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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 \(\alpha(C_ m)\).
62G07 Density estimation
62M09 Non-Markovian processes: estimation
60G10 Stationary stochastic processes
62G30 Order statistics; empirical distribution functions