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Asymptotics for pooled marginal slicing estimator based on SIR[alpha] approach

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  • Saracco, Jérôme

Abstract

Pooled marginal slicing (PMS) is a semiparametric method, based on sliced inverse regression (SIR) approach, for achieving dimension reduction in regression problems when the outcome variable y and the regressor x are both assumed to be multidimensional. In this paper, we consider the SIR[alpha] version (combining the SIR-I and SIR-II approaches) of the PMS estimator and we establish the asymptotic distribution of the estimated matrix of interest. Then the asymptotic normality of the eigenprojector on the estimated effective dimension reduction (e.d.r.) space is derived as well as the asymptotic distributions of each estimated e.d.r. direction and its corresponding eigenvalue.

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  • Saracco, Jérôme, 2005. "Asymptotics for pooled marginal slicing estimator based on SIR[alpha] approach," Journal of Multivariate Analysis, Elsevier, vol. 96(1), pages 117-135, September.
    • Handle: RePEc:eee:jmvana:v:96:y:2005:i:1:p:117-135
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    1. Li K-C. & Aragon Y. & Shedden K. & Thomas Agnan C., 2003. "Dimension Reduction for Multivariate Response Data," Journal of the American Statistical Association, American Statistical Association, vol. 98, pages 99-109, January.
    2. Gannoun, Ali & Girard, Stephane & Guinot, Christiane & Saracco, Jerome, 2004. "Sliced inverse regression in reference curves estimation," Computational Statistics & Data Analysis, Elsevier, vol. 46(1), pages 103-122, May.
    3. Efstathia Bura & R. Dennis Cook, 2001. "Estimating the structural dimension of regressions via parametric inverse regression," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 63(2), pages 393-410.
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    Cited by:

    1. Girard, Stéphane & Lorenzo, Hadrien & Saracco, Jérôme, 2022. "Advanced topics in Sliced Inverse Regression," Journal of Multivariate Analysis, Elsevier, vol. 188(C).
    2. Weng, Jiaying, 2022. "Fourier transform sparse inverse regression estimators for sufficient variable selection," Computational Statistics & Data Analysis, Elsevier, vol. 168(C).
    3. Coudret, R. & Girard, S. & Saracco, J., 2014. "A new sliced inverse regression method for multivariate response," Computational Statistics & Data Analysis, Elsevier, vol. 77(C), pages 285-299.
    4. Wen, Xuerong Meggie, 2010. "On sufficient dimension reduction for proportional censorship model with covariates," Computational Statistics & Data Analysis, Elsevier, vol. 54(8), pages 1975-1982, August.
    5. Kim, Kyongwon, 2022. "On principal graphical models with application to gene network," Computational Statistics & Data Analysis, Elsevier, vol. 166(C).
    6. Marie Chavent & Stéphane Girard & Vanessa Kuentz-Simonet & Benoit Liquet & Thi Nguyen & Jérôme Saracco, 2014. "A sliced inverse regression approach for data stream," Computational Statistics, Springer, vol. 29(5), pages 1129-1152, October.

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