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正则化信号恢复中的噪声估计AI 解读

Several estimators of variance are compared in the context of problems where smoothing is incorporated in the estimation of regression functions. Many of the estimators are scaled quadratic forms in the data, and some incorporate steps that try to accommodate substantial nonconstancy in the response function. The estimators are described and an account is provided of an empirical study based on four one-dimensional source functions of varying degrees of irregularity.

测量误差的影响AI 解读

Measurement error causes the distribution generating data to differ from the distribution that is of substantive interest. To understand the effect of measurement error on the information produced by statistical procedures it is thus necessary to understand the distortions induced by measurement error. This paper sheds light on this by providing small error variance approximations to the distribution of variates subject to contamination by measurement error. These provide…

关于决定系数一般定义的一则札记AI 解读

A generalization of the coefficient of determination R2 to general regression models is discussed. A modification of an earlier definition to allow for discrete models is proposed.

In the exponential regression model, inference concerning the regression parameter is notoriously difficult, even when using the Bayesian noninformative prior approach. The reference prior approach (Bernardo, 1979; Berger & Bernardo, 1989) is considered, and argued to yield very satisfactory inferences. Estimation and credible sets are considered in a specific example.

存在删失时的贝叶斯残差分析AI 解读

Use of the posterior distribution of the realized error terms for residual analysis in a linear model was advocated by Zellner (1975) and Zellner & Moulton (1985). The same idea was used by Chaloner & Brant (1988) to define outliers and calculate posterior probabilities of observations being outliers. This paper extends the same concept to other models, including regression models for lifetime data, by using an approach similar to that of Cox & Snell (1968). Residual plots…

乘法强度模型中对数秩检验的相对效率AI 解读

SUMMARY For large-sample clinical trials with independent individuals randomly allocated to two treatment groups, in which survival times follow a log linear multiplicative intensity model with treatment group as one covariate, this paper calculates the asymptotic relative efficiency of the log rank test for treatment effect as compared with the optimal score test. The method is to exhibit the failure hazard intensity, not of proportional hazards form, obtained by ignoring…

具有高阶卡方近似的修正得分检验统计量AI 解读

We give a general modified score test statistic whose nuil distribution is chi-squared to order n−1, where n is the sample size. The modified statistic depends on the joint cumulants of log likelihood derivatives for the full data. Some applications are discussed. Following Cox & Reid (1987a) we also derive a general formula for Bartlett-type corrections to improve test statistics whose null asymptotic distributions are chi-squared.

修正的带符号对数似然比AI 解读

The signed log likelihood ratio r for a one-dimensional interest parameter can be modified as r* = r + r−1 log (u/r) so that r* is asymptotically standard normally distributed with error of order O(n−/32;), u being interpretable as a test statistic. A new, more direct derivation of this result is given, which leads to a more explicit expression for u and provides a better handle on the error term. The relation of the tail area approximation determined by r* to a…

端点附近的平滑最优核估计量AI 解读

Kernel estimators for smooth curves like density, spectral density or regression functions require modifications when estimating near endpoints of the support, both for practical and asymptotic reasons. The construction of such boundary kernels as solutions of a variational problem is addressed and representations in orthogonal polynomials are given, including explicit solutions for the most important cases. Based on explicit formulae for certain functional of the kernels,…

频率估计的一种快速高效方法AI 解读

A technique is presented for the estimation of the frequency of a sinusoid in the presence of noise. The technique is based on fitting ARMA (2, 2) models iteratively, in a special way. The estimator is shown to be strongly consistent and as efficient as the least squares estimator of the frequency, or the periodogram maximizer. A simple accelerated version of the technique is shown to converge in a small number of iterations, the number depending on the accuracy of the…

Two approximate maximum likelihood estimates of the fractal dimension are suggested for random point patterns and planar curves, based on the distributions of the Palm probability and the spectrum.

