Regression for partially observed variables and nonparametric quantiles of conditional probabilities

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Efficient estimation under bias sampling, censoring or truncation is a difficult question which has been partially answered and the usual estimators are not always consistent. Several biased designs are considered for models with variables $(X,Y)$ where $Y$ is an indicator and $X$ an explanatory variable, or for continuous variables $(X,Y)$. The identifiability of the models are discussed. New nonparametric estimators of the regression functions and conditional quantiles are proposed.
Submitted to the Statistics Surveys (http://www.i-journals.org/ss/) by the Institute of Mathematical Statistics (http://www.imstat.org)

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