scholarly journals On the Tuning Parameter Selection in Model Selection and Model Averaging: A Monte Carlo Study

2019 ◽  
Author(s):  
Hui Xiao ◽  
Yiguo Sun
Keyword(s):  
Monte Carlo ◽  
Model Selection ◽  
Sample Size ◽  
Model Averaging ◽  
Parameter Selection ◽  
Tuning Parameter ◽  
High Dimensional ◽  
Finite Sample ◽  
Sparse Models ◽  
Mallows Model

Model selection and model averaging have been the popular approaches in handling modelling uncertainties. Fan and Li(2006) laid out a unified frame work for variable selection via penalized likelihood. The tuning parameter selection is vital in the optimization problem for the penalized estimators in achieving consistent selection and optimal estimation. Since the OLSpost-LASSO estimator by Belloni and Chernozhukov (2013), few studies have focused on the finite sample performances of the class of OLS post-penalty estimators with the tuning parameter choice determined by different tuning parameter selection approaches. We aim to supplement the existing model selection literature by studying such a class of OLS post-selection estimators. Inspired by the Shrinkage Averaging Estimator (SAE) by Schomaker(2012) and the Mallows Model Averaging (MMA) criterion by Hansen (2007), we further propose a Shrinkage Mallows Model Averaging (SMMA) estimator for averaging high dimensional sparse models. Based on the Monte Carlo design by Wang et al. (2009) which features an expanding sparse parameter space as the sample size increases, our Monte Carlo design further considers the effect of the effective sample size and the degree of model sparsity on the finite sample performances of model selection and model averaging estimators. From our data examples, we find that the OLS post-SCAD(BIC) estimator in finite sample outperforms most of the current penalized least squares estimators as long as the number of parameters does not exceed the sample size. In addition, the SMMA performs better given sparser models. This supports the use of the SMMA estimator when averaging high dimensional sparse models.

scholarly journals On Tuning Parameter Selection in Model Selection and Model Averaging: A Monte Carlo Study

2019 ◽  
Vol 12 (3) ◽  
pp. 109 ◽  
Author(s):  
Hui Xiao ◽  
Yiguo Sun
Keyword(s):  
Monte Carlo ◽  
Model Selection ◽  
Model Averaging ◽  
Ordinary Least Squares ◽  
Parameter Selection ◽  
Tuning Parameter ◽  
High Dimensional ◽  
Finite Sample ◽  
Sparse Models ◽  
Modeling Uncertainties

Model selection and model averaging are popular approaches for handling modeling uncertainties. The existing literature offers a unified framework for variable selection via penalized likelihood and the tuning parameter selection is vital for consistent selection and optimal estimation. Few studies have explored the finite sample performances of the class of ordinary least squares (OLS) post-selection estimators with the tuning parameter determined by different selection approaches. We aim to supplement the literature by studying the class of OLS post-selection estimators. Inspired by the shrinkage averaging estimator (SAE) and the Mallows model averaging (MMA) estimator, we further propose a shrinkage MMA (SMMA) estimator for averaging high-dimensional sparse models. Our Monte Carlo design features an expanding sparse parameter space and further considers the effect of the effective sample size and the degree of model sparsity on the finite sample performances of estimators. We find that the OLS post-smoothly clipped absolute deviation (SCAD) estimator with the tuning parameter selected by the Bayesian information criterion (BIC) in finite sample outperforms most penalized estimators and that the SMMA performs better when averaging high-dimensional sparse models.

OPTIMAL MULTISTEP VAR FORECAST AVERAGING

2020 ◽  
Vol 36 (6) ◽  
pp. 1099-1126
Author(s):  
Jen-Che Liao ◽  
Wen-Jen Tsay
Keyword(s):  
Infinite Order ◽  
Asymptotic Optimality ◽  
Model Misspecification ◽  
Model Averaging ◽  
Finite Sample ◽  
Forecast Horizon ◽  
Simulation Experiments ◽  
Vector Autoregressive ◽  
One Step ◽  
Mallows Model

This article proposes frequentist multiple-equation least-squares averaging approaches for multistep forecasting with vector autoregressive (VAR) models. The proposed VAR forecast averaging methods are based on the multivariate Mallows model averaging (MMMA) and multivariate leave-h-out cross-validation averaging (MCVAh) criteria (with h denoting the forecast horizon), which are valid for iterative and direct multistep forecast averaging, respectively. Under the framework of stationary VAR processes of infinite order, we provide theoretical justifications by establishing asymptotic unbiasedness and asymptotic optimality of the proposed forecast averaging approaches. Specifically, MMMA exhibits asymptotic optimality for one-step-ahead forecast averaging, whereas for direct multistep forecast averaging, the asymptotically optimal combination weights are determined separately for each forecast horizon based on the MCVAh procedure. To present our methodology, we investigate the finite-sample behavior of the proposed averaging procedures under model misspecification via simulation experiments.

