Robust Nonparametric Covariance Technique

Outlier detection and robust estimation are the integral part of data mining and has attracted much attention recently. Generally, the data contain abnormal or extreme values either due to the characteristics of the individual or due to the errors in tabulation, data entry etc. The presence of outliers may badly affect the data modeling and analysis. Analysis of semi-parametric regression with design matrix as the parameter component and covariate as the nonparametric component is considered in this paper. The regression estimate and the cross validation technique can behave very badly in the presence of outliers in the data or when the errors are heavy-tailed. The cross-validation technique to estimate the optimum smoothing parameter will also be affected badly by the presence of outliers. A robust method, which is not influenced by the presence of outliers in the data, is proposed to fit the semi-parametric regression with design matrix as the parameter component and covariate as the nonparametric component. Robust M-kernel weighted local linear regression smoother is used to fit the regression function. The cross-validation technique to estimate the optimum smoothing parameter will also be affected badly by the presence of outliers. A robust cross-validation technique is proposed to estimate the smoothing parameter. The proposed method is useful to compare the treatments after eliminating the covariate effect. The method is illustrated through simulated and field data.