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A General Class of Models for Stationary Two-Dimensional Random Processes

平稳二维随机过程的一般模型类

A parametric family of spectral density-covariance function pairs for stationary spatial processes is introduced. The spectral densities are rational functions of elliptic forms along with factors in the numerator that may be of mixed hyperbolic, parabolic or elliptic form. The resulting covariance functions are linear combinations of modified Bessel functions of the second kind, which have been shown to be the natural basis for two-dimensional covariance functions (Whittle,…

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Exploring an Ozone Spatial Time Series in the Frequency Domain

在频域中探索臭氧的空间时间序列

In 1974, atmospheric scientists (Molina and Rowland; Cicerone et al.) first postulated that man-made chemicals known as CFC's (e.g., freon) deplete the earth's ozone when released into the atmosphere. This article presents an exploratory data analysis (EDA) of a spatial time series of ozone measurements. Frequency domain techniques for the EDA are introduced and used to graphically display global, long-term trends relevant to the CFC issue. My intention is to illustrate the…

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Are Productive People to Be Found? Robust Analysis of Sparse Two-Way Tables

能否识别高生产率员工?稀疏双向表的稳健分析

Data from individual measurements of production in a manufacturing environment may be thought of as a two-way table indexed by worker and task. If there are many tasks, such a table will normally be sparse. Adjustment for task effects is important if workers are to be compared to one another, since any two workers may have no tasks in common. Three techniques are presented for the analysis of such sparse tables: table-stripe regression, rectangle ratios, and network scores.…

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Are Productive People to Be Found? Robust Analysis of Sparse Two-Way Tables

能识别高生产率工人吗?稀疏双向表的稳健分析

Data from individual measurements of production in a manufacturing environment may be thought of as a two-way table indexed by worker and task. If there are many tasks, such a table will normally be sparse. Adjustment for task effects is important if workers are to be compared to one another, since any two workers may have no tasks in common. Three techniques are presented for the analysis of such sparse tables: table-stripe regression, rectangle ratios, and network scores.…

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A Multinomial Logit Model for the Spatial Distribution of Hospital Utilization

医院利用空间分布的多项 Logit 模型

Effective planning and management of multi-institutional health care systems require models to explain and predict hospital utilization in a region. In this study, a multinomial logit model has been formulated and estimated for inpatient hospital utilization in a region. Various measures and indexes that account for the relative attractiveness of hospitals are used in the specification of the model. A data base of more than 130,000 patient records is used to estimate the…

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Statistical Analysis of Multiple Sociometric Relations

多重社会关系的统计分析

Loglinear models are adapted for the analysis of multivariate social networks, a set of sociometric relations among a group of actors. Models that focus on the similarities and differences between the relations and models that concentrate on individual actors are discussed. This approach allows for the partitioning of the actors into blocks or subgroups. Some ideas for combining these models are described, and the various models and computational methods are applied to the…

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Asymptotic Properties of the Generalized Median in the Case of Multivariate Normality

多元正态情形下广义中位数的渐近性质

SUMMARY The generalized affine invariant median proposed by Oja (1983) is, in the case of multivariate normality, shown to be asymptotically at least as efficient as the spatial median.

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Linear models for field trials, smoothing and cross-validation

田间试验的线性模型、平滑与交叉验证

Spatial methods for the analysis of agricultural field experiments are represented here as smoothing methods applied simultaneously with the estimation of treatment effects. Selection of both the form of the smoother and the degree of smoothing required may be based on cross-validation. Particular emphasis is placed in this paper on generalized least squares estimation in linear models, but the principle applies quite generally.

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Chi-plots for assessing dependence

用于评估依赖关系的 Chi 图

This paper presents a graphical method to be used, in conjunction with a scatterplot, to investigate possible association of two variates as manifested in a sample of bivariate measurements. The method is designed so that the plot is approximately horizontal under independence, and under various forms of association it produces corresponding characteristic patterns. Examples given include application to study of regression residuals, dependence of two spatial point…

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A general class of models for stationary two-dimensional random processes

平稳二维随机过程的一般模型类

A parametric family of spectral density-covariance function pairs for stationary spatial processes is introduced. The spectral densities are rational functions of elliptic forms along with factors in the numerator that may be of mixed hyperbolic, parabolic or elliptic form. The resulting covariance functions are linear combinations of modified Bessel functions of the second kind, which have been shown to be the natural basis for two-dimensional covariance functions (Whittle,…

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Likelihood Analysis of Spatial Point Patterns

空间点模式的似然分析

SUMMARY The likelihood procedure for estimating the pairwise interaction potential function is developed for statistical analysis of homogeneous spatial point patterns. Approximation methods of the normalizing factor of Gibbs canonical distribution are discussed both to estimate a scale parameter and to measure the softness (or hardness) of repulsive interactions. The approximations are useful up to a considerably high density. The validity of our procedure is demonstrated…

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Optimal Randomization for Experiments in which Autocorrelation is Present

存在自相关时实验的最优随机化

For a linear or spatial ordering of the experimental units, systematic methods of applying the treatments to the experimental units minimize the variance of linear contrasts of treatment means. In the linear ordering the optimal randomization scheme for the application of k treatments is to apply a treatment to every kth experimental unit, the equivalent of systematic sampling in the sampling literature. In the spatial ordering the optimal randomization schemes are…

