Related papers: Varying Coefficient Model via Adaptive Spline Fitt…
New algorithms for fast wavelet transforms with biorthogonal spline wavelets on nonuniform grids are presented. In contrary to classical wavelet transforms, the algorithms are not based on filter coefficients, but on algorithms for B-spline…
To deal with non-linear relations between the predictors and the response, we can use transformations to make the data look linear or approximately linear. In practice, however, transformation methods may be ineffective, and it may be more…
As a growing number of problems involve variables that are random objects, the development of models for such data has become increasingly important. This paper introduces a novel varying-coefficient Fr\'echet regression model that extends…
We consider the problem of simultaneous variable selection and constant coefficient identification in high-dimensional varying coefficient models based on B-spline basis expansion. Both objectives can be considered as some type of model…
In this article we propose a new adaptive numerical quadrature procedure which includes both local subdivision of the integration domain, as well as local variation of the number of quadrature points employed on each subinterval. In this…
Semiparametric regression offers a flexible framework for modeling non-linear relationships between a response and covariates. A prime example are generalized additive models where splines (say) are used to approximate non-linear functional…
Quantile regression has been successfully used to study heterogeneous and heavy-tailed data. Varying-coefficient models are frequently used to capture changes in the effect of input variables on the response as a function of an index or…
Penalized regression models are popularly used in high-dimensional data analysis to conduct variable selection and model fitting simultaneously. Whereas success has been widely reported in literature, their performances largely depend on…
In this paper we discuss the applications of knotoids to modelling knots in open curves and produce new knotoid invariants. We show how invariants of knotoids generally give rise to well-behaved measures of how much an open curve is…
Varying-coefficient functional linear models consider the relationship between a response and a predictor, where the response depends not only the predictor but also an exogenous variable. It then accounts for the relation of the predictors…
Using neural networks to solve variational problems, and other scientific machine learning tasks, has been limited by a lack of consistency and an inability to exactly integrate expressions involving neural network architectures. We address…
In this paper we analyse the pathwise approximation of stochastic differential equations by polynomial splines with free knots. The pathwise distance between the solution and its approximation is measured globally on the unit interval in…
Variable projection solves structured optimization problems by completely minimizing over a subset of the variables while iterating over the remaining variables. Over the last 30 years, the technique has been widely used, with empirical and…
This study examines the varying coefficient model in tail index regression. The varying coefficient model is an efficient semiparametric model that avoids the curse of dimensionality when including large covariates in the model. In fact,…
The dynamic mode decomposition (DMD) has become a leading tool for data-driven modeling of dynamical systems, providing a regression framework for fitting linear dynamical models to time-series measurement data. We present a simple…
Fitting B-splines to discrete data is especially challenging when the given data contain noise, jumps, or corners. Here, we describe how periodic data sets with these features can be efficiently and robustly approximated with B-splines by…
Statistical learning evolves quickly with more and more sophisticated models proposed to incorporate the complicated data structure from modern scientific and business problems. Varying index coefficient models extend varying coefficient…
The smoothing spline is one of the most popular curve-fitting methods, partly because of empirical evidence supporting its effectiveness and partly because of its elegant mathematical formulation. However, there are two obstacles that…
In this paper, we propose a varying coefficient panel data model with unobservable multiple interactive fixed effects that are correlated with the regressors. We approximate each coefficient function by B-spline, and propose a robust…
Clinical research often focuses on complex traits in which many variables play a role in mechanisms driving, or curing, diseases. Clinical prediction is hard when data is high-dimensional, but additional information, like domain knowledge…