On some techniques of selecting spline smoothing parameters for a correlated dataset with autocorrelation structure in the residual

Abstract

Residuals are minimized in a correlated dataset by selecting a smoothing parameter with optimum performance in the smoothing spline. The selection methods utilized in this study include Generalized Maximum Likelihood (GML), Generalized Cross-Validation (GCV), Unbiased Risk (UBR), and the Proposed Smoothing Method (PSM). The aim of this study is to compare the smoothing parameter selection ability of the four parameter selection methods for a correlated dataset with autocorrelation structure in the error term. To achieve this purpose, a Monte-Carlo simulation was conducted by utilizing program written in R-4.2.2. The performance of the parameter selection methods were evaluated using predictive Mean Squared Error (PMSE). Findings from the study indicated that GCV and GML were mostly affected by the presence of auto correlation in the residual and therefore had an asymptotically similar behavioural pattern. The estimators conformed to the asymptotic properties of the smoothing parameter selection methods considered; this is noticed in all the sample sizes and at all the smoothing parameters. The result also showed that; the most consistent and efficient among the four spline smoothing parameter selection methods considered in this study based on sample size and performance in the presence of autocorrelated residual error is the proposed smoothing method (PSM) because it does not undersmooth relative to the other smoothing method especially for small sample and medium sample size of 50 and 100.