Sweeting, "Uniform asymptotic normality
of the maximum likelihood estimator," Annals of Statistics, vol.
This approximation is reasonable, since [[??].sup.measure.sub.A] is already strongly consistent by assuming only the ergodicity of [[PHI].sub.1] (which is a milder condition than the ones required for the asymptotic normality
As in Section 3.1, sufficient conditions for asymptotic normality
are: i) [[delta].sup.2.sub.i] > 0, and ii) the SDFs of the different models are distinct.
[P-values are computed assuming asymptotic normality
.] IPS W-Statistic P-value AR Lags Total Taxes -8.663 0.000 0 to 4 Property Tax -6.516 0.000 0 to 4 Total Sales & Gross Receipts Tax -6.839 0.000 0 to 4 Individual Income Tax -4.185 0.000 0 to 4 Corporate Net Income Tax -4.532 0.000 0 to 3 Total Income Tax -2.616 0.005 0 to 3 Direct General Expenditure -6.131 0.000 0 to 4 Education Expenditure -5.377 0.000 0 to 4 Public Welfare Expenditure -0.768 0.221 0 to 4 Health & Hospital Expenditure -1.580 0.057 0 to 4 Highway Expenditure -3.650 0.000 0 to 4 Cross- Sections Obs.
The method of moments applies to all these cases and establishes the central limit theorems; similar details are given as in  (the asymptotic normality
of the number of leaves being already proved there as a special case).
Mahmoud, Smythe and Szymanski (12) used a representation with a generalized Polya urn to prove the asymptotic normality
(1996) Consistency and Asymptotic Normality
of the Quasi-maximum Likelihood Estimator in IGARCH (1,1).
The consistency and asymptotic normality
of the QMLE has been established only for specific special cases of the ARFIMA and/or FIGARCH model.
These confidence intervals are constructed based on the asymptotic normality
of the estimators for the sub-indices of the [C.sub.pk] index, and the process distribution need not be normal nor be known.
This assumption can be harder to justify than the asymptotic normality
demanded by the t test, and is rarely evaluated (Petranka 1990).
The topics include algebraic methods, discrete geometric methods, analytic methods, asymptotic normality
in enumeration, trees, planar maps, graphs, words, tilings, lattice path enumeration, permutation classes, parking functions, standard Young tableaux, and computer algebra.
From Lyapunov's theorem, the asymptotic normality
of the penalized spline estimator [??](x) with [[??].sub.opt] can be derived under the same assumption as Theorem 2 and some additional mild conditions.