Estimation of Matrix Variance-Covariance on Nonparametric Regression Spline Truncated for Longitudinal Data

• Published in: Journal of physics. Conference series Vol. 1562; no. 1; pp. 12014 - 12021
• Main Authors: Ramli, Mustain, Ratnasari, Vita, Nyoman Budiantara, I
• Format: Journal Article
• Language: English
• Published: Bristol IOP Publishing 01.06.2020
• Subjects: Covariance matrix; Cross-sections; Maximum likelihood estimates; Nonparametric statistics; Physics; Regression analysis; Regression models; Statistical analysis; Variance
• ISSN: 1742-6588; 1742-6596
• DOI: 10.1088/1742-6596/1562/1/012014

Regression analysis is a statistical analysis used to determine the pattern of relationships between predictor variables and response variables. There are two models estimation approaches in regression analysis, namely parametric regression and nonparametric regression. The parametric regression approach is used if the shape of the regression curve is known. In cases with unknown relationship patterns, the development is done using nonparametric regression. Nonparametric regression is a model estimation method which is based on an approach that is not bound by certain assumptions of the regression curve shape. One of the most commonly used nonparametric regression curve estimates is the spline approach. Spline is one of the nonparametric approaches that is often used and has a very good ability to handle data characters that are smooth as well as data whose behavior changes at certain sub-intervals. Theoretically, the spline approach is not only able to estimate nonparametric regression curves for cross section data, but can also be developed for longitudinal data. Longitudinal data is a combination of cross section data and time series data where the longitudinal data between subjects are mutually independent, but between observations are dependent. This study aims to find the estimation curves of spline truncated multivariable nonparametric regression for longitudinal data using the Weighted Least Square (WLS) method and to find the estimation of variance-covariance matrix using the Maximum Likelihood Estimate (MLE) method.