Estimate the coefficients of penalty spline regression models using the (SOP) method.
DOI:
https://doi.org/10.31272/jae.i141.1011Keywords:
basis splines, penalty splines regression, nested matrix separation (SOP) methodAbstract
Nonparametric regression analysis techniques play a central role in statistical analysis, as the penalty spline regression method is considered one of the most currently used methods for smoothing data, as functions can be estimated directly from noisy data (which contain errors) or polluted (noisy data) instead of Relying on specific parameter models. The estimation method used to fit the penalty spline regression model is mostly based on least squares (OLS) methods, which are known to be sensitive to atypical (extreme) observations. In this research, penalty spline regression models (P-spline) will be estimated. ) The generalized additive using the nested microarray separation method (SOP) proposed by the researcher (Rodríguez) and others in 2015, which takes extreme observations into account, where the estimation is based on the equivalence between (P-spline) and linear mixed models, and the parameters are estimated Variance and smoothing parameters based on the restricted maximum potential (REML) method. One of the most important conclusions reached is that there is no need to use numerical optimization methods, and the SOP method can be easily integrated into the estimation of generalized additive mixed models (GAMM) with independent random effects groups, in addition to the speed of applying the SOP method in implementing calculations .
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