ABSTRACT
Remark 2.2 The assertions of Theorem 2.1-2.4 remain true if the parameters /511 and CJ2 are replaced by a suitable estimators. Namely, the parameter 1511 and CJ2 can be replaced by the estimators bu; and 0"~ defined in Eqns (2.5) and (2.31 ), respectively. Remark 2.3 The explicit form of the distribution of V,1.1 , 17 E [0, I /2], "Y E (0, I), and vn are known. They were derived independently by several authors, e.g., Bhattacharya and Brockwell (1976), Shepp (1979), Yao (1987) and Ferger (1994). Sthryn (1996) showed that random variable
(2.32)
(2.33)
The corresponding distribution function can be calculated taking into
(3.1)
where Jl, b11 =1-0 and m(<n) are unknown parameters and {E1 }~ 1 is a linear process satisfying
t = 1, 2, ... (3.2)
Next, we formulate two theorems that correspond to Theorems 2.1-2.4.
