Search results for " splines"
showing 10 items of 35 documents
Multiple smoothing parameters selection in additive regression quantiles
2021
We propose an iterative algorithm to select the smoothing parameters in additive quantile regression, wherein the functional forms of the covariate effects are unspecified and expressed via B-spline bases with difference penalties on the spline coefficients. The proposed algorithm relies on viewing the penalized coefficients as random effects from the symmetric Laplace distribution, and it turns out to be very efficient and particularly attractive with multiple smooth terms. Through simulations we compare our proposal with some alternative approaches, including the traditional ones based on minimization of the Schwarz Information Criterion. A real-data analysis is presented to illustrate t…
Simulation in the Simple Linear Regression Model
2002
Summary This article presents an activity which simulates the linear regression model in order to verify the probabilistic behaviour of the resulting least-squares statistics in practice.
Varying-coefficient functional linear regression models
2008
This article considers a generalization of the functional linear regression in which an additional real variable influences smoothly the functional coefficient. We thus define a varying-coefficient regression model for functional data. We propose two estimators based, respectively, on conditional functional principal regression and on local penalized regression splines and prove their pointwise consistency. We check, with the prediction one day ahead of ozone concentration in the city of Toulouse, the ability of such nonlinear functional approaches to produce competitive estimations.
Estimating regression models with unknown break-points.
2003
This paper deals with fitting piecewise terms in regression models where one or more break-points are true parameters of the model. For estimation, a simple linearization technique is called for, taking advantage of the linear formulation of the problem. As a result, the method is suitable for any regression model with linear predictor and so current software can be used; threshold modelling as function of explanatory variables is also allowed. Differences between the other procedures available are shown and relative merits discussed. Simulations and two examples are presented to illustrate the method.
Estimating growth charts via nonparametric quantile regression: a practical framework with application in ecology.
2013
We discuss a practical and effective framework to estimate reference growth charts via regression quantiles. Inequality constraints are used to ensure both monotonicity and non-crossing of the estimated quantile curves and penalized splines are employed to model the nonlinear growth patterns with respect to age. A companion R package is presented and relevant code discussed to favour spreading and application of the proposed methods.
Predicting gully occurrence at watershed scale: Comparing topographic indices and multivariate statistical models
2020
In this study, the ability of five topographic indices to predict the gully trajectories observed in two adjacent watersheds located in Sicily (Italy) was evaluated. Two of these indices, named MSPI and MTWI, as far as we know, have never been employed to this aim. They were obtained by multiplying the stream power index (SPI) and the topographic wetness index (TWI), respectively, by the convergence index (CI). The predictive ability of the topographic indices was measured by using both cut-off independent (AUC: area under the receiver operating characteristic curve) and dependent statistics (Cohen's kappa index κ, sensitivity, specificity). These statistics were calculated also for 100 MAR…
Gully Erosion Susceptibility Mapping Using Multivariate Adaptive Regression Splines—Replications and Sample Size Scenarios
2019
Soil erosion is a serious problem affecting numerous countries, especially, gully erosion. In the current research, GIS techniques and MARS (Multivariate Adaptive Regression Splines) algorithm were considered to evaluate gully erosion susceptibility mapping among others. The study was conducted in a specific section of the Gorganroud Watershed in Golestan Province (Northern Iran), covering 2142.64 km2 which is intensely influenced by gully erosion. First, Google Earth images, field surveys, and national reports were used to provide a gully-hedcut evaluation map consisting of 307 gully-hedcut points. Eighteen gully erosion conditioning factors including significant geoenvironmental and morph…
Functional principal component analysis of quantile curves
2017
Literature on functional data analysis is mainly focused on estimation of individuals curves and characterization of average dynamics. The idea underlying this proposal is to focus attention on other particular features of the distribution of the observed data, moving from mean functions towards functional quantiles. The motivating examples are functional data sets that are collections of high frequency data recorded along time. As quantiles provide information on various aspects of a time series, we propose a modelling framework for the joint estimation of functional quantiles, varying along time, and functional principal components, summarizing some common dynamics shared by the functiona…
Growth curves of sorghum roots via quantile regression with P-splines
2014
Plant roots are a major pool of total carbon in the planet and their dynamics are directly relevant to greenhouse gas balance. Composted wastes are increasingly used in agriculture for environmental and economic reasons and their role as a substitute for traditional fertilizers needs to be tested on all plant components. Here we propose a regression quantile approach based on P-splines to assess, quantify and compare the root growth patterns in two treatment groups respectively undergoing compost and traditional fertilization.
Fast Computation by Subdivision of Multidimensional Splines and Their Applications
2016
We present theory and algorithms for fast explicit computations of uni- and multi-dimensional periodic splines of arbitrary order at triadic rational points and of splines of even order at diadic rational points. The algorithms use the forward and the inverse Fast Fourier transform (FFT). The implementation is as fast as FFT computation. The algorithms are based on binary and ternary subdivision of splines. Interpolating and smoothing splines are used for a sample rate convertor such as resolution upsampling of discrete-time signals and digital images and restoration of decimated images that were contaminated by noise. The performance of the rate conversion based spline is compared with the…