Geodesic
Negative $\lambda$-binomial regression in dose-effect relationship
Vestnik Tverskogo gosudarstvennogo universiteta. Seriâ Prikladnaâ matematika, no. 4 (2022), pp. 53-75

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This paper is concern to the problem of estimating the distribution function and its quantiles in the dose-effect relationships with nonparametric negative $\lambda$-binomial regression. Here, a kernel-based estimators of the distribution function are proposed, of which kernel is weighted by the negative $\lambda$-binomial random variable at each covariate. Our estimates are consistent, that is, they converge to their optimal values in probability as $n$, the number of observations, grow to infinity. It is shown that these estimates have a smaller asymptotic variance in comparison, in particular, with estimates of the Nadaray-Watson type and other estimates. Nonparametric quantiles estimators obtained by inverting a kernel estimator of the distribution function are offered. It is shown that the asymptotic normality of this bias-adjusted estimator holds under some regularity conditions. In the first part, the relations between the moments of the negative $\lambda$-binomial distribution are analyzed. A new characterization of the Poisson distribution is obtened.
Mots-clés : negative $\lambda$-binomial response model
Keywords: effective dose level, nonparametric estimate. 
@article{VTPMK_2022_4_a4,
     author = {M. S. Tikhov},
     title = {Negative $\lambda$-binomial regression in dose-effect relationship},
     journal = {Vestnik Tverskogo gosudarstvennogo universiteta. Seri\^a Prikladna\^a matematika},
     pages = {53--75},
     publisher = {mathdoc},
     number = {4},
     year = {2022},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VTPMK_2022_4_a4/}
}
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M. S. Tikhov. Negative $\lambda$-binomial regression in dose-effect relationship. Vestnik Tverskogo gosudarstvennogo universiteta. Seriâ Prikladnaâ matematika, no. 4 (2022), pp. 53-75. http://geodesic.mathdoc.fr/item/VTPMK_2022_4_a4/