Asymptotic Approximations to Distributions

Wallace, David

doi:10.1214/aoms/1177706528

Cited by 247 publications

(119 citation statements)

References 47 publications

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“…This follows from general results on the expansions of cumulants in Wallace (1958), Bhattacharya and Ghosh (1978) and Hall (1992). It now follows from Theorem 1 of Mykland (1999) that k p 0 for p > 3 when T n R n .…”

Section: Introductionmentioning

confidence: 63%

Likelihood Computations without Bartlett Identities

Mykland

2001

Bernoulli

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The signed square root statistic R is given by sgn(, where l is the log-likelihood and è is the maximum likelihood estimator. The pth cumulant of R is typically of the form n À pa2 k p O(n À( p2)a2 ), where n is the number of observations. This paper shows how to symbolically compute k p without invoking the Bartlett identities. As an application, we show how the family of alternatives in¯uences the coverage accuracy of R.

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Section: Introductionmentioning

confidence: 63%

Likelihood Computations without Bartlett Identities

Mykland

2001

Bernoulli

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“…The HPs also constitute the basis of the Edgeworth and Gram-Charlier (Type A) series, which allow, under certain regularity conditions (Cramér 1925), the expression of any pdf, ( ), in terms of an infinite series (Wallace, 1958) as follows 2…”

Section: The Snp Distributionmentioning

confidence: 99%

The Productivity of Top Researchers: A Semi-Nonparametric Approach

2016

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Research productivity distributions exhibit heavy tails because it is common for a few researchers to accumulate the majority of the top publications and their corresponding citations. Measurements of this productivity are very sensitive to the field being analyzed and the distribution used. In particular, distributions such as the lognormal distribution seem to systematically underestimate the productivity of the top researchers. In this article, we propose the use of a (log)semi-nonparametric distribution (log-SNP) that nests the lognormal and captures the heavy tail of the productivity distribution through the introduction of new parameters linked to high-order moments. To compare the results,

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“…The typical situation for an asymptotically normal statistic T n is that the p'th cumulant, p ≥ 2, is of order O(n −(p−2)/2 ), see, for example, Chapters 2.3-2.4 of Hall (1992), along with Wallace (1958), Bhattacharya and Ghosh (1978), and the discussion in Mykland (2001) and the references therein. While the typical situation does remain in effect for realized volatility in the no-noise and no-leverage case (which is, after all, a matter simply of observations that are independent but non-identically distributed), the picture changes for more complex statistics.…”

Section: The Form Of the Edgeworth Expansion In Terms Of Cumulantsmentioning

confidence: 99%

Edgeworth expansions for realized volatility and related estimators

Zhang

Mykland

Aı̈t-Sahalia

2011

Journal of Econometrics

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This paper shows that the asymptotic normal approximation is often insufficiently accurate for volatility estimators based on high frequency data. To remedy this, we derive Edgeworth expansions for such estimators. The expansions are developed in the framework of small-noise asymptotics. The results have application to Cornish-Fisher inversion and help setting intervals more accurately than those relying on normal distribution.

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Asymptotic Approximations to Distributions

Cited by 247 publications

References 47 publications

Likelihood Computations without Bartlett Identities

Likelihood Computations without Bartlett Identities

The Productivity of Top Researchers: A Semi-Nonparametric Approach

Edgeworth expansions for realized volatility and related estimators

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