重尾随机变量和的大偏差

This paper is a further investigation of large deviations for sums of random variables S_n=sum form i=1 to n X_i and S(t)=sum form i=1 to N(t) X_i,(t≥0), where {X_n,n≥1) are independent identically distribution and non-negative random variables, and {N(t),t≥0} is a counting process of non-negative integer-valued random variables, independent of {X_n,n≥1}. In this paper, under the suppose F∈G, which is a bigger heavy-tailed class than C, proved large deviation results for sums of random variables.     

Large deviations for sums of independent random variables with dominatedly varying tails

In this paper the large deviation results for partial and random sums Sn-ESn=n∑i=1Xi-n∑i=1EXi,n≥1;S(t)-ES(t)=N(t)∑i=1Xi-E(N(t)∑i=1Xi),t≥0are proved, where {N(t); t≥ 0} is a counting process of non-negative integer-valued random variables, and {Xn; n ≥ 1} are a sequence of independent non-negative random variables independent of {N(t); t ≥ 0}. These results extend and improve some known conclusions.     

Large deviations for heavy-tailed random sums of independent random variables with dominatedly varying tails

We prove large deviation results on the partial and random sums Sn = ∑i=1n Xi,n≥1; S(t) = ∑i=1N(t) Xi, t≥0, where {N(t);t≥0} are non-negative integer-valued random variables and {Xn;n≥1} are independent non-negative random variables with distribution, Fn, of Xn, independent of {N(t); t≥0}. Special attention is paid to the distribution of dominated variation.     

On estimating the hidden periodicities in linear time series models

In this paper the tollowing modelX(n)=sum from j=1 to p α_je~(inλj)+ξ_nis considered,where p,λ_1,λ_2,…,λ_p,are constants α=(α_1,α_2,…,α_p) is a random vector and {ξ_n;n=0,±1,±2,…} is a wide-sense stationary sequence with zero means.In [4],theorem about thestrong consistent estimates of λ_1,λ_2.…,λ_p and α are proved under the assumption that α is a constantvector and p and δ are known constants such that0<δ<(?){λ_i-λ_j}.The main purpose of the present paper is to prove theorems on the strong consistent estimates ofparameters p,λ_1,λ_2,…,λ_p and random vector α without knowing p and δ.Numerical examples arealso given to illustrate our method of estimation.     

Hardy-Riesz拓广了的Hilbert不等式的一个改进

Let {a_n} and {b_n}be any two sequences of non-negative numbers such that 01).Then Hardy-Riesz′s extension of the Hilbert inequality can be sharpened to the form     

The Lebesgue Constants and Gibbs Phenomenon for Non-negative (f , dn) Summability Method

The ( f,d_n) -summability method is defined as follows^[1,4]: Let f be a nonconstant function, analytic in |z | < R for R > l, and let {d_n} be a sequence of complex numbers,such that for all n,$d_n \ne -f(1)$.Suppose that the elements of the metrix A = (a_nk) are given by the relations $a_00=1,a_0k=0(k \geq 1)$ $[\prod\limits_{j = 1}^n {\frac{{f(z) + {d_j}}}{{f(1) + {d_j}}} = \sum\limits_{k = 0}^\infty {{a_{nk}}{z^k}} } \]$ A sequence {S_n} is said to be ( f, d_n), —summable to s, if \sigma_n = \sum\limits_{k=0}^\infty \arrow s as n \arrow \infty. The ( f, d_n) —summability method is said to be non-negative if for all n, d_n> 0 and the Maclaurin coefficients of f are real and non-negative. The Lebesgue constants for the ( f,d_n)-method are defined by $L_n(A)=2/\pi \int_0^\pi /2 {\frac{|\sum\limits_{k=0}^\infty {a_nk sin(2k+1)t|}{sint}dt}$ In this parer we prove the following two theorems.     

Uniform Convergence Rate of Estimators of Autocovariances in Partly Linear Regression Models with Correlated Errors

Consider the partly linear regression model ,where yi's are responses, xi = (xi1, xi2,…,xip)' and ti ∈T are known and nonrandom design points, T is a compact set in the real line is an unknown parameter vector, g(·) is an unknown function and {Ei} isa linear process, i.e., random variables with zeromean and variance o2e. Drawing upon B-spline estimation of g(·) and least squares estimation of 0, we construct estimators of the autocovariances of {Ei}- The uniform strong convergence rate of these estimators to their true values is then established. These results not only are a compensation for those of [23], but also have some application in modeling error structure. When the errors {Ei} are an ARMA process, our result can be used to develop a consistent procedure for determining the order of the ARMA process and identifying the non-zero coefficients of the process. Moreover, our result can be used to construct the asymptotically efficient estimators for parameters in the ARMA error process.     

