Valid Locally Uniform Edgeworth Expansions for a Class of Weakly Dependent Processes or Sequences of Smooth Transformations

Arvanitis, Stelios; Demos, Antonis

doi:10.1515/jtse-2012-0003

Cited by 3 publications

(21 citation statements)

References 28 publications

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“…a Theorem of Invariance of validity of Edgeworth approximations with respect to sequences of smooth transformations (see also Bhattacharya and Ghosh [8] in an iid framework, where the transformation examined is independent of n). This methodology is justi…ed by lemmas AL.4 and AL.5 in the second part of the appendix (for analytical proofs of these results see Arvanitis and Demos [5]).…”

Section: Validity Of Edgeworth Approximationsmentioning

confidence: 99%

“…pr i;j (x) = (x i ; x i+1 ; :::; x j ) 0 , where naturally 1 i j r. Finally whenever the assertion "locally" appears in the sequel it implies "for all 2 O " ( 0 )" unless otherwise speci…ed. 5 Assumption A.6 c n is uniformly consistent for b ( ) with rate o n a , i.e. This assumption along with the boundeness of B enables the uniform convergence of E c n to b ( ), hence the establishment of the analogous property for the GMR2 estimator.…”

Section: Assumptions Specific To the Validity Of The Edgeworth Approximationsmentioning

confidence: 99%

“…For notational simplicity and without any risk of error, in what follows B C generically denotes the class of convex Borel subsets of any of those spaces. De…nition D. 5 We say that a sequence of random elements (S n ( )) n2N with values in some …nite dimensional Euclidean space has an Edgeworth expansion of order s if there exists an Edgeworth measure n;s ( ) of order s such that…”

Section: Assumptions Specific To the Validity Of The Edgeworth Approximationsmentioning

confidence: 99%

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On the Validity of Edgeworth Expansions and Moment Approximations for Three Indirect Inference Estimators

Arvanitis

Demos²

2016

Journal of Econometric Methods

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This paper deals with higher order asymptotic properties for three indirect inference estimators. We provide conditions that ensure the validity of locally uniform, with respect to the parameter, Edgeworth approximations. When these are of sufficiently high order they also form integrability conditions that validate locally uniform moment approximations. We derive the relevant second order bias and MSE approximations for the three estimators as functions of the respective approximations for the auxiliary estimator. We confirm that in the special case of deterministic weighting and affinity of the binding function, one of them is second order unbiased. The other two estimators do not have this property under the same conditions. Moreover, in this case, the second order approximate MSEs imply the superiority of the first estimator. We generalize to multistep procedures that provide recursive indirect inference estimators which are locally uniformly unbiased at any given order. Furthermore, in a particular case, we manage to validate locally uniform Edgeworth expansions for one of the estimators without any differentiability requirements for the estimating equations. We examine the bias-MSE results in a small Monte Carlo exercise.

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Section: Validity Of Edgeworth Approximationsmentioning

confidence: 99%

Section: Assumptions Specific To the Validity Of The Edgeworth Approximationsmentioning

confidence: 99%

Section: Assumptions Specific To the Validity Of The Edgeworth Approximationsmentioning

confidence: 99%

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On the Validity of Edgeworth Expansions and Moment Approximations for Three Indirect Inference Estimators

Arvanitis

Demos²

2016

Journal of Econometric Methods

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“…Gouriéroux et al (2000) have studied the sample bias correction properties of indirect inference. Arvanitis and Demos (2013) (see also Tauchen, 1996b, Arvanitis andDemos, 2014) define, within the framework of indirect inference, classes of estimators based on analytical approximations of either the binding or the score function of the auxiliary estimator. They study and compare their properties on the resulting bias convergence order.…”

Section: Introductionmentioning

confidence: 99%

Simulation-Based Bias Correction Methods for Complex Models

Guerrier

Dupuis-Lozeron

Victoria‐Feser

2018

Journal of the American Statistical Association

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Along the ever increasing data size and model complexity, an important challenge frequently encountered in constructing new estimators or in implementing a classical one such as the maximum likelihood estimator, is the computational aspect of the estimation procedure. To carry out estimation, approximate methods such as pseudo-likelihood functions or approximated estimating equations are increasingly used in practice as these methods are typically easier to implement numerically although they can lead to inconsistent and/or biased estimators.In this context, we extend and provide refinements on the known bias 1 correction properties of two simulation based methods, respectively indirect inference and bootstrap, each with two alternatives. These results allow one to build a framework defining simulation based estimators that can be implemented for complex models. Indeed, based on a biased or even inconsistent estimator, several simulation based methods can be used to define new estimators that are both consistent and with reduced finite sample bias. This framework includes the classical method of indirect inference for bias correction without requiring specification of an auxiliary model. We demonstrate the equivalence between one version of the indirect inference and the iterative bootstrap, both correct sample biases up to the order n −3 .The iterative method can be thought of as a computationally efficient algorithm to solve the optimization problem of the indirect inference.Our results provide different tools to correct the asymptotic as well as finite sample biases of estimators and give insight on which method should be applied for the problem at hand. The usefulness of the proposed approach is illustrated with the estimation of robust income distributions and generalized linear latent variable models.

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“…This is the methodology employed here. Theorem , in Appendix B, provides a set of sufficient conditions and it is a pointwise reformulation of Theorem 3.2 of Arvanitis and Demos (). Hence, the needed result rests upon the verification of the four conditions of the theorem (see the discussion in Appendix B for more details).…”

Section: Introductionmentioning

confidence: 99%

A class of indirect inference estimators: higher‐order asymptotics and approximate bias correction

Arvanitis

Demos

2015

The Econometrics Journal

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In this paper, we define a set of indirect inference estimators based on moment approximations of the auxiliary estimators. Their introduction is motivated by reasons of analytical and computational facilitation. Their definition provides an indirect inference framework for some classical bias correction procedures. We derive higher-order asymptotic properties of these estimators. We demonstrate that under our assumption framework, and in the special case of deterministic weighting and affinity of the binding function, these are second-order unbiased. Moreover, their second-order approximate mean square errors do not depend on the cardinality of the Monte Carlo or bootstrap samples that our definition might involve. Consequently, the second-order mean square error of the auxiliary estimator is not altered. We extend this to a class of multistep indirect inference estimators that have zero higher-order bias without increasing the approximate mean square error, up to the same order. Our theoretical results are also validated by three Monte Carlo experiments.

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Valid Locally Uniform Edgeworth Expansions for a Class of Weakly Dependent Processes or Sequences of Smooth Transformations

Cited by 3 publications

References 28 publications

On the Validity of Edgeworth Expansions and Moment Approximations for Three Indirect Inference Estimators

On the Validity of Edgeworth Expansions and Moment Approximations for Three Indirect Inference Estimators

Simulation-Based Bias Correction Methods for Complex Models

A class of indirect inference estimators: higher‐order asymptotics and approximate bias correction

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