Discount Weighted Regression

A recursive procedure for discounted multiple linear regression is described, together with a discounted estimator for the residual variance. The method is simple to program and involves no matrix inversion. Two examples are given.     

相依随机序列加权和滑动平均的若干小偏差定理

引入随机序列滑动似然比作为任意二值随机序列相对于Bernoulli分布的独立随机变量序列偏差的一种随机性度量,通过滑动相对熵给出了样本空间的一个子集.在此子集上得到了一类关于随机序列滑动平均的用不等式表示的强极限定理,即小偏差定理,推广了文献[5],[6]等关于随机序列算术平均的结果,这些结果蕴含近期诸多文献的主要结果.     

关于Herz型空间中加权Hardy-Littlewood平均的一个注记

本文给出了加权Hardy-Littlewood平均在Herz型空间中关于权有界的充分必要条件.     

Gaussian Approximation to the Partial Sum Processes of Moving Averages

The authors study approximation to the partial sum processes which is based on the stationary sequences of random variables having the structure of the so-called moving averages of independent identically distributed observations. In particular, the rates of convergence both in Donsker's and Strassen's invariance principles are obtained in the case when the limit Gaussian process is a fractional Brownian motion with an arbitrary Hurst parameter.     

Convergence of Appell Polynomials of Long Range Dependent Moving Averages in Martingale Differences

We study limit distribution of partial sums S_N,k(t) = _{s = 1} ^{[N t]} A_k(X_s) of Appell polynomials of the long-range dependent moving average process X_t> = _{i t} b_{t - i i}, where {_i} is a strictly stationary and weakly dependent martingale difference sequence, and b_i i^{d - 1} (0 < d < 1/2). We show that if k(1-2 d)<1, then suitably normalized partial sums S_N,k(t) converge in distribution to the kth order Hermite process. This result generalizes the corresponding results of Surgailis, and Avram and Taqqu obtained in the case of the i.i.d. sequence { _i}.     

一类非齐次树上关于马氏链场滑动平均的强偏差定理

树指标随机过程已成为近年来发展起来的概率论的研究方向之一.强偏差定理一直是国际概率论界研究的中心课题之一.本文利用Borel-Cantelli引理研究给出了一类非齐次树上马氏链场关于负二项分布滑动平均的强偏差定理.     

Nonlinear Averages in Economics

Kolmogorov nonlinear averaging is complemented by a natural axiom. For this averaging, we prove a theorem on large deviations as well as establish the relationship to the tunnel canonical operator.     

非齐次树上马氏链场滑动平均的若干强偏差定理

树指标随机过程已成为近年来发展起来的概率论的研究方向之一.强偏差定理一直是国际概率论界研究的中心课题之一.通过构造适当的非负鞅,将Doob鞅收敛定理应用于几乎处处收敛的研究,研究给出了一类非齐次树上马氏链场滑动平均的若干强偏差定理.     

Kolmogorov Averages and Approximate Identities

We study the action of Kolmogorov-type nonlinear averaging operators of the form V ⁻¹ AV on smooth functions. Here, A runs through a family of convolution operators A _ε ^[K], ε>0, generated by a single kernel K∈L ¹(ℝ ⁿ ) in the usual way and forming an “approximate identity” as ε→0, while V is a superposition map given by Vf=v○f, with a monotone continuous function v. The main result characterizes the kernels K with the property that the natural estimate

Averages of elliptic curve constants

We compute the averages over elliptic curves of the constants occurring in the Lang–Trotter conjecture, the Koblitz conjecture, and the cyclicity conjecture. The results obtained confirm the consistency of these conjectures with the corresponding “theorems on average” obtained recently by various authors.     

Estimating Dependencies from Spatial Averages

Abstract

Modeling of space-time functions can be done using observations in the form of averages of the function over a set of irregularly shaped regions in space-time. Such observations are most common in applications where the data are gathered for administrative, political, geographic, or agricultural regions. The value of such functions can be predicted by first estimating the dependence structure of the underlying stochastic process. Our proposed method for estimating the covariance function from the integrals of a stationary isotropic stochastic process poses the problem as a set of integral equations. To test this proposal we applied it to epidemiological data on the incidence rates of three diseases in the United States between 1980 and 1994. Spatial correlations obtained in this way reasonably described the mechanism by which those diseases spread. We therefore conclude that it is possible to reliably estimate covariance functions from aggregate observations. The estimate of the covariance functions provides valuable insights into the nature of the space-time process—in the epidemiological data it described a possible mechanism by which the diseases spread.     

Nonlinearity of Averages in Financial Mathematics

Mathematical Notes -     

Averages of operators and their positivity

Let be a bounded linear operator on a Hilbert space. We prove that is positive, if there exists a positive integer such that

for any non-negative integer . For several commuting operators, we can extend this result and get the similar statement.