1 
Central limit theorems for associated random fields with applicationsKim, Taesung 21 November 1985 (has links)
A functional central limit theorem for a strictly stationary
associated random field in the general ddimension case with an added
moment condition is proven. Functional central limit theorems for
associated random measures are also proven. More specifically,
conditions are given that imply weak convergence in the Skorohod
topology of a renormalized random measure to the ddimensional
Wiener process. These results are applied to show new functional
central limit theorems for doubly stochastic point random fields and
Poisson cluster random measures. / Graduation date: 1986

2 
Central limit theorems for associated random fields with applications /Kim, Taesung, January 1985 (has links)
Thesis (Ph. D.)Oregon State University, 1986. / Typescript (photocopy). Includes bibliographical references (leaves 7274). Also available on the World Wide Web.

3 
Central limit theorem for nonparametric regression under dependent data /Mok, Kit Ying. January 2003 (has links)
Thesis (M. Phil.)Hong Kong University of Science and Technology, 2003. / Includes bibliographical references (leaves 44). Also available in electronic version. Access restricted to campus users.

4 
Some limit theorems and inequalities for weighted and nonidentically distributed empirical processesAlexander, Kenneth S January 1982 (has links)
Thesis (Ph.D.)Massachusetts Institute of Technology, Dept. of Mathematics, 1982. / MICROFICHE COPY AVAILABLE IN ARCHIVES AND SCIENCE / Vita. / Bibliography: leaves 135137. / by Kenneth Sidney Alexander. / Ph.D.

5 
Central Limit Theorems for Empirical Processes Based on Stochastic ProcessesYang, Yuping 16 December 2013 (has links)
In this thesis, we study timedependent empirical processes, which extend the classical empirical processes to have a time parameter; for example the empirical process for a sequence of independent stochastic processes {Yi : i ∈ N}:
(1) ν_n(t, y) = n^(−1/2 )Sigma[1_(Y i(t)¬<=y) – P(Yi(t) <= y)] from i=1 to n, t ∈ E, y ∈ R.
In the case of independent identically distributed samples (that is {Yi(t) : i ∈ N} are iid), Kuelbs et al. (2013) proved a Central Limit Theorem for ν_n(t, y) for a large class of stochastic processes.
In Chapter 3, we give a sufficient condition for the weak convergence of the weighted empirical process for iid samples from a uniform process:
(2) α_n(t, y) := n^(−1/2 )Sigma[w(y)(1_(X (t)<=y) – y)] from i=1 to n, t ∈ E, y ∈ [0, 1]
where {X (t), X1(t), X2(t), • • • } are independent and identically distributed uniform processes (for each t ∈ E, X (t) is uniform on (0, 1)) and w(x) is a “weight” function satisfying some regularity properties. Then we give an example when X (t) := Ft(Bt) : t ∈ E = [1, 2], where Bt is a Brownian motion and Ft is the distribution function of Bt.
In Chapter 4, we investigate the weak convergence of the empirical processes for noniid samples. We consider the weak convergence of the empirical process:
(3) β_n(t, y) := n^(−1/2 )Sigma[(1_(Y (t)<=y) – Fi(t,y))] from i=1 to n, t ∈ E ⊂ R, y ∈ R
where {Yi(t) : i ∈ N} are independent processes and Fi(t, y) is the distribution function of Yi(t). We also prove that the covariance function of the empirical process for noniid samples indexed by a uniformly bounded class of functions necessarily uniformly converges to the covariance function of the limiting Gaussian process for a CLT.

6 
On the Asymptotic Theory of Permutation StatisticsStrasser, Helmut, Weber, Christian January 1999 (has links) (PDF)
In this paper limit theorems for the conditional distributions of linear test statistics are proved. The assertions are conditioned by the sigmafield of permutation symmetric sets. Limit theorems are proved both for the conditional distributions under the hypothesis of randomness and under general contiguous alternatives with independent but not identically distributed observations. The proofs are based on results on limit theorems for exchangeable random variables by Strasser and Weber. The limit theorems under contiguous alternatives are consequences of an LANresult for likelihood ratios of symmetrized product measures. The results of the paper have implications for statistical applications. By example it is shown that minimum variance partitions which are defined by observed data (e.g. by LVQ) lead to asymptotically optimal adaptive tests for the ksample problem. As another application it is shown that conditional ksample tests which are based on datadriven partitions lead to simple confidence sets which can be used for the simultaneous analysis of linear contrasts. (author's abstract) / Series: Report Series SFB "Adaptive Information Systems and Modelling in Economics and Management Science"

7 
Limit Theorems for Random Simplicial ComplexesAkinwande, Grace Itunuoluwa 22 October 2020 (has links)
We consider random simplicial complexes constructed on a Poisson point process within a convex set in a Euclidean space, especially the VietorisRips complex and the Cech complex both of whose 1skeleton is the Gilbert graph. We investigate at first the VietorisRips complex by considering the volumepower functionals defined by summing powers of the volume of all kdimensional faces in the complex. The asymptotic behaviour of these functionals is investigated as the intensity of the underlying Poisson point process tends to infinity and the distance parameter goes to zero. This behaviour is observed in different regimes. Univariate and multivariate central limit theorems are proven, and analogous results for the Cech complex are then given. Finally we provide a Poisson limit theorem for the components of the fvector in the sparse regime.

8 
Limit Theorems for Random FieldsZhang, Na 18 October 2019 (has links)
No description available.

9 
Construction and Approximation of Stable Lévy Motion with Values in Skorohod SpaceSaidani, Becem 12 August 2019 (has links)
Under an appropriate regular variation condition, the affinely normalized partial sums
of a sequence of independent and identically distributed random variables converges
weakly to a nonGaussian stable random variable. A functional version of this is
known to be true as well, the limit process being a stable L´evy process. In this thesis,
we developed an explicit construction for the αstable L´evy process motion with values
in D([0, 1]), by considering the cases α < 1 and α > 1. The case α < 1 is the simplest
since we can work with the uniform topology of the supnorm on D([0, 1]) and the
construction follows more or less by classical techniques. The case α > 1 required
more work. In particular, we encountered two problems : one was related to the
construction of a modification of this process (for all time), which is rightcontinuous
and has leftlimit with respect to the J1 topology. This problem was solved by using
the ItobNisio theorem. The other problem was more difficult and we only managed
to solve it by developing a criterion for tightness of probability measures on the space
of cadlag fonction on [0, T] with values in D([0, 1]), equipped with a generalization of
Skorohod’s J1 topology.
In parallel with the construction of the infinitedimensional process Z, we focus
on the functional extension of Roueff and Soulier [29]. This part of the thesis was
completed using the method of point process, which gave the convergence of the
truncated sum. The case α > 1 required more work due to the presence of centering.
For this case, we developed an adhoc result regarding the continuity of the addition
for functions on [0, T] with values in D([0, 1]), which was tailored for our problem.

10 
Central limit theorems for D[0,1]valued random variablesHahn, Marjorie Greene January 1975 (has links)
Thesis. 1975. Ph.D.Massachusetts Institute of Technology. Dept. of Mathematics. / Vita. / Bibliography: leaves 111114. / by Marjorie G. Hahn. / Ph.D.

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