Search results for "Splines"
showing 10 items of 44 documents
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.
A comparison of nonparametric methods in the graduation of mortality: Application to data from the Valencia Region (Spain)
2006
[EN] The nonparametric graduation of mortality data aims to estimate death rates by carrying out a smoothing of the crude rates obtained directly from original data. The main difference with regard to parametric models is that the assumption of an age-dependent function is unnecessary, which is advantageous when the information behind the model is unknown, as one cause of error is often the choice of an inappropriate model. This paper reviews the various alternatives and presents their application to mortality data from the Valencia Region, Spain. The comparison leads us to the conclusion that the best model is a smoothing by means of Generalised Additive Models (GAM) with splines. The most…
A reexamination of voltage distortion for classical carrier-based vs B-Spline modulation of three-phase Voltage Sources Inverters
2015
Voltage waveform improvement has been the object of several investigations for many years and a manifold of different solutions have been proposed to reduce the harmonic content in Voltage Source Inverters (VSI) power application. In many cases this improvements have been obtained by modifying the reference voltage modulating signal. The recent introduction of cardinal B-spline functions, used as carrier signals, has given rise to a new modulation technique whose main characteristic is a lower value of the Total Harmonic Distortion (THD). After the discussion on the B-Spline modulation principle and on its computational effort, a performance comparisons is carried out by means of Total Harm…
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…
ON SOME GENERALIZATION OF SMOOTHING PROBLEMS
2015
The paper deals with the generalized smoothing problem in abstract Hilbert spaces. This generalized problem involves particular cases such as the interpolating problem, the smoothing problem with weights, the smoothing problem with obstacles, the problem on splines in convex sets and others. The theorem on the existence and characterization of a solution of the generalized problem is proved. It is shown how the theorem gives already known theorems in special cases as well as some new results.