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Non‐parametric Regression with Dependent Censored Data
Author(s) -
GHOUCH ANOUAR EL,
KEILEGOM INGRID VAN
Publication year - 2008
Publication title -
scandinavian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.359
H-Index - 65
eISSN - 1467-9469
pISSN - 0303-6898
DOI - 10.1111/j.1467-9469.2007.00586.x
Subject(s) - mathematics , censoring (clinical trials) , estimator , regression function , mixing (physics) , random variable , kernel regression , rate of convergence , statistics , parametric statistics , combinatorics , channel (broadcasting) , physics , quantum mechanics , electrical engineering , engineering
. Let ( Xi , Yi ) ( i = 1 ,…, n ) be n replications of a random vector ( X , Y ), where Y is supposed to be subject to random right censoring. The data ( Xi , Yi ) are assumed to come from a stationary α ‐mixing process. We consider the problem of estimating the function m ( x ) =ℰ( φ ( Y ) | X = x ), for some known transformation φ . This problem is approached in the following way: first, we introduce a transformed variable , that is not subject to censoring and satisfies the relation , and then we estimate m ( x ) by applying local linear regression techniques. As a by‐product, we obtain a general result on the uniform rate of convergence of kernel type estimators of functionals of an unknown distribution function, under strong mixing assumptions.