Nonparametric Regression with Correlated Errors
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Date
2007-02
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Abstract
Linear smoothing is a popular technique in estimating the mean function in a nonparametric regression model y=m(x)+s, where m(x) is a smooth function and e is an iid error with mean zero. The linear smoothing technique is extended to accommodate a correlated error process. The cross-validation criterion for choosing the optimum bandwidth performs very badly when the errors are correlated. A method is proposed to estimate the error covariance function based on the residuals from a linear regression smoother. Using the estimated covariance function, the regression model is transformed to produce uncorrelated transformed errors. The nonparametric regression function estimate is obtained by using the linear smoothing technique on the transformed model. The method is illustrated through simulation studies.
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Keywords
Bandwidth selection, correlated errors, covariance function, cross-validation, nonparametric regression
Citation
53rd Annual Conference of Indian Society of Agricultural Statistics, Tiruchirappalli (2 - 4 Dec, 1999)