基于系数正则的同时回归估计

提取两个随机向量X与Y之间的相关性是非常重要的问题.核方法被用来提取非线性的相关性.本文通过极小化方差Var[f(X)-g(Y)]得到最大相关性,称为同时回归,其中f(X)和g(Y)分别是两个不同的再生核空间中的函数.本文利用正则经验方差极小化得到估计.为了所得的估计函数具有稀疏性,本文采用系数的l_1范数作为惩罚项,在一些常规条件下建立学习率.同时回归问题与典型相关分析、切片逆回归等密切相关.     

纯生过程的变异性(英语)

设{X(t):t≥0}为零初值纯生过程,出生率为λ_n,n≥0.在本文中,我们证明了Faddy[7]的一个猜测:当出生率为单调增加序列λ_0≤λ_1≤λ_2…。时,Var{X(t)}≥E{(t)};当出生率为单调减少序列时Var{X(t)}≤E{(t)}。     

平衡正态方差分量模型参数的UMVU估计

在一定条件下,对于平衡正态方差分量模型,用方差分析法得到的方差分量σ2的估计σ2是UMVU估计,﹀^=(X′X)-1X′y是﹀的UMVU估计.从而推广了[1]中的结果.     

巧构分布列用方差证不等式

若离散型随机变量分布列为P（X=xi）=Pi（i=1,2,…,n,…）,则依方差公式D（X）=E（X^2）-E（X）^2≥0,     

方差非负性的应用

方差的计算公式为S2人教版初中《代数》第三册），它又可化为9一上【】X～上（，IZI方差具有非负性，即5270，当且仅当xl—12一…一xu，SZ＝0，利用方差公式及其非负性，可以将不少数学问题转化为方差问题来解决．例1已知a，heR”，a＋b—1，求证a’＋bZk且2”证考虑a，b二项的方差例3已知实数x，y，z满足x－y＝6，cy＝zZ十9，求证：X一y·证工，y的方差为Y一言【x“十y“一二（x＋y广」”亏以x＋y）“一zry一青（x＋y广」一一子【一子X十一月．t＋o）1一一，J＞几4＝O，于是X一y·例4已知0＜6＜。，求函数y＝／厂工面F肩而十／而百…     

关于两个随机变量的线性关系

设 X,Y 是定义在同一概率空间(Q,(?),P)上的随机变量.称 X 的任意线性形aX+b 为 Y 的一个线性预报.我们要讨论用什么样的线性预报来表达 X,Y 之间的线性关系是合理的.通常是使用均方误差(M.S.E)最小准则,即由 E[Y-(aX+b)]~2取极小来确定 a 和 b.由此得到的线性预报,记为 a_0X+b_0,称为 Y 关于 X 的线性回归.其中 a_0=cov(X,Y)/Var(X),b_0=E(T)-a_0E(X).类似地可定义 X 关于 Y 的线性回归,记为a′_0Y+b′_0,并定义 X,Y 的相关系数为     

不独立和不相关

若随机变量 X 和 Y 的相关系数 r(X,Y)=0,称 X 与 Y 不相关,众所周知,独立变量一定不相关(自然要求方差有限),不独立变量也可以不相关,单位圆内的均匀分布即其一例,这种例子可随意举出很多,这启发我们提出下面的问题任意给定两个一维分布 F 和 G,其方差都非零有限.是否存在两个随机变量 X,Y ,使得:1)X 有分布 F,Y 有分布 G.2)X,Y 不独立.3)r(X,Y)=0.我们的直觉是这问题有肯定的回答,但证明并非一目了然,诚然,这不是什么很重要或很     

(√2X2)-(√2n-1)的近似正态性及多总体标准差的齐性检验

计算了随机变量√(2X2)的数学期望和方差,比较分析了随机变量√(2X2)-√(2n)与√(2X2)-√(2n-1)的近似分布的相同和不同之处,并且利用2X2的近似分布的正态性,建立了多总体标准差的检验法.     

I.I.D.随机变量序列矩完全收敛的精确渐近性

{X,Xn;n≥1}为独立同分布的随机变量序列, EX=0,01 p/2满足E|X|r<∞,且E|X|3<∞,那么其中Z服从均值为0,方差为σ2的正态分布.     

广义熵在统筹时间分布律中的应用

<正> 表示任务的完成时间 X 的数学期望和方差,那么 X 应服从什么分布呢?华罗庚教授在[1]中指出,应用概率论中的极限定理,假设是正态分布.[2]中利用最大 Shannon 熵原则,得到 X 的分布密度函数为     

Simultaneous optimal estimates of fixed effects and variance components in the mixed model

For a general linear mixed model with two variance components, a set of simple conditions is obtained, under which, (i) the least squares estimate of the fixed effects and the analysis of variance (ANOVA) estimates of variance components are proved to be uniformly minimum variance unbiased estimates simultaneously; (ii) the exact confidence intervals of the fixed effects and uniformly optimal unbiased tests on variance components are given; (iii) the exact probability expression of ANOVA estimates of variance components taking negative value is obtained.     

