Perbandingan Estimator Histogram dan Estimator Kernel

  • Christine Krisnandari Ekowati Pendidikan Matematika FKIP Undana
Keywords: Estimator, Histogram, Kernel

Abstract

One of the important things in statistical analysis is the quarterly report of the probability density function which is called the density function. There are two approach methods that are usually used, namely the parameter approach associated with certain distribution assumptions and the non-parametric density calculation method. The non-parametric method that we often encounter is the histogram method.

Some of the weaknesses of the histogram method become a reference for developing other methods, namely the kernel method, where the kernel density estimator has a parameter that needs to be estimated, namely the bandwidth h. The problem formulation in this literature review is how to choose the bandwidth from the kernel density estimator in a density function f in R and compare it with the histogram estimator.

The conclusions that can be drawn include: (1) The estimated density of the histogram is:  

 dengan  , (2) The kernel density estimator is:

 , (3) The kernel estimator overcomes the weaknesses of the histogram estimator, (4) The convergence rate of the kernel estimator is better than the histogram, (5) The selection of bandwidth with the asymptotically unbiased cross validation (least cross validation) method produces the optimum bandwidth.

References

Bartlett, M.S., 1963, Statistikal Estimation of Density Function, Aankhya., 25A, 245-254
Bowman, A., 1984, An Alternative Method of Cross-Validation for Density Estimates, Biometrika, 71, 353-360
Berliner,L.M., 1993, Improving on Inadmissible Estimators in Control Problem, Ann.Statist., 11, 814-826
Berger, J.O., 1980, Statistical Decision Theory: Foundation, Consepts and Methods, Springer-Verlag,New York
Ekowati, Ch.K., 1998, Perbadingan Estimator Klasik dan Estimator Invers dalam Kalibrasi Linear Multi-Univariat, Tesis-UGM Yogyakarta
Hall, P., 1982, Cross-Validation in Density Estimation, 69, 383-390
Published
2021-05-15
How to Cite
Ekowati, C. (2021). Perbandingan Estimator Histogram dan Estimator Kernel. FRAKTAL: JURNAL MATEMATIKA DAN PENDIDIKAN MATEMATIKA, 2(1), 43-53. https://doi.org/10.35508/fractal.v2i1.4036
Section
Articles