REGRESI NONPARAMETRIK DENGAN MENGGUNAKAN METODE ROBUST CROSS-VALIDATION; NONPARAMETRIC REGRESSION WITH ROBUST CROSS-VALIDATION METHOD

RATNA YUNIARTI, Sri Haryatmi

2014 | Disertasi | PROGRAM STUDI S2 MATEMATIKA

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.

Kata Kunci : Nonparametric regression, Estimator Nadaraya-watson, outlier, Robust, Estimasi-M, Cross-validation.