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Abstract:
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Local linear regression by mixture is an alternative nonparametric regression method. The idea of our method is to assume that the data comes from the multivariate normal mixture model (Note any density can be well approximately by normal mixture). Then in each component, condition on the predictors, the regression function is a linear function of the predictors. Without knowing the components label, the regression function is a weighted linear function of the predictors. We also compared this new method with local linear regression method using simulation. The new method is slightly better than local linear, especially in the boundary. For longitudinal data, we have tried several methods to incorporate the correlation structure to our new method. In the simulation study, we found our new method is at least as well as the widely used kernel GEEs method (Lin and Carrol 2000, 2001).
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