Geodesic
On a~new estimation method of the Bernoulli regression function
Teoriâ veroâtnostej i ee primeneniâ, Tome 67 (2022) no. 2, pp. 209-222

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A new estimator for a Bernoulli regression function based on Bernstein polynomials is constructed. Its consistency and asymptotic normality are studied. A criterion for testing the hypothesis on the form of a Bernoulli regression function and a criterion for testing the hypothesis on the equality of two Bernoulli regression functions are constructed. The consistency of these two criteria is studied.
Keywords: Bernstein polynomial, Bernoulli regression function, consistency, power of a criterion, one-sided alternatives. 
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     author = {P. Babilua and \`E. A. Nadaraya},
     title = {On a~new estimation method of the {Bernoulli} regression function},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {209--222},
     publisher = {mathdoc},
     volume = {67},
     number = {2},
     year = {2022},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_2022_67_2_a0/}
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P. Babilua; È. A. Nadaraya. On a~new estimation method of the Bernoulli regression function. Teoriâ veroâtnostej i ee primeneniâ, Tome 67 (2022) no. 2, pp. 209-222. http://geodesic.mathdoc.fr/item/TVP_2022_67_2_a0/