Search results for "Linear"
showing 10 items of 7165 documents
Electricity consumption prediction with functional linear regression using spline estimators
2010
A functional linear regression model linking observations of a functional response variable with measurements of an explanatory functional variable is considered. This model serves to analyse a real data set describing electricity consumption in Sardinia. The interest lies in predicting either oncoming weekends’ or oncoming weekdays’ consumption, provided actual weekdays’ consumption is known. A B-spline estimator of the functional parameter is used. Selected computational issues are addressed as well.
New adaptive synchronization algorithm for a general class of complex hyperchaotic systems with unknown parameters and its application to secure comm…
2022
Abstract The aim of this report is to investigate an adaptive synchronization (AS) for the general class of complex hyperchaotic models with unknown parameters and a new algorithm to achieve this type of synchronization is proposed. Owing to the intricacy behavior of hyperchaotic models that could be effective in secure communications, the special control based on adaptive laws of parameters is constructed analytically, and the corresponding simulated results are performed to validate the algorithm’s accuracy. The complex Rabinovich model is utilized as an enticing example to examine the proposed synchronization technique. A strategy for secure communication improving the overall cryptosyst…
Cutting rules and positivity in finite temperature many-body theory
2022
Abstract For a given diagrammatic approximation in many-body perturbation theory it is not guaranteed that positive observables, such as the density or the spectral function, retain their positivity. For zero-temperature systems we developed a method [2014 Phys. Rev. B 90 115134] based on so-called cutting rules for Feynman diagrams that enforces these properties diagrammatically, thus solving the problem of negative spectral densities observed for various vertex approximations. In this work we extend this method to systems at finite temperature by formulating the cutting rules in terms of retarded N-point functions, thereby simplifying earlier approaches and simultaneously solving the issu…
Efficient Estimation of Non-Linear Finite Population Parameters by Using Non-Parametrics
2013
Summary Currently, high precision estimation of non-linear parameters such as Gini indices, low income proportions or other measures of inequality is particularly crucial. We propose a general class of estimators for such parameters that take into account univariate auxiliary information assumed to be known for every unit in the population. Through a non-parametric model-assisted approach, we construct a unique system of survey weights that can be used to estimate any non-linear parameter that is associated with any study variable of the survey, using a plug-in principle. Based on a rigorous functional approach and a linearization principle, the asymptotic variance of the estimators propose…
Role of sub- and super-Poisson noise sources in population dynamics
2020
In this paper we present a study on pulse noise sources characterized by sub- and super-Poisson statistics. We make a comparison with their uncorrelated counterpart. i.e. pulse noise with Poisson statistics, while showing that the correlation properties of sub- and super-Poisson noise sources can be efficiently applied to population dynamics. Specifically, we consider a termite population, described by a Langevin equation in the presence of a pulse noise source, and we study its dynamics and stability properties for two models. The first one describes a population of several colonies in a new territory with adverse environmental conditions. The second one considers the development of a sing…
Fourth Moments and Independent Component Analysis
2015
In independent component analysis it is assumed that the components of the observed random vector are linear combinations of latent independent random variables, and the aim is then to find an estimate for a transformation matrix back to these independent components. In the engineering literature, there are several traditional estimation procedures based on the use of fourth moments, such as FOBI (fourth order blind identification), JADE (joint approximate diagonalization of eigenmatrices), and FastICA, but the statistical properties of these estimates are not well known. In this paper various independent component functionals based on the fourth moments are discussed in detail, starting wi…
Large-sample properties of unsupervised estimation of the linear discriminant using projection pursuit
2021
We study the estimation of the linear discriminant with projection pursuit, a method that is unsupervised in the sense that it does not use the class labels in the estimation. Our viewpoint is asymptotic and, as our main contribution, we derive central limit theorems for estimators based on three different projection indices, skewness, kurtosis, and their convex combination. The results show that in each case the limiting covariance matrix is proportional to that of linear discriminant analysis (LDA), a supervised estimator of the discriminant. An extensive comparative study between the asymptotic variances reveals that projection pursuit gets arbitrarily close in efficiency to LDA when the…
Contributed discussion on article by Pratola
2016
The author should be commended for his outstanding contribution to the literature on Bayesian regression tree models. The author introduces three innovative sampling approaches which allow for efficient traversal of the model space. In this response, we add a fourth alternative.
A multi-scale approach for testing and detecting peaks in time series
2020
An approach is presented that combines a statistical test for peak detection with the estimation of peak positions in time series. Motivated by empirical observations in neuronal recordings, we aim at investigating peaks of different heights and widths. We use a moving window approach to compare the differences of estimated slope coefficients of local regression models. We combine multiple windows and use the global maximum of all different processes as a test statistic. After rejection, a multiple filter algorithm combines peak positions estimated from multiple windows. Analysing neuronal activity recorded in anaesthetized mice, the procedure could identify significant differences between …
Lévy processes in bounded domains: path-wise reflection scenarios and signatures of confinement
2022
We discuss an impact of various (path-wise) reflection-from-the barrier scenarios upon confining properties of a paradigmatic family of symmetric $\alpha $-stable L\'{e}vy processes, whose permanent residence in a finite interval on a line is secured by a two-sided reflection. Depending on the specific reflection "mechanism", the inferred jump-type processes differ in their spectral and statistical characteristics, like e.g. relaxation properties, and functional shapes of invariant (equilibrium, or asymptotic near-equilibrium) probability density functions in the interval. The analysis is carried out in conjunction with attempts to give meaning to the notion of a reflecting L\'{e}vy process…