scholarly journals Least squares after model selection in high-dimensional sparse models

Bernoulli ◽  
2013 ◽  
Vol 19 (2) ◽  
pp. 521-547 ◽  
Author(s):  
Alexandre Belloni ◽  
Victor Chernozhukov
Keyword(s):  
Model Selection ◽  
Least Squares ◽  
High Dimensional ◽  
Sparse Models

scholarly journals A Survey of Tuning Parameter Selection for High-Dimensional Regression

2020 ◽  
Vol 7 (1) ◽  
pp. 209-226 ◽  
Author(s):  
Yunan Wu ◽  
Lan Wang
Keyword(s):  
Standard Technique ◽  
Penalized Regression ◽  
Optimal Choice ◽  
Parameter Selection ◽  
Tuning Parameter ◽  
High Dimensional ◽  
Design Matrix ◽  
High Dimensional Regression ◽  
Selection For ◽  
Sparsity Level

Penalized (or regularized) regression, as represented by lasso and its variants, has become a standard technique for analyzing high-dimensional data when the number of variables substantially exceeds the sample size. The performance of penalized regression relies crucially on the choice of the tuning parameter, which determines the amount of regularization and hence the sparsity level of the fitted model. The optimal choice of tuning parameter depends on both the structure of the design matrix and the unknown random error distribution (variance, tail behavior, etc.). This article reviews the current literature of tuning parameter selection for high-dimensional regression from both the theoretical and practical perspectives. We discuss various strategies that choose the tuning parameter to achieve prediction accuracy or support recovery. We also review several recently proposed methods for tuning-free high-dimensional regression.

scholarly journals Integral estimation based on Markovian design

2018 ◽  
Vol 50 (3) ◽  
pp. 833-857 ◽  
Author(s):  
Romain Azaïs ◽  
Bernard Delyon ◽  
François Portier
Keyword(s):  
Monte Carlo ◽  
Sample Size ◽  
Convergence Rates ◽  
Finite Sample ◽  
Integration Methods ◽  
Average Value ◽  
Average Temperature ◽  
Integral Estimation ◽  
History Of ◽  
Better Than

AbstractSuppose that a mobile sensor describes a Markovian trajectory in the ambient space and at each time the sensor measures an attribute of interest, e.g. the temperature. Using only the location history of the sensor and the associated measurements, we estimate the average value of the attribute over the space. In contrast to classical probabilistic integration methods, e.g. Monte Carlo, the proposed approach does not require any knowledge of the distribution of the sensor trajectory. We establish probabilistic bounds on the convergence rates of the estimator. These rates are better than the traditional `rootn'-rate, wherenis the sample size, attached to other probabilistic integration methods. For finite sample sizes, we demonstrate the favorable behavior of the procedure through simulations and consider an application to the evaluation of the average temperature of oceans.

scholarly journals Aerosol model selection and uncertainty modelling by adaptive MCMC technique

2008 ◽  
Vol 8 (24) ◽  
pp. 7697-7707 ◽  
Author(s):  
M. Laine ◽  
J. Tamminen
Keyword(s):  
Monte Carlo ◽  
Markov Chain ◽  
Markov Chain Monte Carlo ◽  
Model Selection ◽  
Cross Sections ◽  
Statistical Parameter ◽  
Model Averaging ◽  
Monte Carlo Sampling ◽  
Reversible Jump ◽  
Aerosol Model

Abstract. We present a new technique for model selection problem in atmospheric remote sensing. The technique is based on Monte Carlo sampling and it allows model selection, calculation of model posterior probabilities and model averaging in Bayesian way. The algorithm developed here is called Adaptive Automatic Reversible Jump Markov chain Monte Carlo method (AARJ). It uses Markov chain Monte Carlo (MCMC) technique and its extension called Reversible Jump MCMC. Both of these techniques have been used extensively in statistical parameter estimation problems in wide area of applications since late 1990's. The novel feature in our algorithm is the fact that it is fully automatic and easy to use. We show how the AARJ algorithm can be implemented and used for model selection and averaging, and to directly incorporate the model uncertainty. We demonstrate the technique by applying it to the statistical inversion problem of gas profile retrieval of GOMOS instrument on board the ENVISAT satellite. Four simple models are used simultaneously to describe the dependence of the aerosol cross-sections on wavelength. During the AARJ estimation all the models are used and we obtain a probability distribution characterizing how probable each model is. By using model averaging, the uncertainty related to selecting the aerosol model can be taken into account in assessing the uncertainty of the estimates.

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