Regression analysis is a statistical strategy for establishing relationships between explanatory and response factors in order to estimate response variables given explanatory variables. However, the regression analysis may not always be based on the assumption of two variables. To get over this issue, the non-parametric regression approach is suggested. In the case of non-linear connection data, the estimated parameters create the smoothing curve using the data, also known as the smoothing technique. Six non-parametric regression techniques for sequence data are the subject of this study, which compares their effectiveness. These techniques include kernel smoothing, smoothing spline, natural cubic spline, B-spline, penalised spline, and trend filtering. The non-parametric regression technique’s effectiveness is gauged by its lowest average mean squared error. By applying the cross-validation approach and specifying the number of knots for fitting the curve on the closest data, the smoothing parameter is utilised to adjust the smoothing performance of the curves. When the explanatory variable is described as sequence data, the response variable’s characteristics are mimicked in trend, non-linear, and cycle data. The R software runs each scenario 500 times while using sample sizes of 50, 100, 150, and 200, with 1, 3, and 5 standard deviations of error. According to the findings, the natural cubic spline approach consistently had the lowest average mean squared error. The cycle data exhibited the lowest mean squared error across all sample sizes when the data character was taken into account.
Department of Statistics, School of Science, King Mongkut’s Institute of Technology Ladkrabang, Bangkok 10520, Thailand.
Please see the link here: https://stm.bookpi.org/NRAMCS-V6/article/view/7763
Keywords: B-spline, kernel smoothing, natural cubic spline, penalized spline, smoothing spline, trend filtering