Pollard showed for k-means clustering and a very broad class of sampling distributions that the optimal cluster means converge to the solution of the related population criterion as the size of the data set increases. We extend this consistency result to k-parameters clustering, a method derived...

The transition density of a diffusion process does not admit an explicit expression in general, which prevents the full maximum likelihood estimation (MLE) based on discretely observed sample paths. Aït-Sahalia [J. Finance 54 (1999) 1361–1395; Econometrica 70 (2002) 223–262] proposed asymptotic...

We investigate the asymptotic behavior of the maximum likelihood estimators of the unknown parameters of positive recurrent Ornstein–Uhlenbeck processes driven by Ornstein–Uhlenbeck processes.

While differencing transformations can eliminate nonstationarity, they typically reduce signal strength and correspondingly reduce rates of convergence in unit root autoregressions. The present paper shows that aggregating moment conditions that are formulated in differences provides an orderly...

In this article, consistency and asymptotic normality of the quasi-maximum likelihood estimator (QMLE) in the class of polynomial augmented generalized autoregressive conditional heteroscedasticity models (GARCH) is proven. The result extends the results of the standard GARCH model to the class...