Variance minimization for continuous-time Markov decision processes: two approaches

This paper studies the limit average variance criterion for continuous-time Markov decision processes in Polish spaces. Based on two approaches, this paper proves not only the existence of solutions to the variance minimization optimality equation and the existence of a variance minimal policy that is canonical, but also the existence of solutions to the two variance minimization optimality inequalities and the existence of a variance minimal policy which may not be canonical. An example is given to illustrate all of our conditions.     

多元线性混合模型方差分量矩阵的非负估计

本文研究了带有两个方差分量矩阵的多元线性混合模型方差分量矩阵的估计问题.对于平衡模型,给出了基于谱分解估计的一个方差分量矩阵的非负估计类.对于非平衡模型,给出了方差分量矩阵的广义谱分解估计类,讨论了与ANOVA估计等价的充要条件.同时,在广义谱分解估计的基础上给出了一种非负估计类,并讨论了其优良性.当具有较小二次风险的非负估计不存在时,从估计为非负的概率的角度考虑,将Kelly和Mathew(1993)提出的构造具有更小取负值概率的估计类的方法推广到本文的多元模型下,给出了较谱分解估计相比有更小取负值概率和更小风险的估计类.最后,模拟研究和实例分析表明文中理论结果有很好的表现.     

On the estimation of a monotone conditional variance in nonparametric regression

A monotone estimate of the conditional variance function in a heteroscedastic, nonparametric regression model is proposed. The method is based on the application of a kernel density estimate to an unconstrained estimate of the variance function and yields an estimate of the inverse variance function. The final monotone estimate of the variance function is obtained by an inversion of this function. The method is applicable to a broad class of nonparametric estimates of the conditional variance and particularly attractive to users of conventional kernel methods, because it does not require constrained optimization techniques. The approach is also illustrated by means of a simulation study.     

A Note on Maximum Variance of Order Statistics from Symmetric Populations

The maximum variance of order statistics from a symmetrical parent population is obtained in terms of the population variance. The proof is based on a suitable representation for the variance of order statistics in terms of the parent distribution function.     

Numerical approximation of conditional asymptotic variances using Monte Carlo simulation

We consider in this paper the use of Monte Carlo simulation to numerically approximate the asymptotic variance of an estimator of a population parameter. When the variance of an estimator does not exist in finite samples, the variance of its limiting distribution is often used for inferences. However, in this case, the numerical approximation of asymptotic variances is less straightforward, unless their analytical derivation is mathematically tractable. The method proposed does not assume the existence of variance in finite samples. If finite sample variance does exist, it provides a more efficient approximation than the one based on the convergence of finite sample variances. Furthermore, the results obtained will be potentially useful in evaluating and comparing different estimation procedures based on their asymptotic variances for various types of distributions. The method is also applicable in surveys where the sample size required to achieve a fixed margin of error is based on the asymptotic variance of the estimator. The proposed method can be routinely applied and alleviates the complex theoretical treatment usually associated with the analytical derivation of the asymptotic variance of an estimator which is often managed on a case by case basis. This is particularly appealing in view of the advance of modern computing technology. The proposed numerical approximation is based on the variances of a certain truncated statistic for two selected sample sizes, using a Richardson extrapolation type formulation. The variances of the truncated statistic for the two sample sizes are computed based on Monte Carlo simulations, and the theory for optimizing the computing resources is also given. The accuracy of the proposed method is numerically demonstrated in a classical errors-in-variables model where analytical results are available for the purpose of comparisons.     

Stabilized hard thresholding for an unknown noise level

The effect wa ys of estimating noise variance on the statistical characteristics of the stabilized hard thresholding of signal wavelet coefficients is studied. An unbiased estimator of the mean-square risk is analyzed. It is shown that under certain conditions, the estimator distribution tends to a normal law with variance that depends on the type of noise variance estimate.     

Order selection for heteroscedastic autoregression: A study on concentration

We consider an autoregressive model where the variance is allowed to be a function of time, unconditional on the past. Pötscher (1989) has proven that, regardless of the shape of the variance function, order selection can be made consistently. However, this procedure does not account for the non-stationary behavior. We consider the concentration of the variance function and its effect on order selection. We show that an order free estimate of the variance function can be constructed and propose an order selection criterion based on this estimate. Consistency is established and simulation results verify a large increase in the probability of selecting the correct order for finite samples.     

On some representations of sample variance

The usual formula for variance depending on rounding off the sample mean lacks precision, especially when computer programs are used for the calculation. The well-known simplification of the total sums of squares does not always give benefit. Since the variance of two observations is easily calculated without the use of a sample mean, and the variance of a sample of n observations is the average of the variances of observations based on n(n-1)/2 distinct subsets of units of size 2 from the sample, it is argued that this sense of pairing may result in precision. Some other forms of variance are presented which provide some insight into it. The contribution of a new observation of variance is highlighted, which is important in sequential sampling. Notions are illustrated with examples.     

The Variance of Lead-Time Demand

Many short-term forecasting systems are based on exponentially weighted moving averages. It is usual to forecast the cumulative demand over a lead time or production horizon, and to describe this forecast in terms of its mean and variance. When the forecast horizon is fixed, the variance is often taken as the product of the number of periods and the variance per period. This is a serious error and typically underestimates the variance by a factor of about two. This paper details the need for a proper awareness of the correction factors.