Symmetric quantile and symmetric trimmed mean for linear regression model

Chen, Lin-An; Chiang, Yuang-Chin

doi:10.1080/10485259608832697

Cited by 11 publications

(21 citation statements)

References 8 publications

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“…The proof of this theorem is analogous to Theorem 3.1 of Chen & Chiang (1996) and thus is also skipped. Corollary 1.…”

Section: Symmetric Quantile Classmentioning

confidence: 93%

“…However, these two quantiles are identical when a symmetric error distribution is assumed, which makes them comparable. Here we consider this quantile concept of Chen & Chiang (1996) in a more general setting.…”

Section: Symmetric Quantile Classmentioning

confidence: 99%

“…Unlike the way in which the empirical quantile is constructed based on the cumulative distribution function, the so-called symmetric quantile of Chen & Chiang (1996) is formulated based on a folded distribution function. However, these two quantiles are identical when a symmetric error distribution is assumed, which makes them comparable.…”

Section: Symmetric Quantile Classmentioning

confidence: 99%

“…In order to improve the efficiency of a location estimator, and the trimmed mean, Kim (1992) developed the metrically trimmed mean for a location model which, through comparison of asymptotic variances, was shown to be more efficient than the ordinary trimmed mean. Later, Chen & Chiang (1996) defined the symmetric quantile and used it to propose the symmetric trimmed mean as an extension of Kim's trimmed mean to the linear regression model. They observed that this symmetric trimmed mean of small trimming percentages can have asymptotic variances very close to the Crammer-Rao lower bounds when regression errors obey heavy tail distributions.…”

Section: Introductionmentioning

confidence: 99%

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confidence: 99%

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Symmetric quantiles and their applications

Chiang

Chen

Yang

2006

Journal of Applied Statistics

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To develop estimators with stronger efficiencies than the trimmed means which use the empirical quantile, Kim (1992) and Chen & Chiang (1996), implicitly or explicitly used the symmetric quantile, and thus introduced new trimmed means for location and linear regression models, respectively. This study further investigates the properties of the symmetric quantile and extends its application in several aspects. (a) The symmetric quantile is more efficient than the empirical quantiles in asymptotic variances when quantile percentage α is either small or large. This reveals that for any proposal involving the α th quantile of small or large α s, the symmetric quantile is the right choice; (b) a trimmed mean based on it has asymptotic variance achieving a Cramer-Rao lower bound in one heavy tail distribution; (c) an improvement of the quantiles-based control chart by Grimshaw & Alt (1997) is discussed; (d) Monte Carlo simulations of two new scale estimators based on symmetric quantiles also support this new quantile.Regression quantile, scale estimator, trimmed mean,

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“…The proof of this theorem is analogous to Theorem 3.1 of Chen & Chiang (1996) and thus is also skipped. Corollary 1.…”

Section: Symmetric Quantile Classmentioning

confidence: 93%

Section: Symmetric Quantile Classmentioning

confidence: 99%

Section: Symmetric Quantile Classmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

“…

…”

mentioning

confidence: 99%

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Symmetric quantiles and their applications

Chiang

Chen

Yang

2006

Journal of Applied Statistics

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Parametric and nonparametric improvements in Bland and Altman's assessment of agreement method

Chen

Kao

2021

Statistics in Medicine

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The Bland-Altman method, which assesses agreement via an assessment set constructed by the difference of the measurement variables, has received great attention. Other assessment approaches have been proposed following the same difference-based framework. However, the exact assessment set constructed by the difference is achievable only for measurements with certain joint distributions. To provide a more general assessment framework, we propose two approaches. First, when the measurement distribution is known, we propose a parametric approach that constructs the assessment set through a measure of closeness corresponding to the distribution. Second, when the measurement distribution is unknown, we propose a nonparametric approach that constructs the assessment set through quantile regression. Both approaches quantify the degree of agreement with the presence of both systematic and random measurement errors, and enable one to go beyond the difference-based approach. Results of simulation and data analyses are presented to compare the two approaches.

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Reweighted least trimmed squares: an alternative to one-step estimators

Čı́žek

2013

TEST

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A new class of robust regression estimators is proposed that forms an alternative to traditional robust one-step estimators and that achieves the √ n rate of convergence irrespective of the initial estimator under a wide range of distributional assumptions. The proposed reweighted least trimmed squares (RLTS) estimator employs data-dependent weights determined from an initial robust fit. Just like many existing one-and two-step robust methods, the RLTS estimator preserves robust properties of the initial robust estimate. However contrary to existing methods, the first-order asymptotic behavior of RLTS is independent of the initial estimate even if errors exhibit heteroscedasticity, asymmetry, or serial correlation. Moreover, we derive the asymptotic distribution of RLTS and show that it is asymptotically efficient for normally distributed errors. A simulation study documents benefits of these theoretical properties in finite samples.

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Symmetric quantile and symmetric trimmed mean for linear regression model

Cited by 11 publications

References 8 publications

Symmetric quantiles and their applications

Symmetric quantiles and their applications

Parametric and nonparametric improvements in Bland and Altman's assessment of agreement method

Reweighted least trimmed squares: an alternative to one-step estimators

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