Search results for "Statistics::Methodology"
showing 10 items of 71 documents
Recent Advances in Bayesian Inference in Cosmology and Astroparticle Physics Thanks to the MultiNest Algorithm
2012
We present a new algorithm, called MultiNest, which is a highly efficient alternative to traditional Markov Chain Monte Carlo (MCMC) sampling of posterior distributions. MultiNest is more efficient than MCMC, can deal with highly multi-modal likelihoods and returns the Bayesian evidence (or model likelihood, the prime quantity for Bayesian model comparison) together with posterior samples. It can thus be used as an all-around Bayesian inference engine. When appropriately tuned, it also provides an exploration of the profile likelihood that is competitive with what can be obtained with dedicated algorithms.
On the Efficiency of Affine Invariant Multivariate Rank Tests
1998
AbstractIn this paper the asymptotic Pitman efficiencies of the affine invariant multivariate analogues of the rank tests based on the generalized median of Oja are considered. Formulae for asymptotic relative efficiencies are found and, under multivariate normal and multivariatetdistributions, relative efficiencies with respect to Hotelling'sT2test are calculated.
Upport vector machines for nonlinear kernel ARMA system identification.
2006
Nonlinear system identification based on support vector machines (SVM) has been usually addressed by means of the standard SVM regression (SVR), which can be seen as an implicit nonlinear autoregressive and moving average (ARMA) model in some reproducing kernel Hilbert space (RKHS). The proposal of this letter is twofold. First, the explicit consideration of an ARMA model in an RKHS (SVM-ARMA 2k) is proposed. We show that stating the ARMA equations in an RKHS leads to solving the regularized normal equations in that RKHS, in terms of the autocorrelation and cross correlation of the (nonlinearly) transformed input and output discrete time processes. Second, a general class of SVM-based syste…
Regression with imputed covariates: A generalized missing-indicator approach
2011
A common problem in applied regression analysis is that covariate values may be missing for some observations but imputed values may be available. This situation generates a trade-off between bias and precision: the complete cases are often disarmingly few, but replacing the missing observations with the imputed values to gain precision may lead to bias. In this paper, we formalize this trade-off by showing that one can augment the regression model with a set of auxiliary variables so as to obtain, under weak assumptions about the imputations, the same unbiased estimator of the parameters of interest as complete-case analysis. Given this augmented model, the bias-precision trade-off may the…
A Test of Covariance-Matrix Forecasting Methods
2015
Providing a more accurate covariance matrix forecast can substantially improve the performance of optimized portfolios. Using out-of-sample tests, in this article the author evaluates alternative covariance matrix-forecasting methods by looking at: (1) their forecast accuracy, (2) their ability to track the volatility of a minimum-variance portfolio, and (3) their ability to keep the volatility of a minimum-variance portfolio at a target level. The author finds large differences between the methods. The results suggest that shrinking the sample covariance matrix improves neither the forecast accuracy nor the performance of minimum-variance portfolios. In contrast, switching from the sample …
Estimating Engel curves under unit and item nonresponse
2010
SUMMARY This paper estimates food Engel curves using data from the first wave of the Survey on Health, Aging and Retirement in Europe (SHARE). Our statistical model simultaneously takes into account selectivity due to unit and item nonresponse, endogeneity problems, and issues related to flexible specification of the relationship of interest. We estimate both parametric and semiparametric specifications of the model. The parametric specification assumes that the unobservables in the model follow a multivariate Gaussian distribution, while the semiparametric specification avoids distributional assumptions about the unobservables. Copyright © 2011 John Wiley & Sons, Ltd.
Sampling properties of the Bayesian posterior mean with an application to WALS estimation
2022
Many statistical and econometric learning methods rely on Bayesian ideas, often applied or reinterpreted in a frequentist setting. Two leading examples are shrinkage estimators and model averaging estimators, such as weighted-average least squares (WALS). In many instances, the accuracy of these learning methods in repeated samples is assessed using the variance of the posterior distribution of the parameters of interest given the data. This may be permissible when the sample size is large because, under the conditions of the Bernstein--von Mises theorem, the posterior variance agrees asymptotically with the frequentist variance. In finite samples, however, things are less clear. In this pa…
B-Spline Estimation in a Survey Sampling Framework
2021
Nonparametric regression models have been used more and more over the last years to model survey data and incorporate efficiently auxiliary information in order to improve the estimation of totals, means or other study parameters such as Gini index or poverty rate. B-spline nonparametric regression has the benefit of being very flexible in modeling nonlinear survey data while keeping many similarities and properties of the classical linear regression. This method proved to be efficient for deriving a unique system of weights which allowed to estimate in an efficient way and simultaneously many study parameters. Applications on real and simulated survey data showed its high efficiency. This …
Imputation Procedures in Surveys Using Nonparametric and Machine Learning Methods: An Empirical Comparison
2020
Abstract Nonparametric and machine learning methods are flexible methods for obtaining accurate predictions. Nowadays, data sets with a large number of predictors and complex structures are fairly common. In the presence of item nonresponse, nonparametric and machine learning procedures may thus provide a useful alternative to traditional imputation procedures for deriving a set of imputed values used next for the estimation of study parameters defined as solution of population estimating equation. In this paper, we conduct an extensive empirical investigation that compares a number of imputation procedures in terms of bias and efficiency in a wide variety of settings, including high-dimens…
Weighted-average least squares estimation of generalized linear models
2018
The weighted-average least squares (WALS) approach, introduced by Magnus et al. (2010) in the context of Gaussian linear models, has been shown to enjoy important advantages over other strictly Bayesian and strictly frequentist model averaging estimators when accounting for problems of uncertainty in the choice of the regressors. In this paper we extend the WALS approach to deal with uncertainty about the specification of the linear predictor in the wider class of generalized linear models (GLMs). We study the large-sample properties of the WALS estimator for GLMs under a local misspecification framework that allows the development of asymptotic model averaging theory. We also investigate t…