Asymptotic Properties of the Weighted-average Least Squares (WALS) Estimator PDF Download
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Author: Giuseppe De Luca
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ISBN:
Category :
Languages : en
Pages :
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We investigate the asymptotic behavior of the WALS estimator, a model-averaging estimator with attractive finite-sample and computational properties. WALS is closely related to the normal location model, and hence much of the paper concerns the asymptotic behavior of the estimator of the unknown mean in the normal local model. Since we adopt a frequentist-Bayesian approach, this specializes to the asymptotic behavior of the posterior mean as a frequentist estimator of the normal location parameter. We emphasize two challenging issues. First, our definition of ignorance in the Bayesian step involves a prior on the t-ratio rather than on the parameter itself. Second, instead of assuming a local misspecification framework, we consider a standard asymptotic setup with fixed parameters. We show that, under suitable conditions on the prior, the WALS estimator is √n-consistent and its asymptotic distribution essentially coincides with that of the unrestricted least-squares estimator. Monte Carlo simulations confirm our theoretical results.
Author: Giuseppe De Luca
Publisher:
ISBN:
Category :
Languages : en
Pages :
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Book Description
We investigate the asymptotic behavior of the WALS estimator, a model-averaging estimator with attractive finite-sample and computational properties. WALS is closely related to the normal location model, and hence much of the paper concerns the asymptotic behavior of the estimator of the unknown mean in the normal local model. Since we adopt a frequentist-Bayesian approach, this specializes to the asymptotic behavior of the posterior mean as a frequentist estimator of the normal location parameter. We emphasize two challenging issues. First, our definition of ignorance in the Bayesian step involves a prior on the t-ratio rather than on the parameter itself. Second, instead of assuming a local misspecification framework, we consider a standard asymptotic setup with fixed parameters. We show that, under suitable conditions on the prior, the WALS estimator is √n-consistent and its asymptotic distribution essentially coincides with that of the unrestricted least-squares estimator. Monte Carlo simulations confirm our theoretical results.
Author: Giuseppe De Luca
Publisher:
ISBN:
Category :
Languages : en
Pages : 36
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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 the finite sample properties of this estimator by a Monte Carlo experiment whose design is based on the real empirical analysis of attrition in the first two waves of the Survey of Health, Ageing and Retirement in Europe (SHARE).
Author: Stanford University. Department of Statistics
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ISBN:
Category : Time-series analysis
Languages : en
Pages : 318
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The author considers estimation procedures for the moving average model of order q. Walker's method uses k sample autocovariances (k> or = q). Assume that k depends on T in such a way that k nears infinity as T nears infinity. The estimates are consistent, asymptotically normal and asymptotically efficient if k = k (T) dominates log T and is dominated by (T sub 1/2). The approach in proving these theorems involves obtaining an explicit form for the components of the inverse of a symmetric matrix with equal elements along its five central diagonals, and zeroes elsewhere. The asymptotic normality follows from a central limit theorem for normalized sums of random variables that are dependent of order k, where k tends to infinity with T. An alternative form of the estimator facilitates the calculations and the analysis of the role of k, without changing the asymptotic properties.
Author: Virendra K. Srivastava
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ISBN:
Category : Econometrics
Languages : en
Pages : 18
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Author: Raymond J. Carroll
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ISBN:
Category :
Languages : en
Pages : 19
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This document considers a heteroscedastic linear regression model with replication. To estimate the variances, one can use the sample variances or the sample average squared errors from a regression fit. The authors study the large sample properties of these weighted least squares estimates with estimated weights when the number of replicates is small. The estimates are generally inconsistent for asymmetrically distributed data. If sample variances are used based on m replicates, the weighted least squares estimates are inconsistent for m=2 replicates even when the data are normally distributed. With between 3 and 5 replicates, the rates of convergence are slower than the usual square root of N. With m> or = 6 replicates, the effect of estimating the weights is to increase variances by (m-5)/(m-3), relative to weighted least squares estimates with known weights. (KR).
Author: Katsuto Tanaka
Publisher:
ISBN: 9780868311517
Category : Econometric models
Languages : en
Pages : 38
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Author: Phoebus J. Dhrymes
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ISBN:
Category :
Languages : en
Pages : 36
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Author: J.R Magnus
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ISBN:
Category :
Languages : en
Pages : 0
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Model averaging has become a popular method of estimation, following increasing evidence that model selection and estimation should be treated as one joint procedure. Weighted-average least squares (WALS) is a recent model-average approach, which takes an intermediate position between frequentist and Bayesian methods, allows a credible treatment of ignorance, and is extremely fast to compute. We review the theory of WALS and discuss extensions and applications.
Author: Anders Klevmarken
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ISBN:
Category :
Languages : en
Pages : 22
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Author: Michael Mohr
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Category :
Languages : de
Pages : 25
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