We consider the linear regression model with Gaussian error. We estimate the unknown parameters by a procedure inspired from the Group Lasso estimator introduced in [21]. We show that this estimator satisfies a sparsity oracle inequality, i.e., a bound in terms of the number of non-zero components of the oracle vector. We prove that this bound is better, in some cases, than the one achieved by ...

The artificial neural network (ANN) test of Lee et al. (Journal of Econometrics 56, 269–290, 1993) uses the ability of the ANN activation functions in the hidden layer to detect neglected functional misspecification. As the estimation of the ANN model is often quite difficult, LWG suggested activate the ANN hidden units based on randomly drawn activation parameters. To be robust to the random a...

The lasso, introduced by Robert Tibshirani in 1996, has become one of the most popular techniques for estimating Gaussian linear regression models. An important reason for this popularity is that the lasso can simultaneously estimate all regression parameters as well as select important variables, yielding accurate regression models that are highly interpretable. This paper derives an efficient...

We present a stepwise approach to estimate high dimensional Gaussian graphicalmodels. exploit the relation between partial correlation coefficientsand distribution of prediction errors, and parametrize model in termsof Pearson coefficients errors nodes’best linear predictors. propose novel algorithm for detecting pairsof conditionally dependent variables. compare proposed withexisting methods i...

Abstract: We revisit the adaptive Lasso as well as the thresholded Lasso with refitting, in a high-dimensional linear model, and study prediction error, lq-error (q ∈ {1, 2}), and number of false positive selections. Our theoretical results for the two methods are, at a rather fine scale, comparable. The differences only show up in terms of the (minimal) restricted and sparse eigenvalues, favor...

Predicting stock exchange rates is receiving increasing attention and is a vital financial problem as it contributes to the development of effective strategies for stock exchange transactions. The forecasting of stock price movement in general is considered to be a thought-provoking and essential task for financial time series' exploration. In this paper, a Least Absolute Shrinkage and Selectio...

In 2015, Barber and Candès introduced a new variable selection procedure called the knockoff filter to control the false discovery rate (FDR) and prove that this method achieves exact FDR control. Inspired by the work of Barber and Candès (2015), we propose and analyze a pseudoknockoff filter that inherits some advantages of the original knockoff filter and has more flexibility in constructing ...

We consider the problem of model selection and estimation in sparse high dimensional linear regression models with strongly correlated variables. First, we study the theoretical properties of the dual Lasso solution, and we show that joint consideration of the Lasso primal and its dual solutions are useful for selecting correlated active variables. Second, we argue that correlation among active...