日期精度：到日 5104 篇 · 到月 0 篇 · 到年 0 篇
逆分布函数尾部的同时置信界
Confidence bounds are derived for the upper 100$p$ percentile of an inverse distribution function. These bounds are considerably less conservative than similar bounds which apply to the entire function.
光滑权重下次序统计量线性组合的 Edgeworth 展开
Edgeworth expansions for linear combinations of order statistics are established. The theorems require smooth weight functions and the underlying distribution function must possess a finite fourth moment. In addition a local smoothness condition is imposed on the underlying distribution function.
逐阶段多重检验程序中的方向错误控制
This paper is concerned with jointly testing the hypotheses $\theta_i = \theta_{i0}, i = 1, \cdots, s$, using tests based on independent statistics $T_i$ with distributions $P(T_i \leq t) = F_i(t, \theta_i)$ nonincreasing in $\theta_i$. Holm proposed a sequentially rejective test procedure, applicable to this problem, for which, for fixed $\alpha (0 \leq \alpha \leq 1)$, the probability that the joint conclusion contains no false rejections is $\geq 1 - \alpha$ for all…
最小二乘与偏差最小化样条的渐近积分均方误差
Let $S^d_k$ be the set of $d$th order splines on $\lbrack 0, 1 \rbrack$ having $k$ knots $\xi_1 < \xi_2 \cdots < \xi_k$. We consider the estimation of a sufficiently smooth response function $g$, using $n$ uncorrelated observations, by an element $s$ of $S^d_k$. For large $n$ and $k$ we have discussed the asymptotic behavior of the integrated mean square error (IMSE) for two types of estimators: (i) the least squares estimator and (ii) a bias minimizing estimator. The…
球面对称性的稳健检验及其最小二乘回归应用
Invariance is used to show that Kariya and Eaton's test for multivariate spherical symmetry is UMP invariant against elliptically symmetric distributions. Also both the null and alternative distributions of the test statistic are found to be the same as those which occur when the sample is normally distributed. UMP and UMPU tests for serial correlation derived assuming normality are found to be even more robust against departure from this assumption than was recently…
Robustness and efficiency of a parameter estimate $T$ can be assessed by comparing the fitted parametric distribution $P_T$ with the actual distribution, which is assumed to lie near the parametric family $\{P_\theta:\theta\in\Theta\}$. Asymptotic lower bounds are established for the minimax risk over distributions near the parametric model, taking as loss function a monotone increasing function of the Hellinger distance between the actual distribution of the sample and the…
傅里叶系数的经验分布
Suppose $X_1, X_2, \cdots$ are independent, identically distributed complex-valued $L^2$ random variables with $EX_1 = 0$ and $E(|X_1|^2) = 1$. Let $Y_{nk}$ be the $k$th Fourier coefficient of $X_1, \cdots, X_n$: $Y_{nk} = \sum^n_{j=1} X_j \exp \big(\frac{2\pi(-1)^{1/2}kj}{n}\big).$ Let $\mu_n$ be the empirical distribution of $\{n^{-1/2}Y_{nk}: k = 1, \cdots, n\}$. Then $\mu_n$ converges to the distribution of $U + iV$, where $U$ and $V$ are independent normal variables…
一个序贯估计问题的贝叶斯方法
This paper considers the problem of sequentially estimating the mean of a normal distribution when the variance is unknown. A continuous time analogue of the discrete time problem is studied. For $L$ in a class of loss functions, properties of the value function and optimal continuation region of $L$ are presented. Asymptotic expansions are found for the value function and the optimal boundary function of the loss function $L$.
