# zbMATH — the first resource for mathematics

Some questions of nonparametric statistics of weakly dependent observations. (English. Russian original) Zbl 0748.62023
Theory Probab. Math. Stat. 43, 21-27 (1991); translation from Teor. Veroyatn. Mat. Stat., Kiev 43, 19-26 (1990).
Summary: The author establishes exponential estimates of the probability of exiting from a level by the variables $$w^ 2_ n$$ and $T_ n=\int^{+\infty}_{-\infty}| f_ n(x)-f(x)|^ 2a_ 0(x)dx$ ($$\omega^ 2_ n$$ are statistics of the $$\omega^ 2$$-test, $$f_ n(x)$$ is a nonparametric estimate of the unknown density of the stationary distribution of a sequence of observations) under the assumption that the sequence of observations $$\{x_ 1,x_ 2,\dots,x_ n\}$$ forms a stationary random process in the strict sense, satisfying a strong mixing condition (s.m.c.) with coefficient $$\alpha(C_ m)$$.
##### MSC:
 62G07 Density estimation 62M09 Non-Markovian processes: estimation 60G10 Stationary stochastic processes 62G30 Order statistics; empirical distribution functions