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

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  • Nassira Menni

    (USTHB)

  • Abdelkader Tatachak

    (USTHB)

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.

Suggested Citation

  • Nassira Menni & Abdelkader Tatachak, 2018. "A note on estimating the conditional expectation under censoring and association: strong uniform consistency," Statistical Papers, Springer, vol. 59(3), pages 1009-1030, September.
    • Handle: RePEc:spr:stpapr:v:59:y:2018:i:3:d:10.1007_s00362-016-0801-8
    DOI: 10.1007/s00362-016-0801-8
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    References listed on IDEAS

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    1. Stute, W., 1993. "Consistent Estimation Under Random Censorship When Covariables Are Present," Journal of Multivariate Analysis, Elsevier, vol. 45(1), pages 89-103, April.
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    4. Dominik Wied & Rafael Weißbach, 2012. "Consistency of the kernel density estimator: a survey," Statistical Papers, Springer, vol. 53(1), pages 1-21, February.
    5. Doukhan, Paul & Neumann, Michael H., 2007. "Probability and moment inequalities for sums of weakly dependent random variables, with applications," Stochastic Processes and their Applications, Elsevier, vol. 117(7), pages 878-903, July.
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