对称 Dirichlet 分布及其混合在列联表中的应用：第二部分
This paper is a continuation of a paper in the Annals of Statistics (1976), 4 1159-1189 where, among other things, a Bayesian approach to testing independence in contingency tables was developed. Our first purpose now, after allowing for an improvement in the previous theory (which also has repercussions on earlier work on the multinomial), is to give extensive numerical results for two-dimensional tables, both sparse and nonsparse. We deal with the statistics $X^2, \Lambda$…
噪声条件下大型总体中的个体识别
A new approach is presented to the problem of determining whether an individual (the target) appears in a large file where individuals are identified by measurements subject to error. This approach attaches costs to searching and to missing the individual. It corresponds to testing a simple hypothesis, that the measurements on the target and an element in the library have a given joint distribution, against the alternative that they are independent. Certain measures of…
极大似然估计量的一致渐近正态性
A very general result concerning the weak consistency and uniform asymptotic normality of the maximum likelihood estimator is presented. The result proves to be of particular value in establishing uniform asymptotic normality of randomly normalized maximum likelihood estimators of parameters in stochastic processes. The only conditions imposed are certain regularity conditions on the (random) information function, easily verified in practice. Application of the result is…
非参数估计量的最优收敛速率
Let $d$ denote a positive integer, $\|x\| = (x^2_1 + \cdots + x^2_d)^{1/2}$ the Euclidean norm of $x = (x_1, \cdots, x_d) \in \mathbb{R}^d, k$ a nonnegative integer, $\mathscr{C}_k$ the collection of $k$ times continuously differentiable functions on $\mathbb{R}^d$, and $g_k$ the Taylor polynomial of degree $k$ about the origin corresponding to $g \in \mathscr{C}_k$. Let $M$ and $p > k$ denote positive constants and let $U$ be an open neighborhood of the origin of $\mathbb{R}^d$…
部分信息下的最优选择问题
For a given family $\mathscr{F}$ of continuous cdf's $n$ i.i.d. random variables with cdf $F \in \mathscr{F}$ are observed sequentially with the object of choosing the largest. An upper bound for the greatest asymptotic probability of choosing the largest is $\alpha \doteq .58,$ the optimal asymptotic value when $F$ is known, and a lower bound is $e^{-1},$ the optimal value when the choice is based on ranks. It is known that if $\mathscr{F}$ is the family of all normal…
存在并列值时符号检验的说明
Correcting a result of Krauth we show that there does not exist a UMP sign test for certain nonparametric hypotheses and treat the asymptotic properties of a one-sided sign test.
改进非负核密度估计量的收敛速度
To improve the rate of decrease of integrated mean square error for nonparametric kernel density estimators beyond $0(n^{-\frac{4}{5}}),$ we must relax the constraint that the density estimate be a bonafide density function, that is, be nonnegative and integrate to one. All current methods for kernel (and orthogonal series) estimators relax the nonnegativity constraint. In this paper we show how to achieve similar improvement by relaxing the integral constraint only. This is…
广义残差方差的最优完全等变估计量的不可容许性
The estimation of the generalized residual variance is considered when an observable Wishart random matrix is available. It is shown that when the loss function is normalized squared error, the natural fully equivariant estimator is dominated by an alternative. The latter uses either one of two estimators depending on the result of a preliminary test of significance. This alternate estimator has an everywhere smaller mean normalized squared error than the natural estimator.
利用连分数构造多项式回归的 Ds 最优设计
Consider a polynomial regression of degree $n$ on an interval. Explicit optimal designs are given for minimizing the determinant of the covariance matrix of the least squares estimators of the highest $s$ coefficients. The designs are calculated using continued fractions.
提前截停检验与一致最强序贯检验
The final decision of a fixed-sample likelihood ratio test is often determined before the entire sample is taken. Such a test can be curtailed as soon as the final decision becomes obvious. The construction and properties of these curtailed tests are described. A particular class of such tests contains sequential tests which are uniformly most powerful. The asymptotic efficiency of this class is investigated.
渐近最优序贯检验的风险
The problem considered is that of testing sequentially between two separated composite hypotheses concerning the mean of a normal distribution with known variance. The parameter space is the real line, on which is assumed an a priori distribution, $W,$ with full support. A family $\{\delta(c)\}$ of sequential tests is defined and shown to be asymptotically Bayes, as the cost, $c$, per observation tends to zero, relative to a large class of fully supported a priori…
连续时间过程的离散观测谱估计：正交级数法
Let $\{X(t), - \infty < t < \infty\}$ be a stationary time series with spectral density function $\phi(\lambda).$ Let $\{t_n\}$ be a stationary Poisson point process on the real line. The existence of consistent estimates of $\phi(\lambda)$ based on the discrete-time observations $\{X(t_n)\}^N_{n = 1},$ when the actual sampling times are not known, has been an open question (Beutler). Using an orthogonal series method, a class of spectral estimates is considered and its…
高斯移动平均过程参数最大似然估计的不变性性质
It is shown that the estimation procedure of Walker leads to estimates of the parameters of a Gaussian moving average process which are asymptotically equivalent to the maximum likelihood estimates proposed by Whittle and represented by Godolphin.
纯非确定性时间序列谱参数最小二乘估计的一项最优性
Whittle has proved that the least-squares estimator of a scalar parameter of the spectrum of a purely nondeterministic time series possesses a certain optimality property independently of the distribution of the residuals. In this paper we furnish a proof in full detail of the corresponding result for a vector parameter and also provide some examples which illustrate the application of the result.
ARMA 过程阶数的估计
Under general conditions strong consistency of certain estimates of the maximum lags of an autoregressive moving average process is established. A theorem on weak consistency is also proved and in certain cases where consistency does not hold the probability of over-estimation of a maximum lag is evaluated.