matrix where Sw o
The proof of this theorem is similar to the proof of normality for the unweighted parameter [3n as presented in Dupuy, Grama and Mesbah (2003) and therefore will be omitted.
Hence once again, if model (1.7) is correct, pw,n and f3n will be close to each other since the estimators are consistent. However, if model (1.7) is not correct, then the two estimators will differ from each other. This idea is reiterated in the following conjecture:
Theorem 2. Under the model (1.7), the vector ^/n (f3w,n — ftn)converges in distribution to a bivariate normal distribution with zero mean and a covariance
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