Robust dimension reduction using sliced inverse median regression

Christou, Eliana

doi:10.1007/s00362-018-1007-z

Cited by 5 publications

(5 citation statements)

References 41 publications

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“…Although in this paper we choose the L1 median due to its uniqueness for p ! 2, we expect similar results to hold when other multivariate medians are used, for example Tukey and Oja median which were discussed in the SDR framework by Christou (2018).…”

Section: Discussionsupporting

confidence: 53%

“…The authors demonstrated the robustness in the presence of outliers of this algorithms as well as the good overall performance when there are no outliers. More recently, similar ideas were proposed by Christou (2018) but instead of using the L1 median, they suggest using the Oja and the Tukey median.…”

Section: Sliced Inverse Median (Sime)mentioning

confidence: 99%

“…First is the dependence on moments which suffer on the presence of outliers. To address this, Gather et al (2001), Dong et al (2015) and Christou (2018) suggested using inverse medians instead of means. Second is the dependence on the number of slices the range of Y is discretized into, especially in methods like Sliced Average Variance Estimation (SAVE- Cook and Weisberg 1991) where the second inverse moment is used as well.…”

Section: Introductionmentioning

confidence: 99%

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Sliced inverse median difference regression

Babos

Artemiou

2020

Stat Methods Appl

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In this paper we propose a sufficient dimension reduction algorithm based on the difference of inverse medians. The classic methodology based on inverse means in each slice was recently extended, by using inverse medians, to robustify existing methodology at the presence of outliers. Our effort is focused on using differences between inverse medians in pairs of slices. We demonstrate that our method outperforms existing methods at the presence of outliers. We also propose a second algorithm which is not affected by the ordering of slices when the response variable is categorical with no underlying ordering of its values.

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Section: Discussionsupporting

confidence: 53%

Section: Sliced Inverse Median (Sime)mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Sliced inverse median difference regression

Babos

Artemiou

2020

Stat Methods Appl

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“…Velu et al (1986) have discussed the asymptotic distribution of reduced rank matrix estimators in the multivariate auto-regressive model. Other data reduction methods were proposed in the 1980s see, for example, a review in (Fernández-Macho, 1997) and for more recent developments, see (Christou, 2020). Several recent surveys have been dedicated to dynamic factors models, including stationary and non-stationary times series processes in dierent areas of applications such as environmental, health, and nancial sciences see, for example, (Eichler et al, 2011;Lam et al, 2011;Toman, 2014;Bai and Wang, 2016;Chen et al, 2020;Fan et al, 2021;Lin et al, 2022;Bai and Zheng, 2023) to mention a few.…”

Section: Introductionmentioning

confidence: 99%

A dimension reduction factor approach for multivariate time series with long-memory: a robust alternative method

Reisen,

Lévy-Leduc,

Monte

et al. 2023

Stat Papers

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This paper studies factor modeling for a vector of time series with long-memory properties to investigate how outliers aect the identication of the number of factors and also proposes a robust method to reduce their impact. The number of factors is estimated using an eigenvalue analysis for a non-negative denite matrix introduced by Lam et al (2011). Two estimators are proposed; the rst is based on the classical sample covariance function, and the second uses a robust covariance function estimate. In both cases, it is shown that the eigenvalues estimates have similar convergence rates. Empirical simulations support both estimators for multivariate stationary longmemory time series and show that the robust method is preferable when the data is contaminated with additive outliers. Time series of daily log returns are used as an example of application. In addition to abrupt observations, exchange rates exhibit non-stationarity properties with long memory parameters greater than one. Then we use semi-parametric long memory estimators to estimate the fractional parameters of the series. The number of factors was estimated using the classical and robust approaches. Due to the inuence of the abrupt observations, these tools suggested a dierent number of factors to model the data. The robust method suggested two factors, while the classical approach indicated only one factor.

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“…Existing dimension reduction techniques focus on the entire conditional distribution and include, among others, sliced inverse regression (SIR, Li 1991), principal Hessian directions (pHd, Li 1992), sliced average variance estimation (SAVE, Cook and Weisberg 1991), parametric inverse regression (PIR, Bura and Cook 2001), minimum average variance estimation (MAVE, Xia et al 2002), partial SIR (Chiaromonte et al 2002), contour regression (Li et al 2005), directional regression (DR, Li and Wang 2007), sliced regression (SR, Wang and Xia 2008), and more recently, sliced inverse median regression (SIMR, Christou 2018). See also Hristache et al (2001), Li and Dong (2009), Dong and Li (2010), Yin and Li (2011), Zhang et al (2011), Ma and Zhu (2012), Shin and Artemiou (2017), and Zhu et al (2017).…”

Section: Introductionmentioning

confidence: 99%

Central quantile subspace

Christou

2019

Stat Comput

Self Cite

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Quantile regression (QR) is becoming increasingly popular due to its relevance in many scientific investigations. There is a great amount of work about linear and nonlinear QR models.Specifically, nonparametric estimation of the conditional quantiles received particular attention, due to its model flexibility. However, nonparametric QR techniques are limited in the number of covariates. Dimension reduction offers a solution to this problem by considering low-dimensional smoothing without specifying any parametric or nonparametric regression relation. Existing dimension reduction techniques focus on the entire conditional distribution. We, on the other hand, turn our attention to dimension reduction techniques for conditional quantiles and introduce a new method for reducing the dimension of the predictor X. The novelty of this paper is threefold. We start by considering a single index quantile regression model, which assumes that the conditional quantile depends on X through a single linear combination of the predictors, then extend to a multi index quantile regression model, and finally, generalize the proposed methodology to any statistical functional of the conditional distribution. The performance of the methodology is demonstrated through simulation examples and a real data application. Our results suggest that this method has a good finite sample performance and often outperforms existing methods.

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Robust dimension reduction using sliced inverse median regression

Cited by 5 publications

References 41 publications

Sliced inverse median difference regression

Sliced inverse median difference regression

A dimension reduction factor approach for multivariate time series with long-memory: a robust alternative method

Central quantile subspace

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