The extended Glivenko-Cantelli property for Kernel-Smoothed estimator of the cumulative distribution function in the length-biased sampling

Author(s):

Masoud Ajami * , Raheleh Zamini , Seyed Mahdi Amir Jahanshahi

Message:
Article Type:
Research/Original Article (دارای رتبه معتبر)
Abstract:
‎Let $\{Y_i; i = 1,\ldots,n \}$ be a length-biased sample from a population with cumulative distribution function $F(\cdot)$‎. If the probability of an item selected in the sample is proportional to its length‎, ‎then the distribution of the observed length is known as the length-biased distribution‎.‎We consider the kernel-type estimator $F_n^s(\cdot)$ of $F(\cdot)$‎. ‎Under suitable conditions‎, ‎the extended Glivenko-Cantelli theorem for $F_n^s(\cdot)$ is proved‎.
Keywords:

Extended Glivenko-Cantelli Theorem , Smoothed Estimator , Strong Consistency

Language:
English
Published:
Journal of Mahani Mathematical Research, Volume:13 Issue: 2, Summer and Autumn 2024
Pages:
535 to 545
https://www.magiran.com/p2753623  
سامانه نویسندگان
  • Author (3)
    Sma Jahanshahi
    Assistant Professor Statistics, University of Sistan and Baluchestan, Zahedan, Iran
    Jahanshahi، Sma
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