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56
Integrated variance reduction strategies for simulation
 Operations Research
, 1996
"... We develop strategies for integrated use of certain wellknown variance reduction techniques to estimate a mean response in a finitehorizon simulation experiment. The building blocks for these integrated variance reduction strategies are the techniques of conditional expectation, correlation induc ..."
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Cited by 32 (2 self)
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We develop strategies for integrated use of certain wellknown variance reduction techniques to estimate a mean response in a finitehorizon simulation experiment. The building blocks for these integrated variance reduction strategies are the techniques of conditional expectation, correlation induction (including antithetic variates and Latin hypercube sampling), and control variates; and all pairings of these techniques are examined. For each integrated strategy, we establish sufficient conditions under which that strategy will yield a smaller response variance than its constituent variance reduction techniques will yield individually. We also provide asymptotic variance comparisons between many of the methods discussed, with emphasis on integrated strategies that incorporate Latin hypercube sampling. An experimental performance evaluation reveals that in the simulation of stochastic activity networks, substantial variance reductions can be achieved with these integrated strategies. Both the theoretical and experimental results indicate that superior performance is obtained via joint application of the techniques of conditional expectation and Latin hypercube sampling. Subject classifications: Simulation, efficiency: conditioning, control variates, correlation inArea of review: Simulation.
Unionintersection and samplesplit methods in econometrics with applications to SURE and MA models
, 1998
"... article. In this paper, we develop inference procedures (tests and confidence sets) for two apparently distinct classes of situations: first, problems of comparing or pooling information from several samples whose stochastic relationship is not specified; second, problems where the distributions of ..."
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Cited by 28 (17 self)
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article. In this paper, we develop inference procedures (tests and confidence sets) for two apparently distinct classes of situations: first, problems of comparing or pooling information from several samples whose stochastic relationship is not specified; second, problems where the distributions of standard test statistics are difficult to assess (e.g., because they involve unknown nuisance parameters), while it is possible to obtain more tractable distributional results for statistics based on appropriately chosen subsamples. A large number of econometric models lead to such situations, such as comparisons of regression equations when the relationship between the disturbances across equations is unknown or complicated: seemingly unrelated regression equations (SURE), regressions with moving average (MA) errors, etc. To deal with such problems, we propose a general approach which uses unionintersection techniques to combine tests (or confidence sets) based on different samples. In particular, we make a systematic use of BooleBonferroni inequalities to control the overall level of the procedure. This approach is easy to apply and transposable to a wide spectrum of models. In addition to being robust to various misspecifications of interest, the approach
Building Regression Cost Models for Multidatabase Systems
, 1996
"... A major challenge for performing global query optimization in a multidatabase system (MDBS) is the lack of cost models for local database systems at the global level. In this paper we present a statistical procedure based on multiple regression analysis for building cost models for local database sy ..."
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Cited by 20 (3 self)
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A major challenge for performing global query optimization in a multidatabase system (MDBS) is the lack of cost models for local database systems at the global level. In this paper we present a statistical procedure based on multiple regression analysis for building cost models for local database systems in an MDBS. Explanatory variables that can be included in a regression model are identified and a mixed forward and backward method for selecting significant explanatory variables is presented. Measures for developing useful regression cost models, such as removing outliers, eliminating multicollinearity, validating regression model assumptions, and checking significance of regression models, are discussed. Experimental results demonstrate that the presented statistical procedure can develop useful local cost models in an MDBS.
Flexible Parametric Measurement Error Models
 Biometrics
, 1999
"... SUMMARY. Inferences in measurement error models can be sensitive to modeling assumptions. Specifically, if the model is incorrect, the estimates can be inconsistent. To reduce sensitivity to modeling assumptions and yet still retain the efficiency of parametric inference, we propose using flexible p ..."
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Cited by 15 (2 self)
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SUMMARY. Inferences in measurement error models can be sensitive to modeling assumptions. Specifically, if the model is incorrect, the estimates can be inconsistent. To reduce sensitivity to modeling assumptions and yet still retain the efficiency of parametric inference, we propose using flexible parametric models that can accommodate departures from standard parametric models. We use mixtures of normals for this purpose. We study two cases in detail: a linear errorsinvariables model and a changepoint Berkson model.
Distributed variational inference in sparse Gaussian process regression and latent variable models
 In Cortes and Lawrence
, 2014
"... Abstract Gaussian processes (GPs) are a powerful tool for probabilistic inference over functions. They have been applied to both regression and nonlinear dimensionality reduction, and offer desirable properties such as uncertainty estimates, robustness to overfitting, and principled ways for tuni ..."
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Cited by 15 (1 self)
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Abstract Gaussian processes (GPs) are a powerful tool for probabilistic inference over functions. They have been applied to both regression and nonlinear dimensionality reduction, and offer desirable properties such as uncertainty estimates, robustness to overfitting, and principled ways for tuning hyperparameters. However the scalability of these models to big datasets remains an active topic of research. We introduce a novel reparametrisation of variational inference for sparse GP regression and latent variable models that allows for an efficient distributed algorithm. This is done by exploiting the decoupling of the data given the inducing points to reformulate the evidence lower bound in a MapReduce setting. We show that the inference scales well with data and computational resources, while preserving a balanced distribution of the load among the nodes. We further demonstrate the utility in scaling Gaussian processes to big data. We show that GP performance improves with increasing amounts of data in regression (on flight data with 2 million records) and latent variable modelling (on MNIST). The results show that GPs perform better than many common models often used for big data.
