Search

In the article, the tests are constructed for the hypotheses thatp⩾ 2 independent samples have the same distribution density (homogeneity hypothesis) or have the same well-defined distribution density (goodness-of-fit test). The limiting power of the constructed tests is found for some local “close” alternatives. [ABSTRACT FROM AUTHOR]

We construct new criteria for testing the hypotheses that p ≥ 2 independent samplings have identical densities of distribution (hypothesis of homogeneity) or the same well-defined densities of distribution (goodness-of-fit test). The limiting power of the constructed criteria is established for some local 'close' alternatives. [ABSTRACT FROM AUTHOR]

The limiting distribution of the integral square deviation of a kernel-type nonparametric estimator of the Bernoulli regression function is established. The criterion of testing the hypothesis about the Bernoulli regression function is constructed. The question as to its consistency is studied. The power asymptotics of the constructed test is also studied for certain types of close alternatives. [ABSTRACT FROM AUTHOR]

The problem of estimation of a distribution function is considered in the case where the observer has access only to a part of the indicator random values. Some basic asymptotic properties of the constructed estimates are studied. The limit theorems are proved for continuous functionals related to the estimation of $$ {\hat{F}_n}(x) $$ in the space C[ a, 1 - a], 0 < a < 1/2. [ABSTRACT FROM AUTHOR]

The limit distribution of an integral square deviation with weight in the form of 'delta'-functions for the Rosenblatt-Parzen probability density estimator is determined. In addition, the limit power of the goodness-of-fit test constructed by using this deviation is investigated. [ABSTRACT FROM AUTHOR]

A goodness-of-fit test is constructed by using a Wolverton-Wagner distribution density estimate. The question as to its consistency is studied. The power asymptotics of the constructed goodness-of-fit test is also studied for certain types of close alternatives. [ABSTRACT FROM AUTHOR]