On estimating the Bernoulli regression function using Bernstein polynomials

Abstract

The estimate for the Bernoulli regression function is constructed using the Bernstein polynomial. The question of its consistency and asymptotic normality is studied. Testing hypothesis is constructed on the form of the Bernoulli regression function. Also, the test is constructed for the hypothesis on the equality Bernoulli functions. The question of consistency of the constructed tests is studied.

Keywords:

• Bernstein polynomial
• Bernoulli regression function
• consistency
• power of test
• one-sided alternatives

2010 Mathematics Subject Classification:

• 62G10
• 62G20