Structural estimation of highdimensional factor models
, 2007
"... We develop econometric theory for the estimation of large N, T factor models in structural macrofinance. We employ noncommutative probability theory to derive a new estimator for the number of latent factors based on the moments of the eigenvalue distribution of the empirical covariance matrix. Ou ..."
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Cited by 13 (2 self)
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We develop econometric theory for the estimation of large N, T factor models in structural macrofinance. We employ noncommutative probability theory to derive a new estimator for the number of latent factors based on the moments of the eigenvalue distribution of the empirical covariance matrix. Our test combines a minimum distance procedure for the estimation of structural model parameters with a specification test on the empirical eigenvalues to solve the problem of separating the factors from the noise. We also relate the second order unbiased estimation of factor loadings to instrumental variable methods where the number of instruments is large relative to the sample size, and derive a number of alternatives to principal components with excellent finite sample properties. Using a large dataset of international stock returns, we estimate global supply and demand shocks in a structural New Keynesian macrofinance model of the US economy. We uncover 23 global factors over the period 19732006, many of which impact the supply side of the US economy. We show that omitting these factors masks
Exact sample conditioned MSE performance of the Bayesian MMSE estimator for classification error—Part I: Representation
 IEEE Trans. Signal Process
, 2012
"... Abstract—In Part I of a two part study on the MSE performance of Bayesian error estimation, we have derived analytical expressions for MSE conditioned on the sample for Bayesian error estimators and arbitrary error estimators in two Bayesian models: discrete classification with Dirichlet priors and ..."
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Cited by 7 (2 self)
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Abstract—In Part I of a two part study on the MSE performance of Bayesian error estimation, we have derived analytical expressions for MSE conditioned on the sample for Bayesian error estimators and arbitrary error estimators in two Bayesian models: discrete classification with Dirichlet priors and linear classification of Gaussian distributions with normalinverseWishart priors. Here, in Part II, we examine the consistency of Bayesian error estimation and provide several simulation studies that illustrate the concept of conditional MSE and how it may be used in practice. A salient application is censored sampling, where sample points are collected one at a time until the conditional MSE reaches a stopping criterion. Index Terms—Bayesian estimation, classification, error estimation, genomics, minimum meansquare estimation, small samples.
On Monte Carlo methods for Bayesian multivariate regression models with heavytailed errors
 Journal of Multivariate Analysis
"... We consider Bayesian analysis of data from multivariate linear regression models whose errors have a distribution that is a scale mixture of normals. Such models are used to analyze data on financial returns, which are notoriously heavytailed. Let pi denote the intractable posterior density that re ..."
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Cited by 7 (3 self)
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We consider Bayesian analysis of data from multivariate linear regression models whose errors have a distribution that is a scale mixture of normals. Such models are used to analyze data on financial returns, which are notoriously heavytailed. Let pi denote the intractable posterior density that results when this regression model is combined with the standard noninformative prior on the unknown regression coefficients and scale matrix of the errors. Roughly speaking, the posterior is proper if and only if n ≥ d + k, where n is the sample size, d is the dimension of the response, and k is number of covariates. We provide a method of making exact draws from pi in the special case where n = d + k, and we study Markov chain Monte Carlo (MCMC) algorithms that can be used to explore pi when n> d+ k. In particular, we show how the Haar PXDA technology studied in Hobert and Marchev (2008) can be used to improve upon Liu’s (1996) data augmentation (DA) algorithm. Indeed, the new algorithm that we introduce is theoretically superior to the DA algorithm, yet equivalent to DA in terms of computational complexity. Moreover, we analyze the convergence rates of these MCMC algorithms in the important special case where the regression errors have a Student’s t distribution. We prove that, under conditions on n, d, k, and the degrees of freedom of the t distribution, both algorithms converge at a geometric rate. These convergence rate results are important from a practical standpoint because geometric ergodicity guarantees the existence of central limit theorems which are essential for the calculation of valid asymptotic standard errors for MCMC based estimates.
Use of principal component analysis with instrumental variables (PCAIV) to analyse fisheries catch data
 ICES J. Mar. Sci
, 1997
"... Principal Component Analysis with respect to Instrumental Variables (PCAIV) is a statistical tool for exploratory analysis combining both principal component analysis and multivariate regression analysis. This tool is used to analyse mean fortnightly catches obtained by Senegalese fishermen in two p ..."
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Cited by 6 (0 self)
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Principal Component Analysis with respect to Instrumental Variables (PCAIV) is a statistical tool for exploratory analysis combining both principal component analysis and multivariate regression analysis. This tool is used to analyse mean fortnightly catches obtained by Senegalese fishermen in two ports from 1975 to 1991. The aim of the study is to identify significant sources of variation and to present separately the impact of each of them. These descriptions are used to characterize the initial data.