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Abstract:
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Dimension reduction and variable selection play important roles in high dimensional data analysis. Envelope is a new parsimonious version of the classical multivariate regression model. However, existing Envelope methods assume independent errors in the model. Independence is a very convenient assumption but models that involve dependency are more realistic in some areas. In this paper, we combine the idea of envelope model with multivariate spatial statistics to introduce a spatial envelope model. This new approach can provide an estimate for the parameters of interest with smaller variance compare to MLE, while being able to capture the spatial structure in the data. The effectiveness of the new approach is verified through simulation studies and a real data analysis.
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