An Alternative Asymptotic Analysis of Residual-Based Statistics

E. Andreou, B.J.M. Werker

Research output: Working paperDiscussion paperOther research output

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Abstract

This paper offers an alternative technique to derive the limiting distribution of residual-based statistics or, more general, the limiting distribution of statistics with estimated nuisance parameters.This technique allows us to unify many known results on two-stage estimators and tests and we also derive new results.The technique is especially useful in situations where smoothness of the statistic of interest with respect to the parameters to be estimated does not hold or is difficult to establish, e.g., rank-based statistics.We essentially replace this differentiability condition with a distributional invariance property that is often satisfied in specification tests.Our results on statistics that have not been considered before all use nonparametric statistics.On the technical side, we provide a novel approach to the pre-estimation problem using Le Cam s third lemma.The resulting formula for the correction in the limiting variance as a result of pre-estimation some parameters is a simple expression involving some appropriate covariances.The regularity conditions required fairly minimal.Numerous examples show the strength and wide applicability of our approach.
Original languageEnglish
Place of PublicationTilburg
PublisherEconometrics
Number of pages39
Volume2004-56
Publication statusPublished - 2004

Publication series

NameCentER Discussion Paper
Volume2004-56

Fingerprint

Asymptotic Analysis
Statistics
Alternatives
Limiting Distribution
Nonparametric Statistics
Specification Test
Nuisance Parameter
Regularity Conditions
Differentiability
Statistic
Lemma
Smoothness
Invariance
Limiting
Estimator

Keywords

  • statistics
  • estimation
  • testing

Cite this

Andreou, E., & Werker, B. J. M. (2004). An Alternative Asymptotic Analysis of Residual-Based Statistics. (CentER Discussion Paper; Vol. 2004-56). Tilburg: Econometrics.
Andreou, E. ; Werker, B.J.M. / An Alternative Asymptotic Analysis of Residual-Based Statistics. Tilburg : Econometrics, 2004. (CentER Discussion Paper).
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Andreou, E & Werker, BJM 2004 'An Alternative Asymptotic Analysis of Residual-Based Statistics' CentER Discussion Paper, vol. 2004-56, Econometrics, Tilburg.

An Alternative Asymptotic Analysis of Residual-Based Statistics. / Andreou, E.; Werker, B.J.M.

Tilburg : Econometrics, 2004. (CentER Discussion Paper; Vol. 2004-56).

Research output: Working paperDiscussion paperOther research output

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N2 - This paper offers an alternative technique to derive the limiting distribution of residual-based statistics or, more general, the limiting distribution of statistics with estimated nuisance parameters.This technique allows us to unify many known results on two-stage estimators and tests and we also derive new results.The technique is especially useful in situations where smoothness of the statistic of interest with respect to the parameters to be estimated does not hold or is difficult to establish, e.g., rank-based statistics.We essentially replace this differentiability condition with a distributional invariance property that is often satisfied in specification tests.Our results on statistics that have not been considered before all use nonparametric statistics.On the technical side, we provide a novel approach to the pre-estimation problem using Le Cam s third lemma.The resulting formula for the correction in the limiting variance as a result of pre-estimation some parameters is a simple expression involving some appropriate covariances.The regularity conditions required fairly minimal.Numerous examples show the strength and wide applicability of our approach.

AB - This paper offers an alternative technique to derive the limiting distribution of residual-based statistics or, more general, the limiting distribution of statistics with estimated nuisance parameters.This technique allows us to unify many known results on two-stage estimators and tests and we also derive new results.The technique is especially useful in situations where smoothness of the statistic of interest with respect to the parameters to be estimated does not hold or is difficult to establish, e.g., rank-based statistics.We essentially replace this differentiability condition with a distributional invariance property that is often satisfied in specification tests.Our results on statistics that have not been considered before all use nonparametric statistics.On the technical side, we provide a novel approach to the pre-estimation problem using Le Cam s third lemma.The resulting formula for the correction in the limiting variance as a result of pre-estimation some parameters is a simple expression involving some appropriate covariances.The regularity conditions required fairly minimal.Numerous examples show the strength and wide applicability of our approach.

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Andreou E, Werker BJM. An Alternative Asymptotic Analysis of Residual-Based Statistics. Tilburg: Econometrics. 2004. (CentER Discussion Paper).