An MCMC approach to classical estimation

By Victor Chernozhukov, Han Hong. 2003

839 citations recorded by the source corpus.

This paper studies computationally and theoretically attractive estimators called here Laplace type estimators (LTEs), which include means and quantiles of quasi-posterior distributions defined as transformations of general (nonlikelihood-based) statistical criterion functions, such as those in GMM, nonlinear IV, empirical likelihood, and minimum distance methods. The approach generates an alternative to classical extremum estimation and also falls outside the parametric Bayesian approach. For example, it offers a new attractive estimation method for such important semi-parametric problems as censored and instrumental quantile regression, nonlinear GMM and value-at-risk models. The LTEs are computed using Markov Chain Monte Carlo methods, which help circumvent the computational curse of dimensionality. A large sample theory is obtained and illustrated for regular cases.

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Citations in the corpus

Finite Sample Bernstein -- von Mises Theorem for Semiparametric Problems (2013, methodology): “log dIP˛ d 0 (Y) is the log-likelihood function of the family (IP ˛) for some dominating measure 0 . Under model misspecication, ˛ denes the best parametric t to IP by the considered family; cf. Chernozhukov and Hong (2003), Kleijn and van der Vaart (2006, 2012) and references therein. The target ”
Bernstein - von Mises Theorem for growing parameter dimension (2013, methodology): “In this sense, the Bayes formula (1.4) describes a quasi posterior ; cf. Chernozhukov and Hong (2003).”
Bayesian fractional posteriors (2016, methodology): “The fractional posteriors are a special instance of Gibbs posteriors [31] or quasi-posteriors [15], where the negative exponent of a loss function targeted towards a specific parameter of interest is used as a surrogate for the likelihood function; see [10] for a general framework for updating of pr”
Bayesian Mode Regression (2012, background): “…chain, S , is drawn from the posterior distribution, p ( β data where N is the number of draws after burn-in, a consistent estimate of the inverse of the covariance matrix cov ˆ β can be obtained by multiplying by N the variance-covariance matrix of this MCMC sequence (Chernozhukov and Hong, 2003).”
Tapered Covariance: Bayesian Estimation and Asymptotics (2012, background): “Theorem 5 (Theorem 4 of Chernozhukov and Hong (2003)).”
Code and data files for "Oil Price Shocks and the Optimality of Monetary Policy" (2010, methodology): “I also estimate the key structural parameters of the model by applying the Markov Chain Monte Carlo (MCMC) estimation approach of Chernozhukov and Hong (2003) to the Impulse Response Function Matching estimator.”
Smoothing Quantile Regressions (2019, methodology): “…now boasts a wide array of techniques to tackle this issue, including bootstrapping (Horowitz 1998; Machado and Parente 2005), MCMC methods (Chernozhukov and Hong 2003), empirical likelihood (Whang 2006; Otsu 2008), strong approximation methods (Portnoy 2012), nonstandard inference (Goh…”
Quantiles via moments (2019, methodology): “Although several promising approaches to this problem have been developed, as far as we know, all of them have unappealing features such as requiring the tuning of the optimization algorithm (Chernozhukov and Hong, 2003), the selection of tolerance parameters (Xu”
Critical dimension in the semiparametric Bernstein—von Mises theorem (2014, background): “Under model misspecification, υ∗ defines the best parametric fit to P by the considered family (see [11, 19, 20] and references therein).”
Successful Austerity in the United States, Europe and Japan (2012, unknown): “2 Woodford (2011) and Christiano et al. (2011) theoretical analysis focuses on government spending multipliers when zero lower bound (ZLB) on nominal interest rates is binding.”
Communication-efficient distributed statistical learning (2016, methodology): “In this big data paradigm, it is natural to consider methods that split the dataset across multiple machines and conduct statistical inference in a distributed manner, in either the frequentist framework of obtaining a pointestimator Duchi et al. [2012], Zhang et al. [2013a], Zhang and Lin [2015], K”
Gibbs sampling methods for Bayesian quantile regression (2011, unknown): “In addition, recent work by Chernozhukov and Hong [33] provides a theoretical justification for our approach in a large sample.”
Robust priors in nonlinear panel data models (2007, background): “The thick line shows the integrated likelihood with prior given by the formula (16), obtained using expected quantities.”
Posterior Inference in Bayesian Quantile Regression with Asymmetric Laplace Likelihood (2016, methodology): “International Statistical Review © 2015 International Statistical Institute. adjustments can be attributed to the work of Chernozhukov & Hong (2003), but we feel that the need for adjustments is not widely appreciated yet.”