Abstract
In this article, our proposed kernel estimator, named as Gumbel kernel, which broadened the class of non-negative, asymmetric kernel density estimators. Such kernel estimator can be used in nonparametric estimation of the probability density function (pdf). When the density functions have limited bounded support on [0, ∞) and they are liberated of boundary bias, always non-negative and obtain the optimal rate of convergence for the mean integrated squared error (MISE). The bias, variance and the optimal bandwidth of the proposed estimators are investigated on theoretical grounds as well as on simulation basis. Further, the applicability of the proposed estimator is compared to Weibull kernel estimator, where performance of newly proposed kernel is outstanding.
Highlights
To investigate the properties and features of data or in anomaly detection, density estimation performs a vital role
Our proposed kernel estimator, named as Gumbel kernel, which broadened the class of non-negative, asymmetric kernel density estimators
Such kernel estimator can be used in nonparametric estimation of the probability density function
Summary
To investigate the properties and features of data or in anomaly detection, density estimation performs a vital role. It affects the performance of the estimator at boundary points due to boundary effects, from the interior points That’s why in some cases, parametric method for curve estimation performs better than nonparametric estimation [2] Such problem is happened when variables represent some sort of physical measure such as time or length. By following Chen [7], we are going to propose a new class of density estimator named as a Gumbel kernel estimator along with its bias, variance and optimal bandwidth, which will be the keen addition in category of asymmetrical kernel(s) that solve the problem of boundary bias. The performance of the proposed estimator will be tested via real and simulated data sets in Section 4, while Section 5 concludes
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