Greatest lower bound to the elliptical theory kurtosis parameter

Bentler, Peter M.; Berkane, Maia

doi:10.1093/biomet/73.1.240

Cited by 36 publications

(16 citation statements)

References 7 publications

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“…where H = (X V −1 22 X) −1 and Q = e V −1 22 e. The misspecification adjustment term (1 + κ)QHṼ −1 11 H is positive semidefinite in this case since 1 + κ > 0 (see Bentler and Berkane (1986)) and V −1 11 is positive definite. Note that the adjustment term is positively related to the aggregate pricing-error measure Q and the kurtosis parameter κ.…”

Section: Asymptotic Distribution Ofγ Under Potentially Misspecifiementioning

confidence: 93%

Pricing Model Performance and the Two-Pass Cross-Sectional Regression Methodology

Kan¹,

Robotti²,

Shanken³

2009

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Since Black, Jensen, and Scholes (1972) and Fama and MacBeth (1973), the two-pass cross-sectional regression (CSR) methodology has become the most popular approach for estimating and testing asset pricing models. Statistical inference with this method is typically conducted under the assumption that the models are correctly specified, i.e., expected returns are exactly linear in asset betas. This can be a problem in practice since all models are, at best, approximations of reality and are likely to be subject to a certain degree of misspecification. We propose a general methodology for computing misspecification-robust asymptotic standard errors of the risk premia estimates. We also derive the asymptotic distribution of the sample CSR R2 and develop a test of whether two competing beta pricing models have the same population R2. This provides a formal alternative to the common heuristic of simply comparing the R2 estimates in evaluating relative model performance. Finally, we provide an empirical application which demonstrates the importance of our new results when applied to a variety of asset pricing models.

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Section: Asymptotic Distribution Ofγ Under Potentially Misspecifiementioning

confidence: 93%

Pricing Model Performance and the Two-Pass Cross-Sectional Regression Methodology

Kan¹,

Robotti²,

Shanken³

2009

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show abstract

“…where H = (X V −1 22 X) −1 and Q = e V −1 22 e. The misspecification adjustment term (1 + κ)QHṼ −1 11 H is positive semidefinite in this case since 1 + κ > 0 (see Bentler and Berkane (1986)…”

mentioning

confidence: 98%

Pricing Model Performance and the Two-Pass Cross-Sectional Regression Methodology

Kan

Robotti²,

Shanken

2012

SSRN Journal

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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: Since Black, Jensen, and Scholes (1972) and Fama and MacBeth (1973), the two-pass cross-sectional regression (CSR) methodology has become the most popular approach for estimating and testing asset pricing models. Statistical inference with this method is typically conducted under the assumption that the models are correctly specified, that is, expected returns are exactly linear in asset betas. This assumption can be a problem in practice since all models are, at best, approximations of reality and are likely to be subject to a certain degree of misspecification. We propose a general methodology for computing misspecification-robust asymptotic standard errors of the risk premia estimates. We also derive the asymptotic distribution of the sample CSR R 2 and develop a test of whether two competing linear beta pricing models have the same population R 2. This test provides a formal alternative to the common heuristic of simply comparing the R 2 estimates in evaluating relative model performance. Finally, we provide an empirical application, which demonstrates the importance of our new results when applied to a variety of asset pricing models. JEL classification: G12

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“…Further, due to the definition of the upper bound on q i , it can be shown that q s > 2ns holds. For a scalar random variable, the constraint κ 1 (L 4 11 ) > 1 implies that the kurtosis is greater than unity, which is always true for elliptic distributions [19].…”

Section: Algorithm For Generating Sigma Pointsmentioning

confidence: 99%

A new algorithm for latent state estimation in non-linear time series models

Date

Jalen

Mamon

2008

Applied Mathematics and Computation

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We consider the problem of optimal state estimation for a wide class of nonlinear time series models. A modified sigma point filter is proposed, which uses a new procedure for generating sigma points. Unlike the existing sigma point generation methodologies in engineering where negative probability weights may occur, we develop an algorithm capable of generating sample points that always form a valid probability distribution while still allowing the user to sample using a random number generator. The effectiveness of the new filtering procedure is assessed through simulation examples.

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Greatest lower bound to the elliptical theory kurtosis parameter

Cited by 36 publications

References 7 publications

Pricing Model Performance and the Two-Pass Cross-Sectional Regression Methodology

Pricing Model Performance and the Two-Pass Cross-Sectional Regression Methodology

Pricing Model Performance and the Two-Pass Cross-Sectional Regression Methodology

A new algorithm for latent state estimation in non-linear time series models

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