Ergodicity of a class of nonlinear time series models in random environment domain

In this paper, we study the problem of a variety of p, onlinear time series model Xn＋ 1= TZn＋1（X（n）, … ,X（n - Zn＋l）, en＋1（Zn＋1）） in which {Zn} is a Markov chain with finite state space, and for every state i of the Markov chain, {en（i）} is a sequence of independent and identically distributed random variables. Also, the limit behavior of the sequence {Xn} defined by the above model is investigated. Some new novel results on the underlying models are presented.     

POSITIVE MAPS CONSTRUCTED FROM PERMUTATION PAIRS

A property(C) for permutation pairs is introduced. It is shown that if a pair{π_1, π_2} of permutations of(1,2,…,n) has property(C),then the D-type map Φ_(π_1,π_2) on n× n complex matrices constructed from {π_1,π_2} is positive. A necessary and sufficient condition is obtained for a pair {π_1,π_2} to have property(C),and an easily checked necessary and sufficient condition for the pairs of the form {π~p,π~q} to have property(C) is given, whereπ is the permutation defined by π(i) = i + 1 mod n and 1≤ p q≤ n.     

THE EMBEDDED THEOREM AND ITS APPLICATION TO STATISTICAL METRIC SPACE

We prove the following result in this paper: Let(X, ζ, △) be a T—complete Menger space. If {T_i, i=1, 2, …} are a sequence of the self mapping of the contractive type on X and {m_i(x), i=1, 2, …} are the functional sequence satisfying m_i(x)|m(T_i(x)), i=1, 2, …, then {T_i, i=1, 2, …} have a common fixed point.This result is a generalization to the result obtained in I. Istratescu [7, 14]. Other results are proved concerning the fixed point theorems for G valued metric space. The concept, the embedded theorem of S. M. space, is discussed and its relation to the existence of fixed point for above mapping is also discussed in S. M. space.     

COMPARISON THEOREMS AND OSCILLATION CRITERIA FOR DIFFERENCE EQUATIONS WITH SEVERAL DELAYS

In this paper, we first establish the equivalence of the oscillation of thedifference equations with several delays of the form: Δx_n+sum from i=1 to m(pi(n)x_(n-k_i))=0 for n≥0and the second-order difference equations without delay of the form:where{pj(n)}is a sequence of nonnegative real numbers and{k_i}_(i=1)~m is a setof positive integers. Then we get some "sharp" conditions for oscillation andnon-oscillation of the first equation.     

Some strong laws of large numbers for blockwise martingale difference sequences in martingale type p Banach spaces

For a blockwise martingale difference sequence of random elements {Vn , n ≥ 1} taking values in a real separable martingale type p (1 ≤ p ≤ 2) Banach space, conditions are provided for strong laws of large numbers of the form limn→∞∑ n i=1 Vi /gn = 0 almost surely to hold where the constants gn ↑∞. A result of Hall and Heyde [Martingale Limit Theory and Its Application, Academic Press, New York, 1980, p. 36] which was obtained for sequences of random variables is extended to a martingale type p (1 p ≤ 2) Banach space setting and to hold with a Marcinkiewicz-Zygmund type normalization. Illustrative examples and counterexamples are provided.     

Estimation for Partially Linear Models with Missing Responses:the Fixed Design Case

Suppose that we have a partially linear model Yi=x′iβ+g(ti)+εi with independent zero mean errorsεi,where{xi,ti,i=1,···,n}are non-random and observed completely and{Yi,i=1,···,n}are missing at random(MAR).Two types of estimators ofβand g(t)for fixed t are investigated:estimators based on semiparametric regression and inverse probability weighted imputations.Asymptotic normality of the estimators is established,which is used to construct normal approximation based confidence intervals onβand g(t).Results are reported of a simulation study on the finite sample performance of the estimators and confidence intervals proposed in this paper.     

