A note on estimating the conditional expectation under censoring and association: strong uniform consistency

Nassira Menni () and Abdelkader Tatachak ()
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Nassira Menni: USTHB
Abdelkader Tatachak: USTHB

Statistical Papers, 2018, vol. 59, issue 3, No 8, 1009-1030

Abstract: Abstract Let $$\left\{ (X_{i},Y_{i}), i \ge 1 \right\} $$ ( X i , Y i ) , i ≥ 1 be a strictly stationary sequence of associated random vectors distributed as (X, Y). This note deals with kernel estimation of the regression function $$r(x)=\mathbb {E}[Y|X=x]$$ r ( x ) = E [ Y | X = x ] in the presence of randomly right censored data caused by another variable C. For this model we establish a strong uniform consistency rate of the proposed estimator, say $$r_{n}(x)$$ r n ( x ) . Simulations are drawn to illustrate the results and to show how the estimator behaves for moderate sample sizes.

Keywords: Associated data; Censored data; Kaplan–Meier estimator; Kernel regression estimator; Strong uniform consistency rate; 62G05; 62G20 (search for similar items in EconPapers)
Date: 2018
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DOI: 10.1007/s00362-016-0801-8

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