6533b836fe1ef96bd12a07e6

RESEARCH PRODUCT

Asymptotics for pooled marginal slicing estimator based on SIRα approach

Jérôme Saracco

subject

Statistics and ProbabilityNumerical AnalysisDimensionality reductionStatisticsSliced inverse regressionAsymptotic distributionEstimatorRegression analysisStatistics Probability and UncertaintyMarginal distributionEffective dimensionEigenvalues and eigenvectorsMathematics

description

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"@a 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.

yearjournalcountryeditionlanguage
2005-09-01Journal of Multivariate Analysis
https://doi.org/10.1016/j.jmva.2004.10.003