Application of Bernstein Polynomials for smooth estimation of a distribution and density function

By G. Babu, Angelo J. Canty, Yogendra P. Chaubey. 2002

187 citations recorded by the source corpus.

Subfields: Artificial Intelligence, Control and Systems Engineering, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/325bfac9deb0a015810154941605fa0a96304c6c

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In Artificial Intelligence

In Control and Systems Engineering

In Statistics and Probability

Citations in the corpus

Flexible semiparametric generalized Pareto modeling of the entire range of rainfall amount (2019, unknown): “Note that the choice of m suggested in Babu et al. (2002), that is, m̄(n) = [ n log n ], yields m̄(700) = 106 and m̄(1, 500) = 205, which clearly overfits in our framework.”
Bernstein polynomial probability density estimation (2004, methodology): “Then clearly, all odd moments of Wi are equal to zero, all even moments of Wi are equal to 2x(1 − x), and Pr(x) = r∑ j=0 b2jr (x) = P ( r∑ i=1 Wi = 0 ) (see Babu et al., 2002).”
Smooth estimation of a distribution and density function on a hypercube using Bernstein polynomials for dependent random vectors (2006, methodology): “On the other hand, motivated by the problem of smooth estimation of a continuous distribution function, Babu et al. (2002) obtained the same estimator as that of Vitale (1973) and investigated its large sample properties.”
Arming the public with artificial intelligence to counter social bots (2019, methodology): “duce adequate ts. This is likely due to the shape of the P(S jHuman) curve, with its mode near, but not at, zero. Ultimately we chose a lesser-known family of curves for our t: Bernstein polynomials (Babu et al., 2002). Implementation is straightforward as computing values of a polynomial curve is s”
Most Likely Transformations (2015, background): “Yi m=M/=N corresponding to probabilities evaluated at the quantiles m=M for m D 0; : : : ;M (Babu et al., 2002).”
A bias-reduced approach to density estimation using Bernstein polynomials (2010, methodology): “This estimator was introduced by Vitale (1975) and was further studied by Babu, Canty, and Chaubey (2002) .”