Two-dimensional Bernstein polynomial density estimators |
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Authors: | Axel Tenbusch |
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Institution: | (1) Fachbereich Mathematik/Informatik, Universität Osnabrück, 49069 Osnabrück, Germany |
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Abstract: | A Bernstein polynomial estimator for fnN(x, y) for an unknown probability density functionf(x, y) concentrated on the triangle ={(x, y): 0x, y<1,x+y<1} or on the square =(x, y):0 x, y 1 is developed. As a measure of quality the exact order of magnitude for the pointwise mean squared error is established. It is seen that the quality of these Bernstein polynomial estimators is comparable with the quality of the so-called kernel estimators. Further for such estimators uniform weak consistency results and central limit theorems are developed. |
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