Robust Estimators of Scale: Finite-Sample Performance in Long-Tailed Symmetric Distributions

Lax, David A.

doi:10.2307/2288493

Cited by 49 publications

(37 citation statements)

References 3 publications

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“…This gives a more realistic estimate of the velocity dispersion for groups with more than 10 galaxies, but still a low number, compared to classical estimators. For groups with less than 10 galaxies, there is no significant difference between this robust estimator and the classical estimator of the velocity dispersion (Lax 1985).…”

Section: Velocity Dispersions and Massesmentioning

confidence: 87%

Group analysis in the SSRS2 catalog

Adami¹,

Mazure²

2002

A&A

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Abstract. We present an automated method to detect populations of groups in galaxy redshift catalogs. This method uses both analysis of the redshift distribution along lines of sight in fixed cells to detect elementary structures and a friend-of-friend algorithm to merge these elementary structures into physical structures. We apply this method to the SSRS2 galaxy redshift catalog. The groups detected with our method are similar to group catalogs detected with pure friend-of-friend algorithms. They have similar mass distribution, similar abundance versus redshift, a similar 2-point correlation function (modeled by a power law: (r/r0) γ with r0 = 7 h −1 Mpc and γ = −1.79) and the same redshift completeness limit, close to 5000 km s −1 . If instead of SSRS2, we use catalogs of the new generation (deep redshift surveys obtained with 10 m class telescopes), it would lead to a completeness limit of z ∼ 0.7. We model the luminosity function for nearby galaxy groups by a Schechter function with parameters M * SSRS2 = (−19.99 ± 0.36) + 5 logh and α = −1.46 ± 0.17 to compute the mass to light ratio. The median value of the mass to light ratio is 360 hM /L (in the SSRS2 band, close to a B band magnitude) and we deduce a relation between mass to light ratio and velocity dispersion σ (M/L = (3.79 ± 0.64)σ − (294 ± 570)). The more massive the group, the higher the mass to light ratio, and therefore, the larger the amount of dark matter inside the group. Another explanation is a significant stripping of the gas of the galaxies in massive groups as opposed to low mass groups. This extends to groups of galaxies the mild tendency already detected for rich clusters of galaxies. Finally, we detect a barely significant fundamental plane for these groups (L ∝ R 2.26±1.39 Vir × σ 2.93±1.64 for groups with more than 8 galaxies) but it is much less narrow than for clusters of galaxies.

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Section: Velocity Dispersions and Massesmentioning

confidence: 87%

Group analysis in the SSRS2 catalog

Adami¹,

Mazure²

2002

A&A

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“…For example, in order to locate and compute velocity dispersions for typical group-size substructures (∼100 h −1 kpc) in the dense cluster regions (∼1 h −1 Mpc), one needs about 10 redshifts per 100 × 100 h −2 kpc 2 "pixel" (e.g. Lax 1985), which therefore leads to a total number of redshifts of about 1000. Reaching such a number starts to be feasible by combining all literature redshift catalogues for the Coma cluster.…”

Section: Introductionmentioning

confidence: 99%

The build-up of the Coma cluster by infalling substructures

Adami¹,

Biviano

Durret

et al. 2005

A&A

211

353

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We present a new multiwavelength analysis of the Coma cluster subclustering based on recent X-ray data and on a compilation of nearly 900 redshifts. We characterize subclustering using the Serna & Gerbal (1996, A&A, 309, 65) hierarchical method, which makes use of galaxy positions, redshifts, and magnitudes, and identify 17 groups. One of these groups corresponds to the main cluster, one is the well known group associated with the infalling galaxy NGC 4839, and one is associated with NGC 4911/NGC 4926. About one third of the 17 groups have velocity distributions centered on the velocities of the very bright cluster galaxies they contain (magnitudes R < 13). In order to search for additional substructures, we made use of the isophotes of X-ray brightness residuals left after the subtraction of the best-fit β-model from the overall X-ray gas distribution (Neumann et al. 2003, A&A, 400, 811). We selected galaxies within each of these isophotes and compared their velocity distributions with that of the whole cluster. We confirm in this way the two groups associated, respectively, with NGC 4839, and with the southern part of the extended western substructure visible in X-rays. We discuss the group properties in the context of a scenario in which Coma is built by the accretion of groups infalling from the surrounding large-scale structure. We estimate the recent mass accretion rate of Coma and compare it with hierarchical models of cluster evolution.

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“…The median and MAD are highly resistant to outliers, but are relatively inefficient for normally distributed data. Using more efficient robust estimates of location (Huber, 1964) and scale (Lax, 1985) in the definition of S/N rob could potentially lead to better performance when outliers are less extreme. An alternative approach to consider is to remove the outliers from the original data, and then calculate S/N in the usual way using the sample mean and variance; when the points are omitted in the proper fashion, this leads to highly robust and efficient estimates of location (Simonoff, 1984) and scale (Simonoff, 1987).…”

Section: Discussionmentioning

confidence: 99%

Robust analysis of variance: process design and quality improvement

Giloni

Seshadri

Simonoff

2006

IJPQM

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We discuss the use of robust analysis of variance (ANOVA) techniques as applied to quality engineering. ANOVA is the cornerstone for uncovering the effects of design factors on performance. Our goal is to utilize methodologies that yield similar results to standard methods when the underlying assumptions are satisfied, but also are relatively unaffected by outliers (observations that are inconsistent with the general pattern in the data). We do this by utilizing statistical software to implement robust ANOVA methods, which are no more difficult to perform than ordinary ANOVA. We study several examples to illustrate how using standard techniques can lead to misleading inferences about the process being examined, which are avoided when using a robust analysis. We further demonstrate that assessments of the importance of factors for quality design can be seriously compromised when utilizing standard methods as opposed to robust methods.3

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Robust Estimators of Scale: Finite-Sample Performance in Long-Tailed Symmetric Distributions

Cited by 49 publications

References 3 publications

Group analysis in the SSRS2 catalog

Group analysis in the SSRS2 catalog

The build-up of the Coma cluster by infalling substructures

Robust analysis of variance: process design and quality improvement

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