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A New Method of Prediction for Spatial Regression Models with Correlated Errors

相关误差空间回归模型的一种新预测方法

SUMMARY This paper deals with minimum mean-squared error, unbiased linear interpolation of a continuous domain spatial process based on a sparse set of irregularly spaced observations. The process is assumed to be governed by a linear regression model with errors that follow a second-order stationary Gaussian random field. A new method of prediction is developed that is compatible with the parameter estimation procedures of Vecchia. The result is a new likelihood-based…

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Testing for periodic autocorrelations in seasonal time series data

季节性时间序列中周期自相关的检验

This paper presents statistical procedures for deciding if periodicities exist in the autocorrelation function of a seasonal time series after removal of seasonal means and standard deviations. The procedures are based on asymptotic properties of a Fourier-transformed version of the estimated periodic autocorrelation function. Analyses of simulated and actual data sets illustrate the usefulness of the proposed methods.

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Estimation and Model Identification for Continuous Spatial Processes

连续空间过程的参数估计与模型辨识

SUMMARY Formal parameter estimation and model identification procedures for continuous domain spatial processes are introduced. The processes are assumed to be adequately described by a linear model with residuals that follow a second-order stationary Gaussian random field and data are assumed to consist of noisy observations of the process at arbitrary sampling locations. A general class of two-dimensional rational spectral density functions with elliptic contours is used…

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A General Class of Models for Stationary Two-Dimensional Random Processes

平稳二维随机过程的一般模型类

A parametric family of spectral density-covariance function pairs for stationary spatial processes is introduced. The spectral densities are rational functions of elliptic forms along with factors in the numerator that may be of mixed hyperbolic, parabolic or elliptic form. The resulting covariance functions are linear combinations of modified Bessel functions of the second kind, which have been shown to be the natural basis for two-dimensional covariance functions (Whittle,…

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A general class of models for stationary two-dimensional random processes

平稳二维随机过程的一般模型类

A parametric family of spectral density-covariance function pairs for stationary spatial processes is introduced. The spectral densities are rational functions of elliptic forms along with factors in the numerator that may be of mixed hyperbolic, parabolic or elliptic form. The resulting covariance functions are linear combinations of modified Bessel functions of the second kind, which have been shown to be the natural basis for two-dimensional covariance functions (Whittle,…

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