Several new kernel estimators for population abundance

Albadareen, Baker Ishaq; Ismail, Noriszura

doi:10.1063/1.4981002

Cited by 4 publications

(5 citation statements)

References 20 publications

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“…This function transforms the perpendicular distances by a non-decreasing function that produces estimator (0). The original estimator in equation (2), which is ( ), is applied to the original data and the transformed estimator, (0), is obtained from the back-transformation such that:…”

Section: Methodsmentioning

confidence: 99%

A General Base of Power Transformation to Improve the Boundary Effect in Kernel Density without Shoulder Condition

Albadareen

Ismail

2020

Pak.j.stat.oper.res.

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In this paper, a general base of power transformation under the kernel method is suggested and applied in the line transect sampling to estimate abundance. The suggested estimator performs well at the boundary compared to the classical kernel estimator without using the shoulder condition assumption. The transformed estimator show smaller value of mean squared error and absolute bias from the efficiency results obtained using simulation.

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Section: Methodsmentioning

confidence: 99%

A General Base of Power Transformation to Improve the Boundary Effect in Kernel Density without Shoulder Condition

Albadareen

Ismail

2020

Pak.j.stat.oper.res.

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“…shown in (12) assumes that the sample size is large. We carry out simulation study for comparing and testing the proposed estimator with the kernel estimator using different sample sizes, which are 50,1 00, and 200 n …”

Section: Methodsmentioning

confidence: 99%

“…An advantage of the method is that it is adequate to record only the perpendicular distances of the detected objects. At the end, the recorded distances 12…”

Section: Introductionmentioning

confidence: 99%

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An Adaptation of Kernel Density Estimation for Population Abundance using Line Transect Sampling When the Shoulder Condition is Violated

Albadareen*,

Ismail

2019

IJITEE

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Kernel estimation is a commonly used method to estimate the population density in line transect sampling. In general, the classical kernel estimator of (0) X f , which is the probability density function at perpendicular distance x  0 , inclines to be underestimated. In this study, a power transformation of perpendicular distance is proposed for the kernel estimator when the shoulder condition is violated. The mathematical properties of the proposed estimator are derived. A simulation study is also carried out for comparing the proposed estimator with the classical kernel estimators

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“…In statistics and machine learning, kernel estimators are vital and versatile tools in the estimation of observations. Despite the modern methods of data estimation and numerous kernel functions in literature, new kernel functions are still introduced due to the great influence of kernel function when evaluating its performance empirically [16]- [20]. This paper introduces a new kernel family of the beta polynomial kernel family, and the results of both families revealed that the modified kernel functions outperformed the current beta polynomial family with AMISE as a performance measure.…”

mentioning

confidence: 97%

A new family of kernels from the beta polynomial kernels with applications in density estimation

Siloko

Nwankwo

Siloko

2020

Int. J. Adv. Intell. Informatics

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One of the fundamental data analytics tools in statistical estimation is the non-parametric kernel method that involves probability estimates production. The method uses the observations to obtain useful statistical information to aid the practicing statistician in decision making and further statistical investigations. The kernel techniques primarily examine essential characteristics in a data set, and this research aims to introduce new kernel functions that can easily detect inherent properties in any given observations. However, accurate application of kernel estimator as data analytics apparatus requires the kernel function and smoothing parameter that regulates the level of smoothness applied to the estimates. A plethora of kernel functions of different families and smoothing parameter selectors exist in the literature, but no one method is universally acceptable in all situations. Hence, more kernel functions with smoothing parameter selectors have been propounded customarily in density estimation. This article proposes a distinct kernel family from the beta polynomial kernel family using the exponential progression in its derivation. The newly proposed kernel family was evaluated with simulated and life data. The outcomes clearly indicated that this kernel family could compete favorably well with other kernel families in density estimation. A further comparison of numerical results of the new family and the existing beta family revealed that the new family outperformed the classical beta kernel family with simulation and real data examples with the aid of asymptotic mean integrated squared error (AMISE) as criterion function. The information obtained from the data analysis of this research could be used for decision making in an organization, especially when human and material resources are to be considered. In addition, Kernel functions are vital tools for data analysis and data visualization; hence the newly proposed functions are vital exploratory tools.

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Several new kernel estimators for population abundance

Cited by 4 publications

References 20 publications

A General Base of Power Transformation to Improve the Boundary Effect in Kernel Density without Shoulder Condition

A General Base of Power Transformation to Improve the Boundary Effect in Kernel Density without Shoulder Condition

An Adaptation of Kernel Density Estimation for Population Abundance using Line Transect Sampling When the Shoulder Condition is Violated

A new family of kernels from the beta polynomial kernels with applications in density estimation

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