Related papers: Fitted value shrinkage
We propose a new prediction method for multivariate linear regression problems where the number of features is less than the sample size but the number of outcomes is extremely large. Many popular procedures, such as penalized regression…
The tuning parameter selection strategy for penalized estimation is crucial to identify a model that is both interpretable and predictive. However, popular strategies (e.g., minimizing average squared prediction error via cross-validation)…
The problem of prediction in functional linear regression is conventionally addressed by reducing dimension via the standard principal component basis. In this paper we show that an alternative basis chosen through weighted least-squares,…
We present a linear regression method for predictions on a small data set making use of a second possibly biased data set that may be much larger. Our method fits linear regressions to the two data sets while penalizing the difference…
One of the common challenges faced by researchers in recent data analysis is missing values. In the context of penalized linear regression, which has been extensively explored over several decades, missing values introduce bias and yield a…
We introduce an original method of multidimensional ridge penalization in functional local linear regressions. The nonparametric regression of functional data is extended from its multivariate counterpart, and is known to be sensitive to…
The least absolute shrinkage and selection operator (lasso) and ridge regression produce usually different estimates although input, loss function and parameterization of the penalty are identical. In this paper we look for ridge and lasso…
We propose an $L_{2}$-based penalization algorithm for functional linear regression models, where the coefficient function is shrunk towards a data-driven shape template $\gamma$, which is constrained to belong to a class of piecewise…
We consider the problem of robustly predicting as well as the best linear combination of $d$ given functions in least squares regression, and variants of this problem including constraints on the parameters of the linear combination. For…
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…
This paper introduces a flexible regularization approach that reduces point estimation risk of group means stemming from e.g. categorical regressors, (quasi-)experimental data or panel data models. The loss function is penalized by adding…
Personalization is becoming an important feature in many predictive applications. We introduce a penalized regression method implementing personalization inherently in the penalty. Personalized angle (PAN) regression constructs regression…
Penalized quantile regression (QR) is widely used for studying the relationship between a response variable and a set of predictors under data heterogeneity in high-dimensional settings. Compared to penalized least squares, scalable…
Penalization procedures often suffer from their dependence on multiplying factors, whose optimal values are either unknown or hard to estimate from the data. We propose a completely data-driven calibration algorithm for this parameter in…
It has previously been shown that ordinary least squares can be used to estimate the coefficients of the single-index model under only mild conditions. However, the estimator is non-robust leading to poor estimates for some models. In this…
This paper provides an alternative to penalized estimators for estimation and vari- able selection in high dimensional linear regression models with measurement error or missing covariates. We propose estimation via bias corrected least…
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…
The problem of fitting experimental data to a given model function $f(t; p_1,p_2,\dots,p_N)$ is conventionally solved numerically by methods such as that of Levenberg-Marquardt, which are based on approximating the Chi-squared measure of…
Separation in logistic regression is a common problem causing failure of the iterative estimation process when finding maximum likelihood estimates. Firth's correction (FC) was proposed as a solution, providing estimates also in presence of…
This paper constructs improved estimators of the means in the Gaussian saturated one-way layout with an ordinal factor. The least squares estimator for the mean vector in this saturated model is usually inadmissible. The hybrid shrinkage…