A presmooth estimator of unbiased distributions with length-biased data
نویسندگان
چکیده
منابع مشابه
A Berry-Esseen Type Bound for the Kernel Density Estimator of Length-Biased Data
Length-biased data are widely seen in applications. They are mostly applicable in epidemiological studies or survival analysis in medical researches. Here we aim to propose a Berry-Esseen type bound for the kernel density estimator of this kind of data.The rate of normal convergence in the proposed Berry-Esseen type theorem is shown to be O(n^(-1/6) ) modulo logarithmic term as n tends to infin...
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length-biased data are widely seen in applications. they are mostly applicable in epidemiological studies or survival analysis in medical researches. here we aim to propose a berry-esseen type bound for the kernel density estimator of this kind of data.the rate of normal convergence in the proposed berry-esseen type theorem is shown to be o(n^(-1/6) ) modulo logarithmic term as n tends to infin...
متن کاملSome Asymptotic Results of Kernel Density Estimator in Length-Biased Sampling
In this paper, we prove the strong uniform consistency and asymptotic normality of the kernel density estimator proposed by Jones [12] for length-biased data.The approach is based on the invariance principle for the empirical processes proved by Horváth [10]. All simulations are drawn for different cases to demonstrate both, consistency and asymptotic normality and the method is illustrated by ...
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In simple random sampling, there is an equal chance of selection for each unit in the population. However, there are some practical situations where this might not be ideal. We consider the case of length-biased sampling, whereby the chance of selection of a unit is proportional to the length of the unit, by which the length-biased density is defined. Specifically we consider the case of a cont...
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in this paper, we prove the strong uniform consistency and asymptotic normality of the kernel density estimator proposed by jones [12] for length-biased data.the approach is based on the invariance principle for the empirical processes proved by horváth [10]. all simulations are drawn for different cases to demonstrate both, consistency and asymptotic normality and the method is illustrated by ...
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ژورنال
عنوان ژورنال: Mathematical Sciences
سال: 2019
ISSN: 2008-1359,2251-7456
DOI: 10.1007/s40096-019-00301-z