CURVE ESTIMATION AND ESTIMATOR PROPERTIES OF THE NONPARAMETRIC REGRESSION TRUNCATED SPLINE WITH A MATRIX APPROACH

Abstract

Regression analysis is one of the statistical analyses used to estimate the relationship between the predictor and the response variable. Data are given in pairs, and the relationship between the predictor and the response variable was assumed to follow a nonparametric regression model. This model is flexible in estimating the curve when a typical data pattern does not follow a specific pattern. The nonparametric regression curve was approached by using the truncated spline function with several knots. The truncated spline estimator in nonparametric regression is linear in the observation. It is highly dependent on the knot points. The regression model's random error is assumed to have an independent normal distribution with zero mean and equal variance. The truncated spline's curve estimate was obtained by minimizing the error model through the least squared optimization method. The nonparametric regression truncated spline's estimator properties are linear, unbiased, and if the error is normally distributed, the estimator is normally distributed.