Department of Statistics, University of Abuja, Abuja, Nigeria.
Research Article
World Journal of Advanced Research and Reviews, 2023, 17(02), 068-078
Article DOI: 10.30574/wjarr.2023.17.2.0216
Received on 22 December 2022; revised on 31 January 2023; accepted on 02 February 2023
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.
Autocorrelation; Generalized Maximum Likelihood; Generalized Cross-Validation; Penalized Spline; Splines Smoothing Time series; Spline regression
Preview Article PDF
Samuel Olorunfemi Adams and Mohammed Anono Zubair. On some techniques of selecting spline smoothing parameters for a correlated dataset with autocorrelation structure in the residual. World Journal of Advanced Research and Reviews, 2023, 17(2), 068-078. Article DOI: https://doi.org/10.30574/wjarr.2023.17.2.0216