Consistency result of recursive conditional distribution estimate for dependent data under left truncation, with applications to the conditional quantile
Vol. 17 No. 1 (2022) P.53~P.81
DOI: || https://doi.org/10.21915/BIMAS.2022102 |
| ||10.21915/BIMAS.2022102 |
In this paper, we discuss a question that is often asked repeatedly in the context of statistical studies, namely the presence of incomplete data in the dataset. Therefore, our goal is to study the recursive nonparametric estimation of the conditional distribution function of a vectorial response valued variable Y explained by a Hilbertian random variable X=x, based on the double-kernel approach. And because we are always looking for more credible methods that are in line with the research methodology, then, it is well known that the recursive methods are more efficient than its nonrecursive rival. Whereas, the variable of interest Y is left truncated by another variable T, that is, the random variables Y and T are observed if and only if $Y \geqslant T$; otherwise nothing is observed if Y
Nonparametric recursive estimate, Conditional distribution, Left truncation, Conditional quantile, Functional data, α-mixing, Uniform almost sure convergence.
MATHEMATICAL SUBJECT CLASSIFICATION 2010
Primary: 62G20, 62G08, 62G35, 62E20.
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