In the present paper, the full range Strichartz estimates for homogeneous Schrödinger equations with non-degenerate and non-smooth coefficients are proved. For inhomogeneous equation, the non-endpoint Strichartz estimates are also obtained. [ABSTRACT FROM AUTHOR] more...
In this paper, a general class of estimators for the estimation of a finite population total in multi-character surveys is proposed. It is shown that the estimators proposed by Amab (2002), Amahia et al. (1989) and Bansal and Singh (1985) are the special cases of the proposed class of estimators. The proposed class of estimators is always more efficient than the estimator proposed by Rao (1966). [ABSTRACT FROM AUTHOR] more...
ASYMPTOTIC distribution, DISTRIBUTION (Probability theory), BOX-Jenkins forecasting, ESTIMATION theory, MARTINGALES (Mathematics), SAMPLE size (Statistics), STATISTICAL sampling, SIZE, PAPER
Abstract
In this paper, we derive the asymptotic distributions of AugmentedDickey-Fuller (ADF) tests under very mild conditions. The tests were originally proposed and investigated by Said and Dickey (1984) for testing unit roots in finite-order ARMA models with i.i.d, innovations, and are based on a finite AR process of order increasing with the sample size. Our conditions are significantly weaker than theirs. In particular, we allow for general linear processes with martingale difference innovations, possibly having conditional heteroskedasticities. The linear processes driven by ARCH type innovations are thus permitted. The range for the permissible increasing rates for the AR approximation order is also much wider. For the usual t-type test, we only require that it increase at order o(n[sup ½]) while they assume that it is of order o(n[sub K]) for some k satisfying 0 < k ≤ 1/3. [ABSTRACT FROM AUTHOR] more...