On weighted and locally polynomial directional quantile regression

Bocek, Pavel; Šiman, Miroslav

doi:10.1007/s00180-016-0708-9

Cited by 4 publications

(6 citation statements)

References 32 publications

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“…where ǫ i denotes a p× 1 vector of error terms with univariate component-wise quantiles (at fixed levels τ 1 , .., τ p , respectively) equal to zero. For the regression model in (9), consider now the following MAL p β τ X i , Dξ, DΣD distribution with density function (see Kotz et al, 2001)…”

Section: Joint Quantile Regression and The Mal Distributionmentioning

confidence: 99%

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Joint estimation of conditional quantiles in multivariate linear regression models with an application to financial distress

Petrella

Raponi

2019

Journal of Multivariate Analysis

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This paper proposes a maximum-likelihood approach to jointly estimate marginal conditional quantiles of multivariate response variables in a linear regression framework.We consider a slight reparameterization of the Multivariate Asymmetric Laplace distribution proposed by Kotz et al (2001) and exploit its location-scale mixture representation to implement a new EM algorithm for estimating model parameters. The idea is to extend the link between the Asymmetric Laplace distribution and the well-known univariate quantile regression model to a multivariate context, i.e. when a multivariate dependent variable is concerned. The approach accounts for association among multiple responses and study how the relationship between responses and explanatory variables can vary across different quantiles of the marginal conditional distribution of the responses. A penalized version of the EM algorithm is also presented to tackle the problem of variable selection. The validity of our approach is analyzed in a simulation study, where we also provide evidence on the efficiency gain of the proposed method compared to estimation obtained by separate univariate quantile regressions. A real data application is finally proposed to study the main determinants of financial distress in a sample of Italian firms.

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Section: Joint Quantile Regression and The Mal Distributionmentioning

confidence: 99%

“…For the regression model in (9), consider now the following MAL p β τ X i , D ξ, D ΣD distribution with density function (see Kotz et al, 2001)…”

Section: Joint Quantile Regression and The Mal Distributionmentioning

confidence: 99%

Joint estimation of conditional quantiles in multivariate linear regression models with an application to financial distress

Petrella

Raponi

2019

Journal of Multivariate Analysis

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“…While outliers and heteroscedasticity are well visible from the graph of Y 1 and Y 2 without any sophisticated tools, Figures 2 (right) and 3 confirm their presence in the regression model. It is not possible to compare the results with those of vector quantile regression presented by Carlier et al, (2016), who analyzed the data without the ambition to investigate or interpret the presence of outliers or heteroscedasticity. Directional quantiles order the observations, from the most central to the most outlying; we are not aware of any other ways for doing this.…”

Section: Results Of Directional Quantilesmentioning

confidence: 99%

“…There are other possible approaches to quantile estimation for data with a multivariate response, which deserve to be investigated within future research applications, mainly a nonparametric version of directional quantiles (Boček & Šiman, 2017b) or elliptical quantiles, e.g. those for nonlinear regression (Hlubinka & Šiman, 2015) or elliptical multiple-output regression (Hallin & Šiman, 2016).…”

Section: Discussionmentioning

confidence: 99%

An application of directional quantiles to economic data with a multivariate response

Kalina¹

2020

Serb J Management

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Quantile regression represents a popular and useful methodology for modeling quantiles of a response variable based on one or more independent variables. Directional quantiles represent an available extension to the linear regression model with a multivariate response. However, we are not aware of any application of directional quantiles to real data in the literature. An illustration of directional quantiles to an economic dataset is presented in this paper, particularly a modeling of a two-dimensional response in the classical Engel's dataset on household consumption from the 19th century. The results reveal the directional quantiles to yield meaningful results. They order individual observations according to their depth, i.e. from the most central to the most outlying. We compare their result with those of a (more standard) outlier detection. On the whole, we perceive directional quantiles as a potentially useful tool for the analysis of data, if accompanied by a thorough analysis by standard tools.

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“…Needless to say that there are plenty of shift‐equivariant location functionals

\boldsymbol{\mu}

including the mode, mean, or various medians (Small, 1990) of the multivariate distribution. For example, the mean and the medians induced by the simplicial, halfspace, and projection depths (Serfling & Zuo, 2000) are all fully affine equivariant, and their regression modifications are already available to be used in the regression extensions mentioned below; see, for example, Hallin and Šiman (2017) for a review of some available options, and also Šiman (2011) and Boček and Šiman (2017) with the references therein.…”

Section: Preliminary Considerationsmentioning

confidence: 99%

Multivariate quantiles with both overall and directional probability interpretation

Hlubinka

Kotík

Šiman

2022

Scandinavian J Statistics

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The article introduces multivariate quantiles (or reference regions) that have both overall and directional probability interpretation and need not be necessarily convex. They are defined by means of univariate conditional quantiles along the rays starting at a suitable central point. Their basic properties are investigated, their sample estimators and regression extensions are proposed, and their use is illustrated with both simulated and real data.

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On weighted and locally polynomial directional quantile regression

Cited by 4 publications

References 32 publications

Joint estimation of conditional quantiles in multivariate linear regression models with an application to financial distress

Joint estimation of conditional quantiles in multivariate linear regression models with an application to financial distress

An application of directional quantiles to economic data with a multivariate response

Multivariate quantiles with both overall and directional probability interpretation

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