| Summary: | Regression analysis is a statistical tool that is widely used to determine the
relationship between a pair of variables or more. If the formulation relationship between
the predictor variablesX and Y the response variable is not known,estimation
of the regression function m(:) can use a nonparametric approach. In nonprametric
regression approach, generally just assumed regression function contained in a
function space of infinite dimension. One approach, known in the nonparametric
regression is the kernel regression. Nadaraya-Watson regression estimator is a kernel
that can be used to estimating the regression function m(:). However, when the
data are outliers estimators Nadaraya-Watson produces a large MSE. The influence
of such outliers is causing large residuals of the model is formed, and the variance
the data becomes larger. Therefore, we need a method to cope with outliers.
One method that can overcome the outliers is a robust method. Huber introduced
estimator-M, the idea that a robust estimator against outliers. In addition, also required
a method to estimate the error prediction error a model, it is cross-validation
method. Cross validation is a methods that can be used to obtain the best regression
curve models. Cross-validation can estimate the prediction error of a model and
also compare existing models and then selected models which has a lower prediction
error.
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