced.We present a method to choose an appropriate smoothing parameter for datatapers and obtain better estimates of the spectral densityby improving the properties of the periodogram.The smoothing parameter is selected taking intoaccount the trade-off between bias and variance of the taperedperiodogram. We introduce a new asymptotic approach for spatial datacalled `shrinking asymptotics', which combines theincreasing-domain and the fixed-domain asymptotics.With this approach, the tapered spatial periodogram can be usedto determine uniquely the spectral density of the stationary process,avoiding the aliasing problem. <P>
| Identifer | oai:union.ndltd.org:NCSU/oai:NCSU:etd-20000822-235839 |
| Date | 23 August 2000 |
| Creators | Kim, Hyon-Jung |
| Contributors | Dennis D. Boos, Montserrat Fuentes, Bibhuti B. Bhattacharyya, Marcia L. Gumpertz, Jerry M. Davis |
| Publisher | NCSU |
| Source Sets | North Carolina State University |
| Language | English |
| Detected Language | English |
| Type | text |
| Format | application/pdf |
| Source | http://www.lib.ncsu.edu/theses/available/etd-20000822-235839 |
| Rights | unrestricted, I hereby certify that, if appropriate, I have obtained and attached hereto a written permission statement from the owner(s) of each third party copyrighted matter to be included in my thesis, dissertation, or project report, allowing distribution as specified below. I certify that the version I submitted is the same as that approved by my advisory committee. I hereby grant to NC State University or its agents the non-exclusive license to archive and make accessible, under the conditions specified below, my thesis, dissertation, or project report in whole or in part in all forms of media, now or hereafter known. I retain all other ownership rights to the copyright of the thesis, dissertation or project report. I also retain the right to use in future works (such as articles or books) all or part of this thesis, dissertation, or project report. |
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