论文检索

重复刺激诱发的含噪信号同质性检验AI 解读

Two statistics are proposed for testing the homogeneity of signals, when these are noisy and repeatedly recorded. The distribution of the statistics is well approximated by the $\chi^2$ and the normal distribution, respectively, as shown by theoretical and simulation results. Power and insensitivity to other types of variation are discussed. The approach is developed in the context of analysing recordings of electric brain potentials being evoked by some stimulation, as…

非平稳移动平均过程的谱分解AI 解读

We solve here the general nonstationary multivariate MA spectral factorization problem, i.e. the problem of obtaining all the possible MA models (with time-dependent coefficients) corresponding to a given (time-dependent) autocovariance function. Our result (Theorem 8) relies on a symbolic generalization (Theorem 1) of the classical factorization property of the characteristic polynomial associated with stationary autocovariance functions, and is obtained by means of a…

正则非遍历模型的渐近条件推断及其自回归应用AI 解读

A conditional limit theorem is derived for a certain class of stochastic processes whose distributions constitute a nonergodic family. The limit theorem allows us to study the asymptotic behaviour under the conditional model of some standard statistical procedures by making use of results for ergodic families. Explosive Gaussian autoregressive processes are studied in some detail. Here the conditional process is shown to be a nonexplosive Gaussian autoregression bearing a…

删失观测下一类半马尔可夫过程的非参数推断AI 解读

A class of semi-Markov models, those which have proportional hazards and which are forward-going (if state $j$ can be reached from $i$, then $i$ cannot be reached from $j$), are shown to fit into the multiplicative intensity model of counting processes after suitable random time changes. Standard large-sample results for counting processes following this multiplicative model can therefore be used to make inferences on the above class of semi-Markov models, including the case…

M 与 P 估计量的有限样本崩溃性质AI 解读

The finite sample breakdown properties of $M$-estimators, defined by $\sum\rho(x_i - T) = \min!$, and of the associated Pitman-type or $P$-estimators, defined by $T = \frac{\int \exp\{-\Sigma \rho(x_i - \theta)\}\theta d\theta}{\int \exp\{-\Sigma\rho(x_i - \theta)\} d\theta},$ are investigated. If $\rho$ is symmetric, and $\psi = \rho'$ is monotone and bounded, then the breakdown point of either estimator is $\varepsilon^\ast = 1/2$. If $\psi$ decreases to 0 for large $x$ ("r…

用 Jackknife 近似 Bootstrap 估计AI 解读

Let $\hat{T}_n$ be an estimate of the form $\hat{T}_n = T(\hat{F}_n)$, where $\hat{F}_n$ is the sample $\operatorname{cdf}$ of $n \operatorname{iid}$ observations and $T$ is a locally quadratic functional defined on $\operatorname{cdf's}$. Then, the normalized jackknife estimates for bias, skewness, and variance of $\hat{T}_n$ approximate closely their bootstrap counterparts. Each of these estimates is consistent. Moreover, the jackknife and bootstrap estimates of variance…

广义 L、M 与 R 统计量AI 解读

A class of statistics generalizing $U$-statistics and $L$-statistics, and containing other varieties of statistic as well, such as trimmed $U$-statistics, is studied. Using the differentiable statistical function approach, differential approximations are obtained and the influence curves of these generalized $L$-statistics are derived. These results are employed to establish asymptotic normality for such statistics. Parallel generalizations of $M$- and $R$-statistics are…

线性统计关系的估计AI 解读

This paper on estimating linear statistical relationships includes three lectures on linear functional and structural relationships, factor analysis, and simultaneous equations models. The emphasis is on relating the several models by a general approach and on the similarity of maximum likelihood estimators (under normality) in the different models. In the first two lectures the observable vector is decomposed into a "systematic part" and a random error; the systematic part…

一类贝叶斯非参数估计：第一部分，密度估计AI 解读

Given a positive, normalized kernel and a finite measure on an Euclidean space, we construct a random density by convoluting the kernel with the Dirichlet random probability indexed by the finite measure. The posterior distribution of the random density given a sample is classified. The Bayes estimator of the density function is given.

变量测量误差问题中的影响函数AI 解读

This paper focuses on two aspects of the errors in variables problem--variance estimation of the classical estimators of slope and intercept, and the detection of influential observations. The behaviour of the jackknife, bootstrap, normal theory and influence function estimators of variability is examined under a number of sampling situations by Monte Carlo methods. In the multivariate case, perturbation analysis is used to calculate the influence function of the estimator…

调查数据估计单元比例时多维列联表的卡方检验AI 解读

The impact of survey design on standard multinomial-based methods for a multiway contingency table is studied, under nested loglinear models. The asymptotic null distribution of the Pearson chi-squared test statistic, $X^2$ (or the likelihood ratio test statistic, $G^2$) is obtained as a weighted sum of independent $\chi^2_1$ random variables, and the weights are then related to the familiar design effects (deffs) used by survey samplers. A simple correction to $X^2$ (or $G^2$…

Watson 统计量的渐近分布AI 解读

An integral representation of the positive stable distributions is used to give a tabulation of the asymptotic test statistic for Watson's optimal invariant test for uniformity of distribution on a circle.

