PL
 |
EN
Nowa wersja platformy, zawierająca wyłącznie zasoby pełnotekstowe, jest już dostępna.
Przejdź na https://bibliotekanauki.pl
Preferencje help
Polish version English version Język
Widoczny [Schowaj] Abstrakt
Liczba wyników

Znaleziono wyników: 28

Liczba wyników na stronie
first rewind previous Strona / 2 next fast forward last
Wyniki wyszukiwania
Wyszukiwano:
w słowach kluczowych:  central limit theorem
help Sortuj według:

help Ogranicz wyniki do:
first rewind previous Strona / 2 next fast forward last
1
Content available remote A central limit theorem for processes generated by a family of transformations
100%
Jabłoński M.
Instytut Matematyczny Polskiej Akademii Nauk
EN
Let ${τ_n,n≥0}$ be a sequence of measure preserving transformations of a probability space (Ω,Σ,P) into itself and let ${f_n,n≥0}$ be a sequence of elements of $L^2(Ω,Σ,P)$ with $E{f_n}=0$. It is shown that the distribution of $(∑_{i=0}^{n}f_i∘τ_i∘...∘τ_0)(D(∑_{i=0}^nf_i∘τ_i∘...∘τ_0))^{-1}$ tends to the normal distribution N(0,1) as n → ∞.
XX
CONTENTS 1. Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2. A central limit theorem for martingale differences. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 3. Stationary family of processes and central limit theorems for its elements. . . . . . . . . . . . . . .16 4. Central limit theorems for processes determined by endomorphisms. . . . . . . . . . . . . . . . . . 23 5. The central limit theorems for automorphisms. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .46 6. Final remarks. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .57 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .61
2
Content available Asymptotics of thermal dispersion in periodic media
96%
Timofte C.
Journal of Theoretical and Applied Mechanics
|
1999
|
tom nr 1
95-108
3
Content available remote A central limit theorem for multivariate strongly mixing random fields
96%
Tonelli C.
Probability and Mathematical Statistics
|
2010
|
tom Vol. 30, Fasc. 2
215--222
EN
In this paper we extend a theorem of Bradley under interlaced mixing and strong mixing conditions. More precisely, we study the asymptotic normality of the normalized partial sum of an α-mixing strictly stationary random field of random vectors, in the presence of another dependence assumption.
4
Content available remote Limit Theorems for the Hierarchy of Freeness
96%
Franz U. , Lenczewski R.
Probability and Mathematical Statistics
|
1999
|
tom Vol. 19, Fasc. 1
23--41
EN
The central limit theorem, the invariance principle and the Poisson limit theorem for the hierarchy of freeness are studied. We show that for given m ϵ N the limit laws can be expressed in terms of non-crossing partitions of depth smaller than or equal to m. For A = C[x], we solve the associated moment problems and find explicitly the discrete limit measures.
5
Content available remote Cramér type large deviations for trimmed L-statistics
96%
Gribkova N.
Probability and Mathematical Statistics
|
2017
|
tom Vol. 37, Fasc. 1
101--118
EN
In this paper, we propose a new approach to the investigation of asymptotic properties of trimmed L-statistics and we apply it to the Cramér type large deviation problem. Our results can be compared with those in Callaert et al. (1982) – the first and, as far as we know, the single article where some results on probabilities of large deviations for the trimmed L-statistics were obtained, but under some strict and unnatural conditions. Our approach is to approximate the trimmed L-statistic by a non-trimmed L-statistic (with smooth weight function) based onWinsorized random variables. Using this method, we establish the Cramér type large deviation results for the trimmed L-statistics under quite mild and natural conditions.
6
Content available remote Limit theorems for a higher order time dependent Markov chain model
96%
Kokoszka P. , Kutta T. , Singh D. , Wang H.
Probability and Mathematical Statistics
|
2023
|
tom Vol. 43, Fasc. 1
121--139
EN
The paper establishes a strong law of large numbers and a central limit theorem for a sequence of dependent Bernoulli random variables modeled as a higher order Markov chain. The model under consideration is motivated by problems in quality control where acceptability of an item depends on the past k acceptability scores. Moreover, the model introduces dependence that may evolve over time and thus advances the theory for models with time invariant dependence. We establish explicit assumptions that incorporate this dynamic dependence and show how it enters into the limits describing long-term behavior of the system.
