By Yasui Y.

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**Extra resources for A statistical method for the estimation of window-period risk of transfusion-transmitted HIV in dono**

**Sample text**

The following result due to Nualart and Rascanu (2002) gives sufﬁcient conditions for the existence and uniqueness of the solution. For any λ ∈ (0, 1], let C λ [0, T ] be the space of continuous functions f deﬁned on the interval [0, T ] such that sup 0≤x1 =x2 ≤T |f (x1 ) − f (x2 )| < ∞. |x1 − x2 |λ Deﬁne the norm ||f ||C λ = max |f (x)| + x∈[0,T ] sup 0≤x1 =x2 ≤T |f (x1 ) − f (x2 )| <∞ |x1 − x2 |λ on the space C λ [0, T ]. Let C µ− [0, T ] = ∩λ<µ C λ [0, T ]. 83) and C1 = C0 B 3 3 − H, − H . 85) and w(t, u) = C0 u 2 −H (t − u) 2 −H .

24) where the random variable Z has the standard normal distribution and the random variables Z and η are independent. Proof: This theorem follows as a consequence of the central limit theorem for local martingales (cf. 47 in Prakasa Rao (1999b), p. 65). Observe that IT RT . 2, we obtain the following result. 2 hold. 26) where the random variable Z has the standard normal distribution and the random variables Z and η are independent. Remarks: If the random variable η is a constant with probability one, then the limiting distribution of the MLE is normal with mean zero and variance η−2 .

Let PθT be the measure induced by the process {Xt , 0 ≤ t ≤ T } when θ is the true parameter. 4 T QH,θ (s)dZs − 0 1 2 T 0 Q2H,θ (s)dwsH . 10) Maximum likelihood estimation We now consider the problem of estimation of the parameter θ based on the observation of the process X = {Xt , 0 ≤ t ≤ T } and study its asymptotic properties as T → ∞. Strong consistency Let LT (θ ) denote the Radon–Nikodym derivative dPθT /dP0T . The maximum likelihood estimator (MLE) θˆT is deﬁned by the relation LT (θˆT ) = sup LT (θ ).