泊松回归的样本量计算AI 解读

For the Poisson regression model, an exact expression for Fisher's information matrix, based upon the moment generating function of the distribution of covariates, is calculated. This parallels a similar, approximate, calculation by Whittemore (1981) for logistic regression. The resulting asymptotic variance of the maximum likelihood estimate of the parameters is used to calculate the sample size required to test hypotheses about the parameters at a specified significance…

非正态总体中的向均值回归AI 解读

Regression to the mean is the term used to describe the effect by which individuals selected on the basis of an initial measurement which is particularly high or low compared with other members of the population have, upon remeasurement, values nearer to the population mean. For the normal distribution simple expressions for estimates of the magnitude of this effect are available. Many biological variables, however, are not normally distributed. Estimates for regression to…

核密度估计与边缘化一致性AI 解读

Kernel density estimates, as commonly applied, generally have no exact model-based interpretation since they violate conditions that define coherent joint distributions. The issue of marginalization consistency is considered here. It is shown that most commonly used kernel functions violate this condition. It is also shown that marginalization consistency holds only for classes of kernel estimates based on Laplacian, or double-exponential kernels whose window width…

多次捕获—再捕获模型的贝叶斯分析AI 解读

In multiple capture-recapture surveys, the probability of capture can vary between sampling occasions. The model accounting for this variation is known as Mt. Bayes, empirical Bayes, and Bayes empirical Bayes solutions are given to the problems of interval estimation, decision making, and point estimation of the population size N. When the number of sampling occasions is small to moderate and the number of recaptured units observed on each sampling occasion is moderate,…

分层自适应群集抽样AI 解读

Stratified adaptive cluster sampling refers to designs in which, following an initial stratified sample, additional units are added to the sample from the neighbourhood of any selected unit with an observed value that satisfies a condition of interest. If any of the added units in turn satisfies the condition, still more units are added to the sample. Estimation of the population mean or total with the stratified adaptive cluster designs is complicated by the possibility…

季节差分的若干拉格朗日乘子检验AI 解读

Determining whether a time series has a unit root is an important problem in many time series analyses. For seasonal time series the problem is more complicated as one has to decide whether both regular and seasonal differencing or just one of them would suffice to transform a series into stationarity. This important problem is addressed via the Lagrange multiplier test approach. The large sample representations of the test statistics in terms of integrals of Wiener…

Cox–Reid 条件似然比统计量的 Bartlett 型调整AI 解读

SUMMARY This paper explicitly derives a Bartlett-type adjustment for the conditional likelihood ratio statistic of Cox & Reid via that for the usual likelihood ratio statistic.

拟合优度与独立性的 Rao 得分检验AI 解读

Rao's score statistic is a standard tool for carrying out hypothesis tests. A unified approach is given which encompasses many common tests. When a suitable group structure is present, it is shown how the derivation of the test statistic can be simplified. An omnibus test of multivariate normality is derived as an example of group invariance. As another application of Rao score tests, a general method is given for constructing tests of independence.

有偏治疗分配下的乘法治疗效应估计AI 解读

Suppose that, given θ, x is Poisson with mean θ, while, given θ, y is Poisson with mean αθ or βθ according as treatment 1 or treatment 2 is used. Moreover, suppose that treatment 1 is used if x < a, while treatment 2 is used if x≥ a. Under this biased allocation of treatments we give consistent estimators of the two treatment effects α and β. The method also applies when x is binomial and θ is the odds on success, and to other cases.

抗趋势的两水平析因试验设计AI 解读

Limiting the possible influence of time order effects may be an important consideration in designing a sequential experiment. We consider the problem of finding trend robust run orders of two-level factorials when the time effects are modelled via a first order autoregressive error model or via a time series model. In both cases, run orders are trend robust if the factors change level many times. Other run orders can be quite inefficient, even if they are free of low-degree…

若干纯生过程中最大似然估计的近似AI 解读

We present two simple approximations, one an extension of that given by Choi & Severo (1988), to the maximum likelihood estimate of a parameter λ in the class of birth processes in which the growth rate is the product of λ and some known function of the population size. The data are population sizes taken at a discrete set of time points. The Yule process is discussed in some detail.

基于删失距离的空间点过程强度估计AI 解读

The use of censoring in conjunction with distance-based estimation of the intensity of a spatial point process is considered. Censoring, in this context, may be motivated by practical considerations such as reduction of sampling effort, but it may also be considered as a method for preventing the overlap of search regions and for eliminating edge effects. Maximum likelihood estimators that utilize censored point-plant measurements or censored T-square measurements are…

点过程约化二阶矩测度的一类新估计量AI 解读

A class of edge-corrected estimators for the reduced second moment measure of a stationary isotropic point process is proposed. All estimators in this class have the same unbiasedness properties as previously suggested edge-corrected estimators. One natural element in this class has superior asymptotic properties to existing estimators when the underlying process is Poisson. A simulation study shows that this superiority also holds for certain cluster processes.