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- MakaleYalnız künye2026Scopus SJRQ2A Bernstein polynomial estimation of the moment generating function
Susam, Selim Orhun
We study Bernstein polynomial smoothing for nonparametric estimation of the moment generating function (MGF) of a distribution supported on (Formula presented.). We prove strong consistency of the Bernstein-smoothed MGF estimator and show that, when the smoothing degree m grows sufficiently fast, it shares the same (Formula presented.) asymptotic normal distribution as the empirical MGF estimator, with variance (Formula presented.). A second-order bias–variance expansion reveals that Bernstein smoothing yields a bias of order (Formula presented.) and a variance-reduction term of order (Formula presented.). This leads to the optimal smoothing rate (Formula presented.) for pointwise mean squared error (MSE) minimization. Simulation results confirm that the Bernstein estimator is especially effective in challenging boundary-dominated settings, notably for U-shaped beta models and for larger positive t values. Overall, Bernstein polynomial smoothing provides a simple, theoretically justified, and practically effective tool for nonparametric MGF estimation on compact supports.
- MakaleYalnız künye2026Scopus SJRQ3A multi-parametric unit distribution via Bernstein polynomials
Susam, Selim Orhun
This study develops the method of constructing a multi-parametric distribution on the unit interval using Bernstein polynomials and investigates its key statistical properties. The performance of the proposed distribution’s parameter estimators was evaluated by Monte Carlo simulation under both maximum-likelihood (MLE) and minimum-distance frameworks, with the MLE approach generally yielding lower estimation error. A real data example illustrates the advantages of the construction method. The results reveal that the Bernstein distribution provides superior goodness-of-fit to the dataset compared with competing models.
- MakaleAçık Erişim2022TAIL DEPENDENCE ESTIMATION BASED ON SMOOTH ESTIMATION OF DIAGONAL SECTION
Susam, Selim Orhun
This paper is mainly developed around the diagonal section which is strongly related to tail dependence coefficients as defined in Nelsen [19]. Hence, we propose a flexible method for estimating tail dependence coefficients based on the new smooth estimation of the diagonal section based on the Bernstein polynomial approximation. To assess the performance of the new estimators we conduct the Monte-Carlo simulation study. As a result of the simulation study, both estimators perform satisfactory performance. Also, the estimation methods are illustrated by real data examples.
AtıfWoS1OpenAlex1
İncele - MakaleAçık Erişim2022Scopus SJRQ3A multi-parameter Generalized Farlie-Gumbel-Morgenstern bivariate copula family via Bernstein polynomial
Susam, Selim Orhun
In this paper, we are proposing a flexible method for constructing a bivariate generalized Farlie-Gumbel-Morgenstern (G-FGM) copula family. The method is mainly developed around the function ϕ(t) (t ∈ [0, 1]), where ϕ is the generator of the G-FGM copula. The proposed construction method has useful advantages. The first of which is the direct relationship between the ϕ function and Kendall’s tau. The second advantage is the possibility of constructing a multi-parameter G-FGM copula which allows us to better harmonize empirical instruction with the model. The construction method is illustrated by three real data examples.
AtıfScopus16WoS15OpenAlex15
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