Mar 11, 2004 - i=1 ani ξi, where {ani, 1 ⤠i ⤠n} is a triangular array of nonnegative numbers such that supn. ân i=1 a2 ni < â, max1â¤iâ¤n ani â 0 as n ...
limit theorem for kernel estimators of the distribution function of Xj in the setting of ..... ical considerations as in van der Vaart and Wellner (1996, App. A.2) or from.
Iglehart (1974), and Shimura (1983). Similar conditional limit ..... for a constant 0
bers depending on n. We are interested in the double-indexed permutation ...... and complicated conditional arguments, which will be presented in the proofs. Ž .
_~dimr Ak[F ] is a graded algebra whose Hilbert function is the f-vector. Note that A[F]- k=- of F, i.e., dim Ak[F] =card F k =fk(F). Let f={fl,f2 ..... f,} be a basis of E.
May 28, 1983 - that R°° is paracompact [11, p.298]. ... (Af,d). G is said to be q-LC a t i G M (rei. M) (refer to [18, p.45]) .... (2) d{f{x), g{x)) < e(x), all x € X - X0.
Aug 31, 1994 - a2x = 0 implies ax = 0 and xa2 = 0 implies xa = 0.) Proof. 1 â 2. Denote by S the central closure of R. By Martindale's theorem, S has a minimal ...
Introduction. The purpose of the present paper is first to reformulate a Lipschitz convergence theorem for Riemannian manifolds originally introduced by. Gromov ...
Πn,\ Mn.-^Mat along the normals to M^ induces a C^-diffeomorphism from Mn, onto M*,. Hence we have a sequence of Cuβ metrics{Πn,%gn,} on Moo. We claim ...
here that the Hodge structure of X with codim X= 2, 3 was previously studied by ... For the fundamental properties of Kahler C-spaces with b2 =1, see [6, Part I].
By Adrian CONSTANTIN. University of Vienna, Faculty of Mathematics, ..... of di erential equations, D. C. Heath and Co.,. Boston, Mass., 1965. [ 7 ] M. Nagumo ...
obtained by a slight modification of argument in Durrett and Neuhauser [(1991),. Appendix] for 1-dependent oriented site percolation. [See also Bramson and.
Otherwise we say that capp£'=0. It is clear that the property (8) ... is measurable then there is a sequence of open subsets ^ =) ^2 ^> ⢠of ^ε δ such that x ÏM.
AND QIYING WANG. Carleton University, Carleton University and Australian National University. Let X, X1,X2,... be a sequence of nondegenerate i.i.d. random ...
Here we prove the generalization of Weinstein's theorem for Finsler manifolds: an isometry of a compact oriented Finsler manifold of positive flag curvature has a ...
Jan 23, 2004 - with K. The dimension 1, 2, 3 subspaces are the points, lines, planes of ... M. WILD projectivities in [1] (but in modern texts the meaning of collineation ... U1 â U2. Things get more interesting for n(V ) ⥠3; here is our (not so
ξ e UM, where UM is the unit sphere bundle of M. We can estimate constants α, ε > 0 explicitly, but we omit it to avoid non-essential complexity. Here we call it ...
Jun 28, 1993 - such that if eiλx is replaced by its eigenfunctionals, then does a similar Paley-. Wiener theorem hold? For the sake of simplicity, it is sufficient to.
results are first proved by Bourgain by extending the Newton approach introduced by. Craig-Wayne [11] for periodic solutions. Its main advantage is to require ...
paper, we give a conceptually clear proof of Goodman's theorem, and use the method to solve Friedman's problem just mentioned, as well as to obtain several ...
remarked that for a ring R the following statements are equivalent: (1) dim R =0, (2) Î ;= 1 PA = I Î ;= 1 ÎA for all finitely generated ideals / and all R-modules A, ... The above corollary is false if (p) is a minimal prime ideal. For example, in
It includes the Rieman integral, Riemann-Stieltjes integral, Lebesgue integral,. Denjoy-Perron integral among others. The Kurzweil-Henstock theory on the.
are not almost polycyclic, i.e., possess a soluble normal subgroup of finite index. ... of G is not finitely generated, then the maximum condition is satisfied by the ... C oo of PrÏfer's type satisfies part (b) of every condition (II) to (VIII) of
LIMIT THEOREM FOR MAXIMUM OF STANDARDIZED. U-STATISTICS WITH AN APPLICATION. By Lajos Horváth1 and Qi-Man Shao2. University of Utah and ...
The Annals of Statistics 1996, Vol. 24, No. 5, 2266–2279
LIMIT THEOREM FOR MAXIMUM OF STANDARDIZED U-STATISTICS WITH AN APPLICATION ´ 1 and Qi-Man Shao2 By Lajos Horvath University of Utah and University of Oregon We show that the maximally selected standardized U-statistic goes in distribution to an infinite sum of weighted chi-square random variables in the degenerate case. The result is applied to the detection of possible changes in the distribution of a sequence observation.
1. Introduction and results. Let X1 ; X2 ; : : : ; Xn be independent random variables. We want to test the null hypothesis H0 x X1 ; X2 ; : : : ; Xn are identically distributed against the alternative hypothesis that there is a change-point in the sequence X1 ; X2 ; : : : ; Xn . Namely, HA : there is an integer k∗ , 1 ≤ k∗ < n, such that PX1 ≤ t = PX2 ≤ t = · · · = PXk∗ ≤ t; PXk∗ +1 ≤ t = PXk∗ +2 ≤ t = · · · = PXn ≤ t for all t and PXk∗ ≤ t0 6= PXk∗ +1 ≤ t0 for some t0 : The change-point problem has been studied extensively in the literature. For a survey we refer to Brodsky and Darkhovsky (1993). Wolfe and Schecht´ man (1984) and Cs¨org˝o and Horvath (1987) suggested several tests based on the linear rank statistics with quantile scores and U-statistics. Cs¨org˝o ´ (1988) used U-statistics which are generalizations of Wilcoxon– and Horvath Mann–Whitney-type statistics to detect a possible change-point. For surveys on U-statistics we refer to Serfling (1980), Lee (1990) and Koroljuk and Borovskich (1994). Let hx; y be a symmetric function and define X X Uk; n = hXi ; Xj − kn − kθ (1.1) 1≤i≤k k 0. Then Eh Uk; n 1 (1.2) lim P alog n max ≤ t + blog n = exp−2e−t n→∞ τ 1≤k
