scholarly journals Smoothing splines with varying smoothing parameter

Biometrika ◽  
2013 ◽  
Vol 100 (4) ◽  
pp. 955-970 ◽  
Author(s):  
X. Wang ◽  
P. Du ◽  
J. Shen
Keyword(s):  
Smoothing Splines ◽  
Smoothing Parameter

scholarly journals Dissimilarity for functional data clustering based on smoothing parameter commutation

2017 ◽  
Vol 27 (11) ◽  
pp. 3492-3504 ◽  
Author(s):  
ShengLi Tzeng ◽  
Christian Hennig ◽  
Yu-Fen Li ◽  
Chien-Ju Lin
Keyword(s):  
Functional Data ◽  
Data Clustering ◽  
Smoothing Splines ◽  
Smoothing Parameter ◽  
Multiple Time ◽  
Easy Method ◽  
Time Points ◽  
Methadone Dosage ◽  
Estimation Uncertainty ◽  
Smoothing Parameters

Many studies measure the same type of information longitudinally on the same subject at multiple time points, and clustering of such functional data has many important applications. We propose a novel and easy method to implement dissimilarity measure for functional data clustering based on smoothing splines and smoothing parameter commutation. This method handles data observed at regular or irregular time points in the same way. We measure the dissimilarity between subjects based on varying curve estimates with pairwise commutation of smoothing parameters. The intuition is that smoothing parameters of smoothing splines reflect the inverse of the signal-to-noise ratios and that when applying an identical smoothing parameter the smoothed curves for two similar subjects are expected to be close. Our method takes into account the estimation uncertainty using smoothing parameter commutation and is not strongly affected by outliers. It can also be used for outlier detection. The effectiveness of our proposal is shown by simulations comparing it to other dissimilarity measures and by a real application to methadone dosage maintenance levels.

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.

Modified Ridge Type Estimator in Partially Linear Regression Models and Numerical Comparisons

2016 ◽  
Vol 13 (10) ◽  
pp. 7040-7053 ◽  
Author(s):  
Dursun Aydın ◽  
Bahadır Yüzbaşı ◽  
S. Ejaz Ahmed
Keyword(s):  
Cross Validation ◽  
Risk Estimation ◽  
Real Data ◽  
Information Criterion ◽  
Smoothing Splines ◽  
Smoothing Parameter ◽  
Partially Linear Model ◽  
Linear Regression Models ◽  
Monte Carlo Simulation Study ◽  
Partially Linear

In this article, we introduce a modified ridge type estimator for the vector of parameters in a partially linear model. This estimator is a generalization of the well-known Speckman’s approach and is based on smoothing splines method. Most important in the implementation of this method is the choice of the smoothing parameter. Many Criteria of selecting smoothing parameters such as improved version of Akaike information criterion (AICc), generalized cross-validation (GCV), cross-validation (CV), Mallows’ Cp criterion, risk estimation using classical pilots (REC) and Bayes information criterion (BIC) are developed in literature. In order to illustrate the ideas in the paper, a real data example and a Monte Carlo simulation study are carried out. Thus, the appropriate selection criteria are provided for a suitable smoothing parameter selection.

Spline Fitting

2011 ◽  
pp. 166-171
Author(s):  
Michael Wodny
Keyword(s):  
Optimization Problems ◽  
Smoothing Splines ◽  
Cubic Spline ◽  
Smoothing Parameter ◽  
Spline Functions ◽  
System Of Equations ◽  
Linear System Of Equations ◽  
Spline Fitting ◽  
Natural Cubic Spline ◽  
The Given

Given are the m points (xi,yi), i=1,2,…,m. Spline functions are introduced, and it is noticed that the interpolation task in the case of natural splines has a unique solution. The interpolating natural cubic spline is constructed. For the construction of smoothing splines, different optimization problems are formulated. A selected problem is looked at in detail. The construction of the solution is carried out in two steps. In the first step the unknown Di=s(xi) are calculated via a linear system of equations. The second step is the construction of the interpolating natural cubic spline with respect to these (xi,Di), i=1,2,…,m. Every optimization problem contains a smoothing parameter. A method of estimation of the smoothing parameter from the given data is motivated briefly.

scholarly journals Image smoothing based on global sparsity decomposition and a variable parameter

2021 ◽  
Author(s):  
Xiang Ma ◽  
Xuemei Li ◽  
Yuanfeng Zhou ◽  
Caiming Zhang
Keyword(s):  
Removal Rate ◽  
Variable Parameter ◽  
Smoothing Parameter ◽  
Smoothing Effect ◽  
Image Smoothing ◽  
Sparse Decomposition ◽  
Alternating Direction ◽  
Texture Removal ◽  
Ideal Algorithm ◽  
Better Than

AbstractSmoothing images, especially with rich texture, is an important problem in computer vision. Obtaining an ideal result is difficult due to complexity, irregularity, and anisotropicity of the texture. Besides, some properties are shared by the texture and the structure in an image. It is a hard compromise to retain structure and simultaneously remove texture. To create an ideal algorithm for image smoothing, we face three problems. For images with rich textures, the smoothing effect should be enhanced. We should overcome inconsistency of smoothing results in different parts of the image. It is necessary to create a method to evaluate the smoothing effect. We apply texture pre-removal based on global sparse decomposition with a variable smoothing parameter to solve the first two problems. A parametric surface constructed by an improved Bessel method is used to determine the smoothing parameter. Three evaluation measures: edge integrity rate, texture removal rate, and gradient value distribution are proposed to cope with the third problem. We use the alternating direction method of multipliers to complete the whole algorithm and obtain the results. Experiments show that our algorithm is better than existing algorithms both visually and quantitatively. We also demonstrate our method’s ability in other applications such as clip-art compression artifact removal and content-aware image manipulation.

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