Estimation in the correlation-regression model and the dominant measure method. (English. Ukrainian original) Zbl 0921.62111

Kozachenko, Yu. V.; Majboroda, R. E.

Theory Probab. Math. Stat. 55, 111-120 (1997); translation from Teor. Jmovirn. Mat. Stat. 55, 107-116 (1996).

The authors consider the problem of estimation of the correlation function for the model \[ X(t)=\sum_{k=1}^M g_k(t)\xi_k(t), \;0\leq t\leq T_0, \] where \(g_k(t)\) are unknown nonrandom functions, and \(\xi_k(t)\) are Gaussian stationary processes. Consistency in the uniform norm of estimates of the correlations \(r_{ij}(\tau)=E\xi_i(0)\xi_j(\tau)\) is examined. The method of majorizing measures and properties of the square-Gaussian processes are used to estimate the probability of deviation in the uniform norm.

Reviewer: M.P.Moklyachuk (Kyïv)

MSC:

62M10	Time series, auto-correlation, regression, etc. in statistics (GARCH)
62G09	Nonparametric statistical resampling methods
60G15	Gaussian processes
62G07	Density estimation

Keywords:

correlation coefficients; square-Gaussian processes; consistency; majorizing measures