The asymptotic distribution of magnitude-Winsorized sums via self-normalization

Hahn, Marjorie G.; Kuelbs, J.; Weiner, Daniel C.

doi:10.1007/bf01063331

Cited by 14 publications

(10 citation statements)

References 8 publications

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“…Of the three cases, (3-9) is of most interest to us since it pertains to asymptotic normality. However, we should remark that (3)(4)(5)(6)(7)(8)(9)(10)(11) is an analogue of the result of Darling [3] on the dominance of the maximal summand when the tails of the underlying distribution are slowly varying.…”

Section: P( Max Y T £))mentioning

confidence: 98%

“…This is the case studied for example in Csorgo, Haeusler, and Mason [2], Griffin and Pruitt [6], Hahn, Kuelbs and Weiner [7] and Hahn and Weiner [8]. Further references and a discussion of other types of trimming can be found in any of the above references.…”

Section: P H I L I P S G R I F F I N and D A V I D M M A S O Nmentioning

confidence: 99%

“…The equivalence of the analytic condition (1-4) to asymptotic normality (1-2) is due to Griffin and Pruitt( [6], lemma 3-11) as is the form the normalizing sequence y n in (1*2) must take. A sufficient condition, which is not necessary, for (1-6) can be found in Hahn, Kuelbs and Weiner [7].…”

Section: P H I L I P S G R I F F I N and D A V I D M M A S O Nmentioning

confidence: 99%

“…This could enable one to guess the right conditions for asymptotic normality ahead of time, then check that they are correct. This approach was set forward in Hahn, Kuelbs and Weiner [7]. In that case the situation was made clearer by the fact that asymptotic normality of the self-normalized sum always held.…”

Section: P H I L I P S G R I F F I N and D A V I D M M A S O Nmentioning

confidence: 99%

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On the asymptotic normality of self-normalized sums

Griffin

Mason

1991

Math. Proc. Camb. Phil. Soc.

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Let X1, …, Xn be a sequence of non-degenerate, symmetric, independent identically distributed random variables, and let Sn(rn) denote their sum when the rn largest in modulus have been removed. We obtain necessary and sufficient conditions for asymptotic normality of the studentized version of Sn(rn), and compare this to the condition for asymptotic normality of the scalar normalized version. In particular, when rn = r these conditions are the same, but when rn → ∞the former holds more generally.

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Section: P( Max Y T £))mentioning

confidence: 98%

Section: P H I L I P S G R I F F I N and D A V I D M M A S O Nmentioning

confidence: 99%

Section: P H I L I P S G R I F F I N and D A V I D M M A S O Nmentioning

confidence: 99%

Section: P H I L I P S G R I F F I N and D A V I D M M A S O Nmentioning

confidence: 99%

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On the asymptotic normality of self-normalized sums

Griffin

Mason

1991

Math. Proc. Camb. Phil. Soc.

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“…For example, it is sensitive to outliers of feature values. Some other normalization methods which are robust to feature outliers (e.g., quantile normalization [16] and winsorization [17]) merit further investigation. In addition to this, the Z-score normalization assumes that all the subjects have similar proportions of sleep stages over night.…”

Section: Resultsmentioning

confidence: 99%

Automatic detection of overnight deep sleep based on heart rate variability: A preliminary study

Long

Fonseca

Haakma

et al. 2014

2014 36th Annual International Conference of the IEEE Engineering in Medicine and Biology Society

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Citation for published version (APA):Long, X., Fonseca, P., Haakma, R., Foussier, J., & Aarts, R. M. (2014). Automatic detection of overnight deep sleep based on heart rate variability : a preliminary study. In Proceedings of the 36th Annual International Conference of the IEEE Engineering in Medicine and Biology Society (EMBC'14), 26-30 August 2014, Chicago, Illinois (pp. 50-53 Please check the document version of this publication:• A submitted manuscript is the version of the article upon submission and before peer-review. There can be important differences between the submitted version and the official published version of record. People interested in the research are advised to contact the author for the final version of the publication, or visit the DOI to the publisher's website.• The final author version and the galley proof are versions of the publication after peer review.• The final published version features the final layout of the paper including the volume, issue and page numbers. Link to publication General rightsCopyright and moral rights for the publications made accessible in the public portal are retained by the authors and/or other copyright owners and it is a condition of accessing publications that users recognise and abide by the legal requirements associated with these rights.• Users may download and print one copy of any publication from the public portal for the purpose of private study or research.• You may not further distribute the material or use it for any profit-making activity or commercial gain • You may freely distribute the URL identifying the publication in the public portal.If the publication is distributed under the terms of Article 25fa of the Dutch Copyright Act, indicated by the "Taverne" license above, please follow below link for the End User Agreement: www.tue.nl/taverne Take down policyIf you believe that this document breaches copyright please contact us at:openaccess@tue.nl providing details and we will investigate your claim. Abstract-This preliminary study investigated the use of cardiac information or more specifically, heart rate variability (HRV), for automatic deep sleep detection throughout the night. The HRV data can be derived from cardiac signals, which were obtained from polysomnography (PSG) recordings. In total 42 features were extracted from the HRV data of 15 single-night PSG recordings (from 15 healthy subjects) for each 30-s epoch, used to perform epoch-by-epoch classification of deep sleep and non-deep sleep (including wake state and all the other sleep stages except deep sleep). To reduce variation of cardiac physiology between subjects, we normalized each feature per subject using a simple Z-score normalization method by subtracting the mean and dividing by the standard deviation of the feature values. A correlation-based feature selection (CFS) method was employed to select informative features as well as removing feature redundancy and a linear discriminant (LD) classifier was applied for deep and non-deep sleep classification. Results show th...

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Asymptotics for Multivariate t-Statistic and Hotelling′s T2-Statistic Under Infinite Second Moments via Bootstrapping

Sepanski

1994

Journal of Multivariate Analysis

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The asymptotic distribution of magnitude-Winsorized sums via self-normalization

Cited by 14 publications

References 8 publications

On the asymptotic normality of self-normalized sums

On the asymptotic normality of self-normalized sums

Automatic detection of overnight deep sleep based on heart rate variability: A preliminary study

Asymptotics for Multivariate t-Statistic and Hotelling′s T2-Statistic Under Infinite Second Moments via Bootstrapping

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