An Information-Theoretic Alternative to Generalized Method of Moments Estimation

Kitamura, Yuichi; Stutzer, Michael J.

doi:10.2307/2171942

Cited by 452 publications

(469 citation statements)

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“…For the speci cation test described at the end of the preceding subsection, we could in principle have relied on the information theoretic alternative to GMM due to Kitamura and Stutzer (1997), who consider solving the sample analog of the unconstrained problem where k ( ) is a given nite-dimensional vector-valued function. Note that neither VaR measure nests the other, and traditional nested hypothesis testing cannot be used for comparing these two VaR measures.…”

Section: Nonnested Var Comparisonmentioning

confidence: 99%

Testing and comparing Value-at-Risk measures

Christoffersen

Hahn

Inoue

2001

Journal of Empirical Finance

176

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Section: Nonnested Var Comparisonmentioning

confidence: 99%

Testing and comparing Value-at-Risk measures

Christoffersen

Hahn

Inoue

2001

Journal of Empirical Finance

176

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“…The GEL estimator is then defined aŝ β = arg min β∈B sup λ∈Λn(β)P n (β, λ) , (2.4) whereΛ n (β) = {λ : λ 0 g i (β) ∈ V, i = 1, ..., n}; see NS andSmith (1997, 2001). EL and ET estimators are obtained with ρ(v) = log(1 − v) and V = (−∞, 1) [Qin and Lawless (1994), Smith (1997)] and ρ(·) = − exp(v) [Kitamura and Stutzer, 1997, Imbens et al, 1998, Smith, 1997 whereas CUEβ CUE = arg min β∈Bĝ (β) 0Ω (β) −1ĝ (β) [Pakes andPollard, 1989, Hansen et al, 1996] is a GEL estimator when ρ(·) is quadratic [NS,Theorem 2.1,p.223]. Moreover, MD estimators [Corcoran, 1998] are GEL if the discrepancy function belongs to the Cressie and Read (1984) family [NS,Theorem 2.2,p.224].…”

Section: Gmm and Gelmentioning

confidence: 99%

“…7 A consistency proof for ET is given in Kitamura and Stutzer (1997) which also does not require moment indicator differentiability.…”

Section: Asymptotic Propertiesmentioning

confidence: 99%

“…[9] Imbens et al (1998), Kitamura and Stutzer (1997) and Smith (1997Smith ( , 2000Smith ( , 2001, have proposed alternative test statistics based on classical principles. Theorem 3.1 shows that these statistics are also valid when the moment conditions are non-smooth.…”

Section: Overidentifying Moment Conditionsmentioning

confidence: 99%

“…A number of authors have considered GEL-based tests of additional moment and parametric restrictions based on GEL and its variants. See, e.g., Kitamura and Stutzer (1997) and Smith (1997Smith ( , 2000Smith ( , 2001.…”

Section: Specification Testsmentioning

confidence: 99%

See 2 more Smart Citations

Gel Methods for Nonsmooth Moment Indicators

Parente

Smith

2010

Econom. Theory

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This paper considers the first order large sample properties of the GEL class of estimators for models specified by non-smooth indicators. The GEL class includes a number of estimators recently introduced as alternatives to the efficient GMM estimator which may suffer from substantial biases in finite samples. These include EL, ET and the CUE. This paper also establishes the validity of tests suggested in the smooth moment indicators case for over-identifying restrictions and specification. In particular, a number of these tests avoid the necessity of providing an estimator for the Jacobian matrix which may be problematic for the sample sizes typically encountered in practice.JEL Classification: C13, C30

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Power Divergence Methods

Imrey

2005

Encyclopedia of Biostatistics

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Power divergences are measures of discrepancy between two distributions, with roots in information theory. For two multinomials with common support, the power divergence of order λ is based on the weighted sum ∑ i p j ( p j / q j ) λ of exponentiated ratios of the probabilities p j , q j respectively assigned to the j th possible outcome. Note that these measures are directional rather than symmetric. The limiting logarithmic forms as λ → 0 or −1 are also considered power divergences. Asymptotically chi‐square goodness‐of‐fit statistics for count data are generally multiples of power divergences, and hence, general theoretical results and computational approaches for the power‐divergence family apply to these statistics and to estimators that minimize them. In particular, comparisons within this framework of tests and estimators based on the Pearson, Neyman, Freeman–Tukey, likelihood ratio, and discrimination information chi‐square statistics have shed considerable light on their absolute and relative performance in small sample settings, sparse contingency tables, and in the presence of outlying or zero counts. The “Cressie–Read” statistic, for which λ = 2/3, has been suggested as a possible replacement for the classical test statistics due to its good performance from several perspectives. This article defines the power divergence class of goodness‐of‐fit statistics and associated estimators, summarizes some basic comparative results, and briefly surveys the increasing use of power divergence in various statistical estimation settings.

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An Information-Theoretic Alternative to Generalized Method of Moments Estimation

Cited by 452 publications

References 0 publications

Testing and comparing Value-at-Risk measures

Testing and comparing Value-at-Risk measures

Gel Methods for Nonsmooth Moment Indicators

Power Divergence Methods

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