Asymptotic Behaviors of Nearest Neighbor Kernel Density Estimator in Left-truncated Data

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Zamini R.; FAKOOR V.; SARMAD M.

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Journal Paper

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Journal: Journal of Sciences, Islamic Republic of Iran Year:2014 | Volume:25 | Issue:1 Page(s): 57-67

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Information Journal Paper

Title

Asymptotic Behaviors of Nearest Neighbor Kernel Density Estimator in Left-truncated Data

Author(s)

Zamini R. | FAKOOR V. | SARMAD M. | Issue Writer Certificate

Keywords

Asymptotic normality

Left-truncation

Nearest neighbor

Strong consistency

Abstract

Kernel density estimators are the basic tools for density estimation in non-parametric statistics. The k-Nearest neighbor kernel estimators represent a special form of kernel density estimators, in which the bandwidth is varied depending on the location of the sample points. In this paper, we initially introduce the k-Nearest neighbor kernel density estimator in the random Left-truncation model, and then prove some of its asymptotic behaviors, such as strong uniform consistency and Asymptotic normality. In particular, we show that the proposed estimator has truncation-free variance. Simulations are presented to illustrate the results and show how the estimator behaves for finite samples. Moreover, the proposed estimator is used to estimate the density function of a real data set.

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APA: Copy

Zamini, R., FAKOOR, V., & SARMAD, M.. (2014). Asymptotic Behaviors of Nearest Neighbor Kernel Density Estimator in Left-truncated Data. JOURNAL OF SCIENCES ISLAMIC REPUBLIC OF IRAN, 25(1), 57-67. SID. https://sid.ir/paper/718184/en

Vancouver: Copy

Zamini R., FAKOOR V., SARMAD M.. Asymptotic Behaviors of Nearest Neighbor Kernel Density Estimator in Left-truncated Data. JOURNAL OF SCIENCES ISLAMIC REPUBLIC OF IRAN[Internet]. 2014;25(1):57-67. Available from: https://sid.ir/paper/718184/en

IEEE: Copy

R. Zamini, V. FAKOOR, and M. SARMAD, “Asymptotic Behaviors of Nearest Neighbor Kernel Density Estimator in Left-truncated Data,” JOURNAL OF SCIENCES ISLAMIC REPUBLIC OF IRAN, vol. 25, no. 1, pp. 57–67, 2014, [Online]. Available: https://sid.ir/paper/718184/en

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