Related papers: Leave-one-out cross-validation is risk consistent …
One of the common goals of time series analysis is to use the observed series to inform predictions for future observations. In the absence of any actual new data to predict, cross-validation can be used to estimate a model's future…
Recent literature provides many computational and modeling approaches for covariance matrices estimation in a penalized Gaussian graphical models but relatively little study has been carried out on the choice of the tuning parameter. This…
We propose a test of the significance of a variable appearing on the Lasso path and use it in a procedure for selecting one of the models of the Lasso path, controlling the Family-Wise Error Rate. Our null hypothesis depends on a set A of…
Recently, financial industry and regulators have enhanced the debate on the good properties of a risk measure. A fundamental issue is the evaluation of the quality of a risk estimation. On the one hand, a backtesting procedure is desirable…
This text is a survey on cross-validation. We define all classical cross-validation procedures, and we study their properties for two different goals: estimating the risk of a given estimator, and selecting the best estimator among a given…
The Lasso regression is a popular regularization method for feature selection in statistics. Prior to computing the Lasso estimator in both linear and generalized linear models, it is common to conduct a preliminary rescaling of the feature…
Nowadays, l1 penalized likelihood has absorbed a high amount of consideration due to its simplicity and well developed theoretical properties. This method is known as a reliable method in order to apply in a broad range of applications…
The Lasso has become a benchmark data analysis procedure, and numerous variants have been proposed in the literature. Although the Lasso formulations are stated so that overall prediction error is optimized, no full control over the…
The Lasso is a prominent algorithm for variable selection. However, its instability in the presence of correlated variables in the high-dimensional setting is well-documented. Although previous research has attempted to address this issue…
In this paper, for Lasso penalized linear regression models in high-dimensional settings, we propose a modified cross-validation method for selecting the penalty parameter. The methodology is extended to other penalties, such as Elastic…
The present work aims at deriving theoretical guaranties on the behavior of some cross-validation procedures applied to the $k$-nearest neighbors ($k$NN) rule in the context of binary classification. Here we focus on the leave-$p$-out…
In high-dimensional statistical inference in which the number of parameters to be estimated is larger than that of the holding data, regularized linear estimation techniques are widely used. These techniques have, however, some drawbacks.…
In this study, we investigate the bias and variance properties of the debiased Lasso in linear regression when the tuning parameter of the node-wise Lasso is selected to be smaller than in previous studies. We consider the case where the…
In this article we prove that estimator stability is enough to show that leave-one-out cross validation is a sound procedure, by providing concentration bounds in a general framework. In particular, we provide concentration bounds beyond…
We study how correlations in the design matrix influence Lasso prediction. First, we argue that the higher the correlations are, the smaller the optimal tuning parameter is. This implies in particular that the standard tuning parameters,…
In a polynomial regression model, the divisibility conditions implicit in polynomial hierarchy give way to a natural construction of constraints for the model parameters. We use this principle to derive versions of strong and weak hierarchy…
In modern data analysis, sparse model selection becomes inevitable once the number of predictors variables is very high. It is well-known that model selection procedures like the Lasso or Boosting tend to overfit on real data. The…
Cross validation is commonly used for selecting tuning parameters in penalized regression, but its use in penalized Cox regression models has received relatively little attention in the literature. Due to its partial likelihood…
Leave-one-out cross-validation (LOO) and the widely applicable information criterion (WAIC) are methods for estimating pointwise out-of-sample prediction accuracy from a fitted Bayesian model using the log-likelihood evaluated at the…
The Lasso is a popular regression method for high-dimensional problems in which the number of parameters $\theta_1,\dots,\theta_N$, is larger than the number $n$ of samples: $N>n$. A useful heuristics relates the statistical properties of…