A generalized quantile regression model

Nassiri, Vahid; Loris, Ignace

doi:10.1080/02664763.2013.780158

Cited by 7 publications

(13 citation statements)

References 19 publications

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“…For the special standard setting that D 0 and D 1, Expressions (2.2) and (2.3) can be found in Nassiri & Loris (2013).…”

Section: Properties Of the Asymmetric Family Of Densitiesmentioning

confidence: 99%

“…For constructing an asymmetric density, Nassiri & Loris () started from a given symmetric around 0 density f , and positive real parameters λ 1 and λ 2 , and defined

f_{λ_{1}, λ_{2}} false(y false) = \frac{2 λ_{1} λ_{2}}{λ_{1} + λ_{2}} ({, \begin{matrix} array f (λ_{1} y) & array if y \leq 0 \\ array f (λ_{2} y) & array if y > 0 \end{matrix}) .

For any λ 1 = λ 2 , the density

f_{λ_{1}, λ_{2}}

is symmetric, with a special case

f_{λ_{1}, λ_{2}} = f

when λ 1 = λ 2 =1. When λ 1 is larger (respectively, smaller) than λ 2 , one obtains a right‐skew (respectively, left‐skew) density.…”

Section: Introductionmentioning

confidence: 99%

“…When λ 1 is larger (respectively, smaller) than λ 2 , one obtains a right‐skew (respectively, left‐skew) density. Note that the family of densities in is a special case of the more general family of Nassiri & Loris () by taking λ 1 = γ and

λ_{2} = \frac{1}{γ}

. The Arellano‐Valle et al () family given in is also a special case of the Nassiri & Loris () family with

λ_{1} = \frac{1}{b false(α false)}

and

λ_{2} = \frac{1}{a false(α false)}

.…”

Section: Introductionmentioning

confidence: 99%

“…For a given unimodal and symmetric around 0 density When taking a.˛/ D b.˛/, the density f˛.y/ reduces to a symmetric density. For constructing an asymmetric density, Nassiri & Loris (2013) started from a given symmetric around 0 density f , and positive real parameters 1 and 2 , and defined…”

Section: Introductionmentioning

confidence: 99%

“…Note that the family of densities in (1.2) is a special case of the more general family of Nassiri & Loris (2013) by taking 1 D and 2 D 1 . The family given in (1.3) is also a special case of the Nassiri & Loris (2013) family with 1 D 1 b.˛/ and 2 D 1 a.˛/ . The family of asymmetric densities (1.4) is thus quite broad, and a detailed study of it has not been performed yet.…”

Section: Introductionmentioning

confidence: 99%

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On Quantile‐based Asymmetric Family of Distributions: Properties and Inference

Gijbels

Karim

Verhasselt

2019

Int Statistical Rev

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Summary In this paper, we provide a detailed study of a general family of asymmetric densities. In the general framework, we establish expressions for important characteristics of the distributions and discuss estimation of the parameters via method‐of‐moments as well as maximum likelihood estimation. Asymptotic normality results for the estimators are provided. The results under the general framework are then applied to some specific examples of asymmetric densities. The use of the asymmetric densities is illustrated in a real‐data analysis.

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“…For the special standard setting that D 0 and D 1, Expressions (2.2) and (2.3) can be found in Nassiri & Loris (2013).…”

Section: Properties Of the Asymmetric Family Of Densitiesmentioning

confidence: 99%

“…For constructing an asymmetric density, Nassiri & Loris () started from a given symmetric around 0 density f , and positive real parameters λ 1 and λ 2 , and defined

f_{λ_{1}, λ_{2}} false(y false) = \frac{2 λ_{1} λ_{2}}{λ_{1} + λ_{2}} ({, \begin{matrix} array f (λ_{1} y) & array if y \leq 0 \\ array f (λ_{2} y) & array if y > 0 \end{matrix}) .

For any λ 1 = λ 2 , the density

f_{λ_{1}, λ_{2}}

is symmetric, with a special case

f_{λ_{1}, λ_{2}} = f

when λ 1 = λ 2 =1. When λ 1 is larger (respectively, smaller) than λ 2 , one obtains a right‐skew (respectively, left‐skew) density.…”

Section: Introductionmentioning

confidence: 99%

λ_{2} = \frac{1}{γ}

. The Arellano‐Valle et al () family given in is also a special case of the Nassiri & Loris () family with

λ_{1} = \frac{1}{b false(α false)}

and

λ_{2} = \frac{1}{a false(α false)}

.…”

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

On Quantile‐based Asymmetric Family of Distributions: Properties and Inference

Gijbels

Karim

Verhasselt

2019

Int Statistical Rev

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An efficient algorithm for structured sparse quantile regression

Nassiri

Loris

2014

Comput Stat

Self Cite

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Quantile regression is studied in combination with a penalty which promotes structured (or group) sparsity. A mixed ℓ 1,∞ -norm on the parameter vector is used to impose structured sparsity on the traditional quantile regression problem. An algorithm is derived to calculate the piece-wise linear solution path of the corresponding minimization problem. A Matlab implementation of the proposed algorithm is provided and some applications of the methods are also studied.

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