We propose an extensive framework for additive regression models for correlated functional responses, allowing for multiple partially nested or crossed functional random effects with flexible correlation structures for, e.g., spatial, temporal, or longitudinal functional data. Additionally, our framework includes linear and nonlinear effects of functional and scalar covariates that may vary smo...

We introduce the functional generalized additive model (FGAM), a novel regression model for association studies between a scalar response and a functional predictor. We model the link-transformed mean response as the integral with respect to t of F{X(t), t} where F(·,·) is an unknown regression function and X(t) is a functional covariate. Rather than having an additive model in a finite number ...

We suggest a new method, called Functional Additive Regression, or FAR, for efficiently performing high dimensional functional regression. FAR extends the usual linear regression model involving a functional predictor, X(t), and a scalar response, Y , in two key respects. First, FAR uses a penalized least squares optimization approach to efficiently deal with high dimensional problems involving...

In commonly used functional regression models, the regression of a scalar or functional response on the functional predictor is assumed to be linear. This means the response is a linear function of the functional principal component scores of the predictor process. We relax the linearity assumption and propose to replace it by an additive structure. This leads to a more widely applicable and mu...

In this work, we study the formal connections between non-linear Fokker-Planck Equation associated with non-additive entropy and Boltzmann correlation functional. The collisional term following $q$-algebra is adopted. derivation of Equation, two constraints are imposed on final result: i) that entropic index $q$ a characteristic parameter systems value does not change time, ii) for $q \rightarr...

in this present work, the kudryashov method and the functional variable method are used to construct exact solutions of the complex kdv equation. the kudryashov method and the functional variable method are powerful methods for obtaining exact solutions of nonlinear evolution equations.

We study the effect of Gaussian perturbations on a hyperbolic partial differential equation with double characteristics in two spatial dimensions. The coefficients our operator depend polynomially space variables, while noise is additive, white time and coloured space. provide sufficient condition spectral measure covariance functional describing that allows for existence random field solution ...

In the present paper a solution of the generalizedquadratic functional equation$$f(kx+ y)+f(kx+sigma(y))=2k^{2}f(x)+2f(y),phantom{+} x,yin{E}$$ isgiven where $sigma$ is an involution of the normed space $E$ and$k$ is a fixed positive integer. Furthermore we investigate theHyers-Ulam-Rassias stability of the functional equation. TheHyers-Ulam stability on unbounded domains is also studied.Applic...