PARAMETER ESTIMATION OF SPATIAL AR MODEL

Consider a stable AR model of two parameter spatial series {X_t, t∈N~2}, i. e. {X_(t)t∈N~2} is homogeneous and satisfies the following difference equationX_t-sum from n=s∈相似文献   

STRONG APPROXIMATION FOR MOVING AVERAGE PROCESSES UNDER DEPENDENCE ASSUMPTIONS

Let {Xt,t ≥ 1} be a moving average process defined by Xt = ∑^∞ k=0 αkξt-k, where {αk,k ≥ 0} is a sequence of real numbers and {ξt,-∞ 〈 t 〈 ∞} is a doubly infinite sequence of strictly stationary dependent random variables. Under the conditions of {αk, k ≥ 0} which entail that {Xt, t ≥ 1} is either a long memory process or a linear process, the strong approximation of {Xt, t ≥ 1} to a Gaussian process is studied. Finally, the results are applied to obtain the strong approximation of a long memory process to a fractional Brownian motion and the laws of the iterated logarithm for moving average processes.     

Strong Consistency of Non-parametric Regression Estimates with Censored Data

Let (X,Y) be an R~d×R valued random vector with E|Y|<∞ and(X_1,Y_1) (X_2,Y_2), …, (X_n,Y_n) be i.i.d.observations of (X,Y). To estimate the regression function m(x)=E(Y|X=x), Stone suggested m_n(x)=sum from i=1 to n(W_(ni)(x)Y_i), where W_(ni)(x)=W_(ni)(x,X_1,X_2,…,X_n)(i=1,2,…,n) are weight functions. Devroye and Chen Xiru established the strong consistency of m_n(x). In this paper, we discuss the case that{Y_i} are censored by {t_i}, where{t_i} are i.i.d. random variables and also independent of{Y_i}. Under certainconditions we still obtain the strong consistency of m_n(x).     

ON THE GROWTH OF SOME RANDOM HYPERDIRICHLET SERIES

The paper considers the random L-Dirichlet seriesf(s,ω)=sum from n=1 to ∞ P_n(s,ω)exp(-λ_ns)and the random B-Dirichlet seriesψτ_0(s,ω)=sum from n=1 to ∞ P_n(σ iτ_0,ω)exp(-λ_ns),where {λ_n} is a sequence of positive numbers tending strictly monotonically to infinity, τ_0∈R is a fixed real number, andP_n(s,ω)=sum from j=1 to m_n ε_(nj)a_(nj)s~ja random complex polynomial of order m_n, with {ε_(nj)} denoting a Rademacher sequence and {a_(nj)} a sequence of complex constants. It is shown here that under certain very general conditions, almost all the random entire functions f(s,ω) and ψ_(τ_0)(s,ω) have, in every horizontal strip, the same order, given byρ=lim sup((λ_nlogλ_n)/(log A_n~(-1)))whereA_n=max |a_(nj)|.Similar results are given if the Rademacher sequence {ε_(nj)} is replaced by a steinhaus seqence or a complex normal sequence.     

Self-normalized moderate deviations for independent random variables

Let X1,X2,...be a sequence of independent random variables(r.v.s) belonging to the domain of attraction of a normal or stable law.In this paper,we study moderate deviations for the self-normalized sum ∑ni=1 Xi/Vn,p,where Vn,p =(∑ni=1 |Xi|p)1/p(p>1).Applications to the self-normalized law of the iterated logarithm,Studentized increments of partial sums,t-statistic,and weighted sum of independent and identically distributed(i.i.d.) r.v.s are considered.     

Oscillatory behavior of solutions of general third order mixed neutral difference equations

The objective of this paper is to study the oscillatory and asymptotic properties of the general mixed type third order neutral difference equation of the form△(aαn△2(xn+ bnxn-τ1+ cnxn+τ2)) + qnx n+1-σ+ p1nxβn+1+= 0,σ2where {an}, {bn}, {cn}, {qn} and {pn} are positive real sequences, both α and β are ratios of odd positive integers, τ1, τ2, σ1 and σ2 are positive integers. We establish some sufficient conditions which ensure all solutions are either oscillatory or converge to zero.     

Approximate Representation of Bergman Submodules

In the present paper, the author shows that if a homogeneous submodule M of the Bergman module L_a~2(B_d) satisfies P_M-sum from i to ( M_(zi)P_MM*_(zi))≤c/(N + 1)P_M for some number c 0, then there is a sequence {f_j } of multipliers and a positive number c such that c'P_M ≤sum from j to ( M_(fj)M*_(fj))≤ P_M, i.e., M is approximately representable. The author also proves that approximately representable homogeneous submodules are p-essentially normal for p d.