Related papers: Inference for penalized spline regression: Improvi…
This paper considers a high dimensional linear regression model with corrected variables. A variety of methods have been developed in recent years, yet it is still challenging to keep accurate estimation when there are complex correlation…
Overlapping asymmetric datasets are common in data science and pose questions of how they can be incorporated together into a predictive analysis. In healthcare datasets there is often a small amount of information that is available for a…
In this paper, we propose a new regularization technique called "functional SCAD". We then combine this technique with the smoothing spline method to develop a smooth and locally sparse (i.e., zero on some sub-regions) estimator for the…
We study a new penalty reformulation of constrained convex optimization based on the softplus penalty function. We develop novel and tight upper bounds on the objective value gap and the violation of constraints for the solutions to the…
This paper is concerned with asymptotic theory for penalized spline estimator in bivariate additive model. The focus of this paper is put upon the penalized spline estimator obtained by the backfitting algorithm. The convergence of the…
P-splines are penalized B-splines, in which finite order differences in coefficients are typically penalized with an $\ell_2$ norm. P-splines can be used for semiparametric regression and can include random effects to account for…
The paper considers functional linear regression, where scalar responses $Y_1,...,Y_n$ are modeled in dependence of random functions $X_1,...,X_n$. We propose a smoothing splines estimator for the functional slope parameter based on a…
The Lasso is biased. Concave penalized least squares estimation (PLSE) takes advantage of signal strength to reduce this bias, leading to sharper error bounds in prediction, coefficient estimation and variable selection. For prediction and…
While shrinkage is essential in high-dimensional settings, its use for low-dimensional regression-based prediction has been debated. It reduces variance, often leading to improved prediction accuracy. However, it also inevitably introduces…
We consider spline estimates which preserve prescribed piecewise convex properties of the unknown function. A robust version of the penalized likelihood is given and shown to correspond to a variable halfwidth kernel smoother where the…
In this work we consider numerical efficiency and convergence rates for solvers of non-convex multi-penalty formulations when reconstructing sparse signals from noisy linear measurements. We extend an existing approach, based on reduction…
This paper develops a general theory on rates of convergence of penalized spline estimators for function estimation when the likelihood functional is concave in candidate functions, where the likelihood is interpreted in a broad sense that…
A new method is proposed for variable screening, variable selection and prediction in linear regression problems where the number of predictors can be much larger than the number of observations. The method involves minimizing a penalized…
We consider model selection and estimation for partial spline models and propose a new regularization method in the context of smoothing splines. The regularization method has a simple yet elegant form, consisting of roughness penalty on…
In many classification problems it is desirable to output well-calibrated probabilities on the different classes. We propose a robust, non-parametric method of calibrating probabilities called SplineCalib that utilizes smoothing splines to…
This paper addresses the deconvolution problem of estimating a square-integrable probability density from observations contaminated with additive measurement errors having a known density. The estimator begins with a density estimate of the…
Penalized regression methods aim to retrieve reliable predictors among a large set of putative ones from a limited amount of measurements. In particular, penalized regression with singular penalty functions is important for sparse…
Sparse estimation methods are aimed at using or obtaining parsimonious representations of data or models. They were first dedicated to linear variable selection but numerous extensions have now emerged such as structured sparsity or kernel…
Smoothing splines can be thought of as the posterior mean of a Gaussian process regression in a certain limit. By constructing a reproducing kernel Hilbert space with an appropriate inner product, the Bayesian form of the V-spline is…
When developing risk prediction models, shrinkage methods are recommended, especially when the sample size is limited. Several earlier studies have shown that the shrinkage of model coefficients can reduce overfitting of the prediction…