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A note on estimating the conditional expectation under censoring and association: strong uniform consistency. (English) Zbl 1401.62052

Summary: Let \(\{ (X_{i},Y_{i}), i \geq 1 \} \) be a strictly stationary sequence of associated random vectors distributed as \((X,Y)\). This note deals with kernel estimation of the regression function \(r(x)=\mathbb {E}[Y|X=x]\) 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 \(r_{n}(x)\). Simulations are drawn to illustrate the results and to show how the estimator behaves for moderate sample sizes.

MSC:

62G07 Density estimation
62N02 Estimation in survival analysis and censored data
62G05 Nonparametric estimation
62G20 Asymptotic properties of nonparametric inference

Software:

KernSmooth
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Full Text: DOI

References:

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