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随机空间模式分形维数的极大似然估计AI 解读

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.

无重复观测的超结构模型AI 解读

Dolby's (1976) ultrastructural model is investigated with emphasis on the case with no replications and one of the error variances known. It is shown that, in this situation, the maximum likelihood estimators are not consistent. The method of moments estimators are consistent and asymptotically normal and best in Fisher's sense within a broad class of asymptotically normal estimators discussed by Gleser (1983). Some connections with the errors-in-variables model are examined.

离散化误差对核密度估计带宽选择的影响AI 解读

It is well known that the cross-validation score function of discretized data often tends to -∞ as the bandwidth tends to zero. This disturbing property causes some difficulty in applying cross-validation to discretized data. Since all data are rounded to some degree, the phenomenon limits the application of cross-validation in practice. Based on characteristic functions, the cause of the difficulty is explained, and a simple modification is suggested. Under some conditions,…

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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…

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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…

有偏处理分配下乘法处理效应的估计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.

趋势稳健的两水平析因设计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.

空间点过程的删失距离强度估计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…

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核密度估计中最优的数据驱动带宽选择AI 解读

A bandwidth selection method is proposed for kernel density estimation. This is based on the straightforward idea of plugging estimates into the usual asymptotic representation for the optimal bandwidth, but with two important modifications. The result is a bandwidth selector with the, by nonparametric standards, extremely fast asymptotic rate of convergence of n−½ where n ↑ ∞ denotes sample size. Comparison is given to other bandwidth selection methods, and small sample…

平滑信号检测：基于累积和程序的最优性AI 解读

Cox et al. (1988) show that under a random smooth function model with signal covariance matrix V, a locally most powerful test for the presence of a nonpolynomial signal is based on the statistic yTVy. We show that if a well-known difference-based roughness measure is used to derive a natural choice for V then this statistic is the sum of squares of a residual cusum sequence. Thus we confirm theoretically the long-held impression that the residual cusum sequence is powerful…

利用非参数曲线进行模型检验AI 解读

The use of local likelihood curve estimates in model checking is described. Test statistics are based on deviance differences, and are interpreted using nonparametric bootstrap Monte Carlo. Some theoretical aspects are discussed. Methods are illustrated for regression with discrete data.

逻辑回归相对于线性判别分析的渐近效率AI 解读

We calculate the asymptotic efficiency of logistic regression relative to linear discriminant analysis for testing hypotheses about the parameters when the explanatory variables are normally distributed. The Pitman asymptotic efficiency for hypothesis tests in this context is the same as the asymptotic relative efficiency calculated using mis-classification rates and is independent of the number of explanatory variables and the number of parameters to be tested.

非正态总体中的均值回归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…

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Cox–Reid 条件似然比统计量的 Bartlett 型调整AI 解读

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.

类间相关系数的渐近方差AI 解读

In genetics, the term interclass correlation has been used to refer to the parent-offspring and son-daughter correlations within families. Under the assumption of variable family sizes and normality, we derive the asymptotic variance of the maximum likelihood estimator of the son-daughter interclass correlation.

检验多个总体斜率的似然比统计量及 Bartlett 校正AI 解读

Inference about the slopes of two or more populations when the explanatory variables are measured with error is studied. We concentrate on the construction of a likelihood based test statistic and its Bartlett correction factor. The improvement of the chi-squared approximation is appreciable in the unknown variance case.