Local Properties of Distributions of
                    Stochastic Functionals

Davydov, Youri; Lifshits, Mikhail; Smorodina, N. V.

doi:10.1090/mmono/173

Cited by 98 publications

(113 citation statements)

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“…The continuity of the distribution function L on (0 ∞) follows from Davydov, Lifshits, and Smorodina (1998) and from the assumption that the covariance function of G is nondegenerate, i.e., inf θ∈Θ Var(G(θ)) > 0. The probability that L is greater than zero is equal to the probability that max j sup θ∈Θ G j (θ) > 0, which is greater than the probability that G j (θ ) > 0 for some fixed j and θ , but the latter is equal to 1/2.…”

Section: Appendix C: Proofsmentioning

confidence: 99%

Inference on sets in finance

Chernozhukov

Kocatulum²,

Menzel

2015

Quantitative Economics

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We consider the problem of inference on a class of sets describing a collection of admissible models as solutions to a single smooth inequality. Classical and recent examples include the Hansen-Jagannathan sets of admissible stochastic discount factors, Markowitz-Fama mean-variance sets for asset portfolio returns, and the set of structural elasticities in Chetty's (2012) analysis of demand with optimization frictions. The econometric structure of the problem allows us to construct convenient and powerful confidence regions based on the weighted likelihood ratio and weighted Wald statistics. Our statistics differ from existing statistics in that they enforce either exact or first-order equivariance to transformations of parameters, making them especially appealing in the target applications. We show that the resulting inference procedures are more powerful than the structured projection methods. Last, our framework is also useful for analyzing intersection bounds, namely sets defined as solutions to multiple smooth inequalities, since multiple inequalities can be conservatively approximated by a single smooth inequality. We present two empirical examples showing how the new econometric methods are able to generate sharp economic conclusions.

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Section: Appendix C: Proofsmentioning

confidence: 99%

Inference on sets in finance

Chernozhukov

Kocatulum²,

Menzel

2015

Quantitative Economics

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“…For the equations with an additive noise, such a differentiability holds true without a specific moment condition (see [14], [19]). Thus, we can apply the results obtained in [13] to the solution to (8), not requiring the moment condition (1.1) [13] to hold true. Statement A of Theorem 1.1 [13] is formulated in the terms of a certain subspace generated by a sequence of vector fields, associated with the initial equation.…”

Section: Proof Let Us Prove the Implication (I) ⇒ (Ii) Under Supposimentioning

confidence: 99%

“…Statement A of Theorem 1.1 [13] is formulated in the terms of a certain subspace generated by a sequence of vector fields, associated with the initial equation. In the partial case of a linear equation (8), these fields are defined as…”

Section: Proof Let Us Prove the Implication (I) ⇒ (Ii) Under Supposimentioning

confidence: 99%

“…Write W = W 1 + W 2 , Z = Z 1 + Z 2 , W 2 = 0, Z 2 (t) = t 0 u R d >1 uν(ds, du), and denote X 1,2 the solutions to SDE of the type (8) with W, Z replaced by W 1,2 , Z 1,2 , respectively. Then the solution to (8) has the form X = X 1 + X 2 , and X 1 , X 2 are independent. The density p X(t) is equal p X(t) (x) = R m p X 1 (t) (x − y)µ X 2 (t) (dy), x ∈ R m , where µ X 2 (t) denotes the law of X 2 (t).…”

Section: Asymptotic Properties Of the Derivatives Of The Distributionmentioning

confidence: 99%

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Conditions for the existence and smoothness of the distribution density of the Ornstein–Uhlenbeck process with Lévy noise

Bodnarchuk

Kulik

2009

Theor. Probability and Math. Statist.

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“…(Continuity of the Limit Distributions). The continuity of the distribution function L on (0, ∞) follows from Davydov et al (1998) and from the assumption that 40 the covariance function of G is non-degenerate, i.e. inf θ∈Θ Var(G(θ)) > 0.…”

Section: It Follows From Lemma 4 Thatmentioning

confidence: 99%

Inference on sets in finance

Chernozhukov¹,

Kocatulum²,

Menzel³

2012

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Standard-Nutzungsbedingungen:Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden.Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen.Sofern die Verfasser die Dokumente unter Open-Content-Lizenzen (insbesondere CC-Lizenzen) zur Verfügung gestellt haben sollten, gelten abweichend von diesen Nutzungsbedingungen die in der dort genannten Lizenz gewährten Nutzungsrechte. Abstract. In this paper we consider the problem of inference on a class of sets describing a collection of admissible models as solutions to a single smooth inequality. Classical and recent examples include, among others, the Hansen-Jagannathan (HJ) sets of admissible stochastic discount factors, Markowitz-Fama (MF) sets of meanvariances for asset portfolio returns, and the set of structural elasticities in Chetty (2012)'s analysis of demand with optimization frictions. We show that the econometric structure of the problem allows us to construct convenient and powerful confidence regions based upon the weighted likelihood ratio and weighted Wald (directed weighted Hausdorff) statistics. The statistics we formulate differ (in part) from existing statistics in that they enforce either exact or first order equivariance to transformations of parameters, making them especially appealing in the target applications. Moreover, the resulting inference procedures are also more powerful than the structured projection methods, which rely upon building confidence sets for the frontier-determining sufficient parameters (e.g. frontier-spanning portfolios), and then projecting them to obtain confidence sets for HJ sets or MF sets. Lastly, the framework we put forward is also useful for analyzing intersection bounds, namely sets defined as solutions to multiple smooth inequalities, since multiple inequalities can be conservatively approximated by a single smooth inequality. We present two empirical examples that show how the new econometric methods are able to generate sharp economic conclusions. Terms of use: Documents in

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Local Properties of Distributions of Stochastic Functionals

Cited by 98 publications

References 0 publications

Inference on sets in finance

Inference on sets in finance

Conditions for the existence and smoothness of the distribution density of the Ornstein–Uhlenbeck process with Lévy noise

Inference on sets in finance

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