Wu (1980) defined the consistent directions of the least squares estimator in a linear model as the linear combinations of parameter estimates that are asymptotically consistent. For the polynomial regression model, a characterization of the space of consistent directions $S$ was obtained in terms of the convergence rates of the corresponding design sequence to its limit points. By employing a more general and yet simpler approach, we obtain here a similar result for any…

Stein 两阶段程序的稳健性AI 解读

The expressions for coverage probability and ASN of the Stein's two-stage confidence interval procedure for estimating the normal mean have been obtained under the assumption that the underlying distribution is, in fact, different from normal but could be approximated by the first four terms of Edgeworth series. The comparison of coverage probabilities with the corresponding probabilities obtained for the normal distribution shows that the procedure is quite insensitive to…

主成分向量的一类渐近检验AI 解读

In this paper, the hypothesis that a set of vectors lie in the subspace spanned by a prescribed subset of the principal component vectors for a normal population is considered. A class of invariant asymptotic tests based on the sample covariance matrix is derived. Tests in this class are shown to be consistent and their local power functions are given. The arguments used in deriving the class of tests are not heavily dependent on the assumption of normality nor on the use of…

总体重根局部备择下主成分特征根的渐近分布AI 解读

The asymptotic distribution for the principal component roots under local alternatives to multiple population roots is derived. The asymptotic theory assumes the estimate of the population covariance or scatter matrix to be asymptotically normal and to possess certain invariance properties. These assumptions are satisfied for the affine-invariant $M$-estimates of scatter for an elliptical distribution. The local alternative framework is used in deriving a local power…

事件的估计AI 解读

The problem of estimating an event, having positive probability content, based on a sample of $n$ observations is considered. A natural metric is shown to exist on the space of possible values for the event. This leads to the definition of optimal estimators. We derive optimal estimators for events which correspond to quantiles for the univariate exponential model. Further optimal estimators are derived for the events bounded by the ellipsoidal contours of the density…

样本谱分布泛函的极限行为AI 解读

The parameters of a stationary process can be viewed as functions of the spectral distribution function. This work concerns (estimators) parameters defined as integrals of $m (\geq 1)$-dimensional kernel functions with respect to the (sample) spectral distribution function. Conditions for asymptotic normality, almost sure convergence, and probability one bounds are derived for such estimators. The approach taken is based upon the reduction of an $m$-dimensional problem to…

极大似然型方程泛函解的唯一性与 Fréchet 可微性AI 解读

Solutions of simultaneous equations of the maximum likelihood type or $M$-estimators can be represented as functionals. Existence and uniqueness of a root in a local region of the parameter space are proved under conditions that are easy to check. If only one root of the equation exists, the resulting statistical functional is Frechet differentiable and robust. When several solutions exists, conditions on the loss criterion used to select the root for the statistic ensure…

位置参数R估计量的极小极大性质AI 解读

Consider the problem of estimating the unknown location parameter $\theta$ based on a random sample from $F(x - \theta)$, where $F$ is an unknown member of the class of distribution functions $\mathscr{F} = \{F: F$ is symmetric about 0 and $\sup_x |F(x) - \Phi(x)| \leq \varepsilon\}$, where $\Phi$ denotes the standard normal distribution function. Huber (1964) showed that $M$-estimation has a minimax property for this model, whereas Sacks and Ylvisaker (1972) showed that $L$-…

两样本最优非参数得分函数的秩估计与相应自适应秩统计量AI 解读

In the general two-sample testing problem, $X_1, \cdots, X_m$ i.i.d. with continuous c.d.f. $F, Y_1, \cdots, Y_n$ i.i.d. with continuous c.d.f. $G$, and null hypothesis $H_0: F = G$ versus alternative $H_1: F \leq G, F \neq G$, we construct uniformly consistent and tractable rank estimators of the underlying optimal nonparametric score-function for a large subclass of (fixed) alternatives. Moreover, we prove asymptotic normality of the corresponding adaptive rank statistics…

密度估计中最小二乘交叉验证的大样本最优性AI 解读

We prove that the method of cross-validation suggested by A. W. Bowman and M. Rudemo achieves its goal of minimising integrated square error, in an asymptotic sense. The tail conditions we impose are only slightly more severe than the hypothesis of finite variance, and so least squares cross-validation does not exhibit the pathological behaviour which has been observed for Kullback-Leibler cross-validation. This is apparently the first time that a cross-validatory procedure…

非参数判别中趋近贝叶斯风险的最优收敛速率AI 解读

Consider the multiclassification (discrimination) problem with known prior probabilities and a multi-dimensional vector of observations. Assume the underlying densities corresponding to the various classes are unknown but a training sample of size $N$ is available from each class. Rates of convergence to Bayes risk are investigated under smoothness conditions on the underlying densities of the type often seen in nonparametric density estimation. These rates can be…

核非参数回归中交叉验证的一致性AI 解读

For the nonparametric regression model $Y(t_i) = \theta(t_i) + \varepsilon(t_i)$ where $\theta$ is a smooth function to be estimated, $t_i$'s are nonrandom, $\varepsilon(t_i)$'s are i.i.d. errors, this paper studies the behavior of the kernel regression estimate $\hat{\theta}(t) = \big\lbrack \sum^n_{j=1}K \big(\frac{t_j - t}{\lambda}\big) Y(t_j) \big\rbrack / \big\lbrack\ sum^n_{j=1} K \big(\frac{t_j - t}{\lambda}\big) \big\rbrack$ when $\lambda$ is chosen by…