7
Content available remote Asymptotics for products of a random number of partial sums
96%
Przystalski M.
Bulletin of the Polish Academy of Sciences. Mathematics
|
2009
|
tom Vol. 57, no 2
163-167
EN
We consider products of a random number of partial sums of independent, identically distributed, positive square-integrable random variables. We show that the distribution of these products is asymptotically lognormal.
8
Content available Limit distributions of extreme order statistics
96%
Dziubdziela W.
Mathematica Applicanda
|
1977
|
tom 5
|
nr 9
PL
Artykuł nie zawiera streszczenia
EN
MR0482946
9
Content available remote On the almost sure central limit theorem for associated random variables
96%
Matula P.
Probability and Mathematical Statistics
|
1998
|
tom Vol. 18, Fasc. 2
411--416
EN
The aim of this note is to prove the strong version of the CLT for associated sequences without any strong approximation theorems. In the proofs we only apply the weighted convergence result for averages of associated random variables and the standard CLT.
10
Content available remote On a gap series of Mark Kac
96%
Fukuyama K.
Colloquium Mathematicum
|
1999
|
tom 81
|
nr 2
157-160
EN
Mark Kac gave an example of a function f on the unit interval such that f cannot be written as f(t)=g(2t)-g(t) with an integrable function g, but the limiting variance of $n^{-1/2}\sum_{k=0}^{n-1} f(2^kt)$ vanishes. It is proved that there is no measurable g such that f(t)=g(2t)-g(t). It is also proved that there is a non-measurable g which satisfies this equality.
11
Content available remote Limit theory for planar Gilbert tessellations
96%
Schreiber T. , Soja N.
Probability and Mathematical Statistics
|
2011
|
tom Vol. 31, Fasc. 1
149--160
EN
A Gilbert tessellation arises by letting linear segments (cracks) in R2 unfold in time with constant speed, starting from a homogeneous Poisson point process of germs in randomly chosen directions. Whenever a growing edge hits an already existing one, it stops growing in this direction. The resulting process tessellates the plane. The purpose of the present paper is to establish a law of large numbers, variance asymptotics and a central limit theorem for geometric functionals of such tessellations. The main tool applied is the stabilization theory for geometric functionals.
12
Content available remote Limit theorems for products of sums of independent random variables
96%
Krajka T. K. , Rychlik Z.
Probability and Mathematical Statistics
|
2010
|
tom Vol. 30, Fasc. 1
73--85
EN
Let {Xn; n ≥ 1} be a sequence of independent random variables with finite second moments and {Nn; n ≥ 1} be a sequence of positive integer-valued random variables. Write Sn. =Σnk-1(Xk−EXk); n ≥1; and let N be a standard normal random variable. In the paper the convergences...[formula], are considered for some sequences {an} and {γn} of positive integer numbers such that Sn + an≥ 0 a.e. The case when γn are random variables is also considered. The main results generalize the main theorems presented by Pang et al. [3].
13
Content available remote A Wick functional limit theorem
96%
Parczewski P.
Probability and Mathematical Statistics
|
2014
|
tom Vol. 34, Fasc. 1
127--145
EN
We prove that weak convergence of multivariate discrete Wiener integrals towards the continuous counterparts carries over to the application of discrete and continuous Wick calculus. This is done by the representation of arbitrary Wick products of Wiener integrals in terms of generalized Hermite polynomials and a discrete analog of the Hermite recursion. The result is a multivariate non-central limit theorem in the form of a Wick functional limit theorem. As an application we give approximations of multivariate processes based on fractional Brownian motions for arbitrary Hurst parameters H ∈ (0, 1).
14
Content available remote The limiting behaviour of sums and maximums of iid random variables from the viewpoint of different observers
96%
Krajka T. K. , Rychlik Z.
Probability and Mathematical Statistics
|
2014
|
tom Vol. 34, Fasc. 2
237--252
EN
The limiting behaviour of observed and all random variables in the max limit schema was considered by Mladenović and Piterbarg (2006) and Krajka (2011). Here those results are generalised in two directions: we allow more than one observer and one superobserver; we consider the max limit schema as well as the sum limit schema.
