Sign-Based Methods in Linear Statistical
                    Models

Boldin, M. V.; Simonova, G. I.; Tyurin, Yu. N.

doi:10.1090/mmono/162

Cited by 28 publications

(38 citation statements)

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“…These tests are exact even when the disturbances are asymmetric, non-normal, and heteroskedastic. Boldin, Simonova and Tyurin (1997) propose locally optimal sign-based inference and estimation for linear models. Coudin and Dufour (2008) extend the work by Boldin et al (1997) to account for serial dependence and discrete distributions.…”

Section: Introductionmentioning

confidence: 99%

“…Boldin, Simonova and Tyurin (1997) propose locally optimal sign-based inference and estimation for linear models. Coudin and Dufour (2008) extend the work by Boldin et al (1997) to account for serial dependence and discrete distributions. Wright (2000) proposes variance-ratio tests based on the signs and ranks 1 to test the null hypothesis that the series of interest is a martingale difference sequence.…”

Section: Introductionmentioning

confidence: 99%

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Exact optimal inference in regression models under heteroskedasticity and non-normality of unknown form

Dufour

Taamouti

2010

Computational Statistics & Data Analysis

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Simple point-optimal sign-based tests are developed for inference on linear and nonlinear regression models with non-Gaussian heteroskedastic errors. The tests are exact, distribution-free, robust to heteroskedasticity of unknown form, and may be inverted to build confidence regions for the parameters of the regression function. Since point-optimal sign tests depend on the alternative hypothesis considered, an adaptive approach based on a split-sample technique is proposed in order to choose an alternative that brings power close to the power envelope. The performance of the proposed quasi-point-optimal sign tests with respect to size and power is assessed in a Monte Carlo study. The power of quasi-point-optimal sign tests is typically close to the power envelope, when approximately 10% of the sample is used to estimate the alternative and the remaining sample to compute the test statistic. Further, the proposed procedures perform much better than common least-squares-based tests which are supposed to be robust against heteroskedasticity.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Exact optimal inference in regression models under heteroskedasticity and non-normality of unknown form

Dufour

Taamouti

2010

Computational Statistics & Data Analysis

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“…Boldin, Simonova, and Tyurin (1997) show that these statistics can be associated with locally most powerful tests in the case of i.i.d. disturbances under some regularity conditions and Coudin and Dufour extend that proof to disturbances that satisfy the mediangale property.…”

Section: Confidence Setsmentioning

confidence: 93%

Testing Linear Factor Pricing Models With Large Cross Sections: A Distribution-Free Approach

Gungor

Luger

2013

Journal of Business & Economic Statistics

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We develop a finite-sample procedure to test the beta-pricing representation of linear factor pricing models that is applicable even if the number of test assets is greater than the length of the time series. Our distribution-free framework leaves open the possibility of unknown forms of non-normalities, heteroskedasticity, time-varying correlations, and even outliers in the asset returns. The power of the proposed test procedure increases as the time-series lengthens and/or the cross-section becomes larger. This stands in sharp contrast to the usual tests that lose power or may not even be computable if the crosssection is too large. Finally, we revisit the CAPM and the Fama-French three factor model. Our results strongly support the mean-variance efficiency of the market portfolio. JEL classification: C12, C14, C33, G11, G12 Bank classification: Econometric and statistical methods; Financial markets RésuméLes auteurs élaborent une procédure permettant de tester, en échantillon fini, la représentation des coefficients bêta donnés par les modèles linéaires d'évaluation factorielle, et ce, même si le nombre des actifs dépasse celui des valeurs de la série chronologique. Leur cadre autorise des formes inconnues de distribution autres que la loi normale ainsi que la présence d'hétéroscédasticité, de structures de corrélation variables dans le temps, voire de rendements aberrants. La puissance de la procédure s'accroît avec l'allongement de la série chronologique et la hausse du nombre des actifs. Cette propriété tranche avec les limites des tests habituels, qui perdent de leur puissance ou peuvent même devenir inexécutables si le nombre des actifs est trop élevé. Pour finir, les auteurs réexaminent le modèle d'évaluation des actifs financiers et le modèle trifactoriel de Fama et French. Leurs résultats indiquent clairement que le portefeuille de marché se situe sur la frontière efficiente dans le plan moyenne-variance.

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“…1 Using that the noises form an independent sequence and they are also independent from the i.i.d. signs, the probability P that measures the event {θ * ∈ Θ} is a product measure of the marginal distributions P t of N t , t = 1, .…”

Section: Robustness Of Sps With Asymmetric Noisementioning

confidence: 99%

“…The LAD variant of SPS connects finite sample methods in the system identification literature (SPS [10], LSCR [4], dataset-perturbed methods [13]) and an independent, rich thread in econometrics [1], [6] which deserves the attention of the system identification community. In the terminology of econometrics, LAD-SPS is a confidence set construction method that relies on Monte Carlo sign-based joint tests, [6].…”

Section: Remark 2 (Lad-sps and Sign-tests In Econometrics)mentioning

confidence: 99%

Sign-Perturbed Sums (SPS) with asymmetric noise: Robustness analysis and robustification techniques

Carè

Csáji

Campi

2016

2016 IEEE 55th Conference on Decision and Control (CDC)

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Abstract-Sign-Perturbed Sums (SPS) is a recently developed finite sample system identification method that can build exact confidence regions for linear regression problems under mild statistical assumptions. The regions are well-shaped, e.g., they are centred around the least-squares (LS) estimate, star-convex and strongly consistent. One of the main assumptions of SPS is that the distribution of the noise terms are symmetric about zero. This paper analyses how robust SPS is with respect to the violation of this assumption and how it could be robustified with respect to non-symmetric noises. First, some alternative solutions are overviewed, then a robustness analysis is performed resulting in a robustified version of SPS. We also suggest a modification of SPS, called LAD-SPS, which builds exact confidence regions around the least-absolute deviation (LAD) estimate instead of the LS estimate. LAD-SPS requires less assumptions as the noise needs only to have a conditionally zero median (w.r.t. the past). Furthermore, that approach can also be robustified using similar ideas as in the LS-SPS case. Finally, some numerical experiments are presented.

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Sign-Based Methods in Linear Statistical Models

Cited by 28 publications

References 0 publications

Exact optimal inference in regression models under heteroskedasticity and non-normality of unknown form

Exact optimal inference in regression models under heteroskedasticity and non-normality of unknown form

Testing Linear Factor Pricing Models With Large Cross Sections: A Distribution-Free Approach

Sign-Perturbed Sums (SPS) with asymmetric noise: Robustness analysis and robustification techniques

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