GNSS-Based Continuous Estimation of Speed Using the Smoothing Splines with an A Priori Uncertain Smoothing Parameter

2021 ◽  
Author(s):  
D. A. Koshaev
Keyword(s):  
A Priori ◽  
Smoothing Splines ◽  
Smoothing Parameter ◽  
Continuous Estimation

scholarly journals Smoothing and Interpolating Noisy GPS Data with Smoothing Splines

2020 ◽  
Vol 37 (3) ◽  
pp. 449-465 ◽  
Author(s):  
Jeffrey J. Early ◽  
Adam M. Sykulski
Keyword(s):  
Gaussian Noise ◽  
A Priori ◽  
Smoothing Splines ◽  
Sampled Data ◽  
Trajectory Data ◽  
Tension Parameter ◽  
Comprehensive Method ◽  
Gps Trajectory Data ◽  
Non Gaussian ◽  
Irregularly Sampled Data

AbstractA comprehensive method is provided for smoothing noisy, irregularly sampled data with non-Gaussian noise using smoothing splines. We demonstrate how the spline order and tension parameter can be chosen a priori from physical reasoning. We also show how to allow for non-Gaussian noise and outliers that are typical in global positioning system (GPS) signals. We demonstrate the effectiveness of our methods on GPS trajectory data obtained from oceanographic floating instruments known as drifters.

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.

A new method for estimating the morphometric size at maturity of crabs

1998 ◽  
Vol 55 (3) ◽  
pp. 704-714 ◽  
Author(s):  
George Watters ◽  
Alistair J Hobday
Keyword(s):  
Body Size ◽  
A Priori ◽  
Smoothing Splines ◽  
The Body ◽  
New Method ◽  
Second Derivative ◽  
Size At Maturity ◽  
Relative Growth ◽  
Wide Range ◽  
Body Sizes

Existing techniques for estimating the morphometric size at maturity of crabs are based on assumptions that may be unnecessary. Here we demonstrate a new method of detecting changes in relative growth (or allometric) relationships and estimating morphometric size at maturity. This method involves fitting several smoothing splines to relationships between body size and claw size, selecting the "best" spline, and finding this spline's maximum second derivative. The body size where the second derivative of the best spline is maximized estimates the morphometric size at maturity. Monte Carlo simulations suggest that uncertainty and bias in the estimate of morphometric size at maturity can be decreased by measuring a large number of crabs from a wide range of body sizes. Our spline method does not require a priori assumptions about the shape of the relative growth relationship; it can detect multiple changes in the relative growth rate; and it is robust to outliers. The modeling technique may also be used to identify regions of allometric change in other types of relationships. We demonstrate the new technique by estimating the morphometric size at sexual maturity for males of both brachyuran (Chionoecetes tanneri) and anomuran (Paralomis spinosissima and P. formosa) crabs.

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 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
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