15
Content available On the universal constant in the Katz-Petrov and Osipov inequalities
84%
Korolev V. , Popov S.
Discussiones Mathematicae Probability and Statistics
|
2011
|
tom 31
|
nr 1-2
29-39
EN
Upper estimates are presented for the universal constant in the Katz-Petrov and Osipov inequalities which do not exceed 3.1905.
16
Content available TEST ZGODNOŚCI χ2 OPARTY NA PRÓBACH NIEPROSTYCH
73%
Domański C.
Metody Ilościowe w Badaniach Ekonomicznych
|
2016
|
tom 17
|
nr 3
33-42
PL
Klasyczna teoria wnioskowania statystycznego dostarcza nam metod estymacji nieznanych parametrów rozkładu, szacowania postaci funkcji określającej ten rozkład oraz weryfikację hipotez na podstawie prób prostych, tzn. takich, w których obserwacje są stochastycznie niezależne i mają ten sam rozkład prawdopodobieństwa. Problemy związane z estymacją, w szczególności metody adaptacji centralnego twierdzenia granicznego dla prób nieprostych oraz weryfikację hipotez o zgodności rozkładów dla prób nieprostych za pomocą testu χ2 będą przedmiotem tego artykułu.
EN
Classical theory of statistical inference provides methods of estimation of unknown population parameters, density estimation and statistical hypothesis testing, based on simple random sampling, that is sampling scheme, in which all individuals are stochastically independent and identically distributed. Problems with estimation, especially with adaptation of central limit theorem to non-simple sampling and verification of goodness of fit hypothesis with χ2 test will be subject of this article.
17
Content available remote Optimality of the auxiliary particle filter
73%
Douc R. , Moulines É. , Olsson J.
Probability and Mathematical Statistics
|
2009
|
tom Vol. 29, Fasc. 1
1--28
EN
In this article we study asymptotic properties of weighted samples produced by the auxiliary particle filter (APF) proposed by Pitt and Shephard [17]. Besides establishing a central limit theorem (CLT) for smoothed particle estimates, we also derive bounds on the Lp error and bias of the same for a finite particle sample size. By examining the recursive formula for the asymptotic variance of the CLT we identify first-stage importance weights for which the increase of asymptotic variance at a single iteration of the algorithm is minimal. In the light of these findings, we discuss and demonstrate on several examples how the APF algorithm can be improved.
18
Content available remote Convergence rate in CLT for vector-valued random fields with self-normalization
73%
Bulinski A. , Kryzhanovskaya N.
Probability and Mathematical Statistics
|
2006
|
tom Vol. 26, Fasc. 2
261--281
EN
Statistical version of the central limit theorem (CLT) with random matrix normalization is established for random fields with values in a space Rk (k ≥ 1). Dependence structure of the field under consideration is described in terms of the covariance inequalities for the class of bounded Lipschitz ”test functions” defined on finite disjoint collections of random vectors constituting the field. The main result provides an estimate of the convergence rate, over a family of convex bounded sets, in the CLT with random normalization.
19
Content available remote bm-Central Limit Theorems associated with non-symmetric positive cones
73%
Oussi L. , Wysoczański J.
Probability and Mathematical Statistics
|
2019
|
tom Vol. 39, Fasc. 1
183--197
EN
Analogues of the classical Central Limit Theorem are proved in the non-commutative setting of random variables which are bm-independent and indexed by elements of positive non-symmetric cones, such as the circular cone, sectors in Euclidean spaces and the Vinberg cone. The geometry of the cones is shown to play a crucial role and the related volume characteristics of the cones is shown.
20
Content available remote Finite difference equations and convergence rates in the central limit theorem
73%
Lindhagen L.
Probability and Mathematical Statistics
|
2007
|
tom Vol. 27, Fasc. 2
153--166
EN
We apply the theory of finite difference equations to the central limit theorem, using interpolation of Banach spaces and Fourier multipliers. Let S*n be a normalized sum of i.i.d. random vectors, converging weakly to a standard normal vector N. When does ǁEg (x + S*n) -E g (X + N)ǁLp(dx)tend to zero at a specified rate? We show that, under moment conditions, membership of g in various Besov spaces is often sufficient and sometimes necessary. The results extend to signed probability.
first rewind previous Strona / 2 next fast forward last
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.