現實中，高斯隨機過程常被當作空間資料背後之模型假設。過去為了方便估計，我們通常對於模型有較強的假設，例如: 期望值為零或是觀測資料間相互獨立，但這些假設並不一定符合實際情況。本文中，我們考慮資料服從一般高斯隨機過程，並提出一個二階段配適演算法估計該隨機過程的期望值結構和相關性。

The Gaussian stochastic processes are widely used in practice as models for spatial data. In the past, we usually have strong assumptions about the model to facilitate the estimation, for example, the mean is zero or the observations are independent of each other. However, these assumptions may not satisfy the realistic. In this paper, we consider a general Gaussian stochastic process of the data and develop a two-stage approximation to estimate the mean structure and the correlation dependence.

1 Introduction 1
2 Main Problem 3
2.1 Non-parametric Approximation 3
2.2 Lasso and Group Lasso penalty 6
2.3 Fixed Rank Kriging 8
2.4 Algorithm 10
3 Tests for Varying Assumption 13
4 Simulation Study and Real Data Analysis 15
4.1 Simulation 15
4.2 Real data analysis 25
5 Conclusion 29
References 31

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