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Spline Smoothing is a popular method of estimating the functions in a non-parametric regression model, its performance depends on the choice of smoothing parameter. The two most important methods for choosing the spline smoothing parameter are the Generalized Cross-Validation (GCV) and Generalized Maximum Likelihood (GML). A Monte Carlo Method using a program written in R, evaluated these two estimators to compare their performance. The Monte Carlo experiment was designed to see if the asymptotic results in the smooth case were evident in small, medium, and large sample sizes, the Mean Square error (MSE) criterion was used for the comparison. It was discovered that GML was better than GCV because it is stable and works well in all simulations and at all sample size and it does not overfit data when the sample size is small. Mathematics Subject Classification: JSEM -39-94-119

Smoothing Parameter Estimation of The Generalized CrossValidation And Generalized Maximum Likehood