scholarly journals Direct Determination of Smoothing Parameter for Penalized Spline Regression

2014 ◽  
Vol 2014 ◽  
pp. 1-11
Author(s):  
Takuma Yoshida
Keyword(s):  
Goodness Of Fit ◽  
Direct Determination ◽  
Smoothing Parameter ◽  
Additive Models ◽  
Penalized Splines ◽  
Smoothing Methods ◽  
Penalized Spline ◽  
Smoothing Parameter Selection ◽  
Penalized Spline Regression

Penalized spline estimator is one of the useful smoothing methods. To construct the estimator, having goodness of fit and smoothness, the smoothing parameter should be appropriately selected. The purpose of this paper is to select the smoothing parameter using the asymptotic property of the penalized splines. The new smoothing parameter selection method is established in the context of minimization asymptotic form of MISE of the penalized splines. The mathematical and the numerical properties of the proposed method are studied. First we organize the new method in univariate regression model. Next we extend to the additive models. A simulation study to confirm the efficiency of the proposed method is addressed.

scholarly journals Robust fitting for generalized additive models for location, scale and shape

2021 ◽  
Vol 31 (1) ◽  
Author(s):  
William H. Aeberhard ◽  
Eva Cantoni ◽  
Giampiero Marra ◽  
Rosalba Radice
Keyword(s):  
Generalized Additive Models ◽  
Nonlinear Effects ◽  
Smoothing Splines ◽  
Parameter Selection ◽  
Information Criteria ◽  
Smoothing Parameter ◽  
Additive Models ◽  
Robust Estimators ◽  
Smoothing Parameter Selection ◽  
Smoothing Parameters

AbstractThe validity of estimation and smoothing parameter selection for the wide class of generalized additive models for location, scale and shape (GAMLSS) relies on the correct specification of a likelihood function. Deviations from such assumption are known to mislead any likelihood-based inference and can hinder penalization schemes meant to ensure some degree of smoothness for nonlinear effects. We propose a general approach to achieve robustness in fitting GAMLSSs by limiting the contribution of observations with low log-likelihood values. Robust selection of the smoothing parameters can be carried out either by minimizing information criteria that naturally arise from the robustified likelihood or via an extended Fellner–Schall method. The latter allows for automatic smoothing parameter selection and is particularly advantageous in applications with multiple smoothing parameters. We also address the challenge of tuning robust estimators for models with nonlinear effects by proposing a novel median downweighting proportion criterion. This enables a fair comparison with existing robust estimators for the special case of generalized additive models, where our estimator competes favorably. The overall good performance of our proposal is illustrated by further simulations in the GAMLSS setting and by an application to functional magnetic resonance brain imaging using bivariate smoothing splines.

The Direct Determination of I131 in Heterogeneous Fecal Specimens

1961 ◽  
Vol 41 (4) ◽  
pp. 380-384 ◽  
Author(s):  
Arthur F. Dratz ◽  
James C. Coberly
Keyword(s):  
Direct Determination

A New Method for Direct Determination of the Recoilless Fraction with Application to Magnetic Nanoparticles

2002 ◽  
Vol 721 ◽  
Author(s):  
Monica Sorescu
Keyword(s):  
Room Temperature ◽  
Average Particle Size ◽  
Direct Determination ◽  
Average Particle ◽  
Lattice Method ◽  
Recoilless Fraction ◽  
Single Room ◽  
Magnetite Particles ◽  
Physical Mixtures

AbstractWe propose a two-lattice method for direct determination of the recoilless fraction using a single room-temperature transmission Mössbauer measurement. The method is first demonstrated for the case of iron and metallic glass two-foil system and is next generalized for the case of physical mixtures of two powders. We further apply this method to determine the recoilless fraction of hematite and magnetite particles. Finally, we provide direct measurement of the recoilless fraction in nanohematite and nanomagnetite with an average particle size of 19 nm.

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