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Monte Carlo Methods of Inference for Implicit Statistical Models

隐式统计模型推断的蒙特卡洛方法

SUMMARY A prescribed statistical model is a parametric specification of the distribution of a random vector, whilst an implicit statistical model is one defined at a more fundamental level in terms of a generating stochastic mechanism. This paper develops methods of inference which can be used for implicit statistical models whose distribution theory is intractable. The kernel method of probability density estimation is advocated for estimating a log-likelihood from…

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Maximum likelihood estimation of models for residual covariance in spatial regression

空间回归中残差协方差模型的最大似然估计

We describe the maximum likelihood method for fitting the linear model when residuals are correlated and when the covariance among the residuals is determined by a parametric model containing unknown parameters. Observations are assumed to be Gaussian. We give conditions which ensure consistency and asymptotic normality of the estimators. Our main concern is with the analysis of spatial data and in this context we describe some simulation experiments to assess the small…

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Optimal randomization for experiments in which autocorrelation is present

存在自相关时实验的最优随机化

SUMMARY For a linear or spatial ordering of the experimental units, systematic methods of applying the treatments to the experimental units minimize the variance of linear contrasts of treatment means. In the linear ordering the optimal randomization scheme for the application of k treatments is to apply a treatment to every kth experimental unit, the equivalent of systematic sampling in the sampling literature. In the spatial ordering the optimal randomization schemes are…

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Statistical Uses of the Spatial Median

空间中位数的统计用途

SUMMARY The spatial median, called the mediancentre in an earlier paper by J. C. Gower, is defined as the bivariate location measure to minimize the sum of absolute distances to observations. its asymptotic efficiency relative to the sample mean vector with normal data is shown to exceed the usual univariate 2/π = 0.637. its estimating equations have an angular aspect and are used to develop “angle tests”, which are analogues of sign tests in one dimension.

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A Test of Autoregression in Gaussian Spatial Processes

高斯空间过程的自回归参数检验

A simple test is given of the autoregression parameter in Gaussian spatial processes using a conditional model. The test statistic is derived from the pseudolikelihood. Exact and approximate null distributions of the test statistic are given. Its efficiency for the local alternatives has also been considered. An interval estimate of the parameter is also given.

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A Network Algorithm for Performing Fisher's Exact Test in r × c Contingency Tables

用于多行多列列联表 Fisher 精确检验的网络算法

An exact test of significance of the hypothesis that the row and column effects are independent in an r × c contingency table can be executed in principle by generalizing Fisher's exact treatment of the 2 × 2 contingency table. Each table in a conditional reference set of r × c tables with fixed marginal sums is assigned a generalized hypergeometric probability. The significance level is then computed by summing the probabilities of all tables that are no larger (on the…

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The Infectiousness of a Disease in a Community of Households

家庭组成社区中的疾病传染性

Procedures for making inference about both the mean potential that an infective has for infecting a given susceptible from the same household, and the mean potential he has for infecting a given susceptible from another household are proposed. These estimation procedures provide a check for the assumption that the disease spreads homogeneously through the community, that is the assumption of homogeneous mixing. They also provide a means of checking whether or not the spread…

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A test of autoregression in Gaussian spatial processes

高斯空间过程自回归参数的检验

A simple test is given of the autoregression parameter in Gaussian spatial processes using a conditional model. The test statistic is derived from the pseudolikelihood. Exact and approximate null distributions of the test statistic are given. Its efficiency for the local alternatives has also been considered. An interval estimate of the parameter is also given.

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Nonparametric Maximum Likelihood Estimation of Spatial Patterns

空间模式的非参数最大似然估计

Let $\mathbf{X}$ be an absolutely continuous random variable in $\mathbb{R}^k$ with distribution function $F(\mathbf{x})$ and density $f(\mathbf{x})$. Let $\mathbf{X}_1, \cdots, \mathbf{X}_n$ be independent random variables distributed according to $F$. Mapping the spatial distribution of $\mathbf{X}$ normally entails drawing a map of the isopleths, or level curves, of $f$. In this paper, it is shown how to map the isopleths of $f$ nonparametrically according to the…

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Cluster Inference by using Transitivity Indices in Empirical Graphs

利用经验图传递性指标进行聚类推断

A random graph model is introduced for similarities observed between the objects sampled from an unknown cluster structure. We investigate this model and show how some common transitivity indices in empirical graphs can be used for making statistical inferences about cluster structures.

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Round Robin Analysis of Variance via Maximum Likelihood

基于最大似然的循环配对方差分析

A class of two-way random-effects models is presented for analyzing data that arise in a large variety of round robin designs. Examples of such designs can be found in numerous games, tournaments, and social interactions. The proposed models provide information not only about individual differences but also about the mutual contingency of the behaviors of interaction dyads. The statistical inference of the linear effects is discussed and a converging algorithm based on the…

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Round Robin Analysis of Variance Via Maximum Likelihood

基于最大似然的循环配对设计方差分析

A class of two-way random-effects models is presented for analyzing data that arise in a large variety of round robin designs. Examples of such designs can be found in numerous games, tournaments, and social interactions. The proposed models provide information not only about individual differences but also about the mutual contingency of the behaviors of interaction dyads. The statistical inference of the linear effects is discussed and a converging algorithm based on the…

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