非平穩過程之建模與應用

張雅梅

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非平穩過程之建模與應用

Nonstationary Spatial Modeling and Application

張雅梅 , Ph.D　　Advisor：徐南蓉;黃信誠　　

英文

空間統計；非平穩過程； HASH(0x1cccd290) ； HASH(0x1cccd330) ； constrained least squares ； least angle regression ； positive Lasso ； spatial prediction

Abstract │ Reference (160) │ Altmetrics

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In this thesis, we develop two approaches for approximating nonstationary spatial covariance function
and predicting missing data. The first approach is proposed for handling spatial data with
multiple replications and the second is for spatial data with single replication. The first method
represents a spatial process as a linear combination of some local basis
functions with uncorrelated random coefficients plus some independent stationary processes.
The covariance function estimation problem is
formulated as a regression problem and a constrained least squared method proposed by Tibshirani
(1996) is applied for selecting appropriate basis functions and stationary processes, and
estimating parameters. The best linear unbiased prediction is then used for prediction.

The second approach is constructed on the wavelet domain. It can be applied to lattice data
with single measurement. In wavelet domain, the log variances of the
transformed data are assumed to follow the conditional autoregressive model (Besag, 1974).
Bayesian inference is implemented for estimation and prediction.
Since missing data are allowed in this approach, it can be adopted to irregularly spaced data by
mapping irregular data on a finer grid.

Both approaches are computationally efficient for handling large data sets since the
covariance matrix of either method is diagonal or nearly diagonal under a certain transformation.
Simulation experiments show that the proposed methods approximate both stationary and
nonstationary dependence structures very well. Both methods also perform well in
prediction for real applications.

Reference ( 160 ) 〈TOP〉

Besag, J. (1974). Spatial interaction and the statistical analysis of lattice systems (with discussions).Journal of the Royal Statistical Society, Series B, 36, 192-236.
連結：
Besag, J. and Kooperberg, C. (1995). On condition and intrinsic autoregressions. Biometrika, 82, 733-746.
連結：
Besag, J., York, J. and Mollie, A. (1991). Bayesian image restoration, with two applications in spatial statistics. Annals of the Institute of Statistical Mathematics, 43,1-20.
連結：
Burgees, T. M. and Webster, R. (1980). Optimal interpolation and isarithmic mapping of soil
連結：
Cerioli, A. and Riani, M. (2003). Robust methods for the analysis of spatially autocorrelated
連結：

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