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多类型 Boolean 模型中团块边界的维数AI 解读

In a fascinating article on models for particulate microstructure, Hermann and Ohser argue that the superposition of stochastically independent Boolean models may be thought of as producing sets whose boundaries have unusual properties of dimension. Hermann and Ohser employ such superposition models to analyse the particulate structure of rust. In the present paper we provide a theoretical foundation for their work, with respect to both the definition of dimension and its…

The coordinatewise median of a multivariate data set is a highly robust location estimator, but it depends on the choice of coordinates. A popular alternative which avoids this drawback is the spatial median, defined as the value that minimizes the sum of distances to the individual data points. In this paper we introduce and discuss another orthogonal equivariant version of the multivariate median, obtained by averaging the coordinatewise median over all orthogonal…

重复样本直方图AI 解读

The “replicate histogram” is introduced as a simple diagnostic tool for describing the sampling distribution of a general statistic. It can be applied to virtually any statistic that has an asymptotic distribution, and the data on which the statistic is computed may be serially or spatially dependent. The method is completely sample based, requiring no theoretical analysis by the user, no knowledge of the proper standardization for the statistic, and no specification of the…

多元数据分位数的几何定义AI 解读

An extension of the concept of quantiles in multidimensions that uses the geometry of multivariate data clouds has been considered. The approach is based on blending as well as generalization of the key ideas used in the construction of spatial median and regression quantiles, both of which have been extensively studied in the literature. These geometric quantiles are potentially useful in constructing trimmed multivariate means as well as many other L estimates of…

空间周期图的固定域渐近理论AI 解读

The periodogram for a spatial process observed on a lattice is often used to estimate the spectral density. The bases for such estimators are two asymptotic properties that periodograms commonly possess: (1) the periodogram at a particular frequency is approximately unbiased for the spectral density, and (2) the correlation of the periodogram at distinct frequencies is approximately zero. For spatial data, it is often appropriate to use fixed-domain asymptotics in which the…

居民用电实时定价：一项实验的计量分析AI 解读

Under real-time pricing, a network operator sets the price level for a period according to a predefined scheme which depends on the state of demand and costs, and announces this price shortly before the period begins. The French state-owned electric utility experimented with a six-rate real-time tariff, which divides the year into three types of days and each day into two periods. The number of days of each type is known in advance to the consumer, but the type of any…

使用前馈与循环神经网络预测汇率AI 解读

Abstract In this paper we investigate the out‐of‐sample forecasting ability of feedforward and recurrent neural networks based on empirical foreign exchange rate data. A two‐step procedure is proposed to construct suitable networks, in which networks are selected based on the predictive stochastic complexity (PSC) criterion, and the selected networks are estimated using both recursive Newton algorithms and the method of nonlinear least squares. Our results show that PSC is a…

若干二维中位数的影响函数AI 解读

SUMMARY The asymptotic efficiency, influence function and breakdown properties of the multivariate median proposed by Oja are investigated and comparisons are made with two other generalizations of the median: the spatial median and the vector of marginal medians. It is shown that, for distributions with finite expectations, the Oja median has a bounded influence function although this median has 0% breakdown. For circular distributions, the influence functions of the Oja…

局部多项式拟合的数据驱动带宽选择：可变带宽与空间适应AI 解读

SUMMARY When estimating a mean regression function and its derivatives, locally weighted least squares regression has proven to be a very attractive technique. The present paper focuses on the important issue of how to select the smoothing parameter or bandwidth. In the case of estimating curves with a complicated structure, a variable bandwidth is desirable. Furthermore, the bandwidth should be indicated by the data themselves. Recent developments in nonparametric smoothing…

小波收缩：渐近理想之境？AI 解读

SUMMARY Much recent effort has sought asymptotically minimax methods for recovering infinite dimensional objects—curves, densities, spectral densities, images—from noisy data. A now rich and complex body of work develops nearly or exactly minimax estimators for an array of interesting problems. Unfortunately, the results have rarely moved into practice, for a variety of reasons—among them being similarity to known methods, computational intractability and lack of spatial…

圆形数据的统计分析AI 解读

Preface 1. The purpose of the book 2. Survey of contents 3. How to use the book 4. Notation, terminology and conventions 5. Acknowledgements Part I. Introduction: Part II. Descriptive Methods: 2.1. Introduction 2.2. Data display 2.3. Simple summary quantities 2.4. Modifications for axial data Part III. Models: 3.1. Introduction 3.2. Notation trigonometric moments 3.3. Probability distributions on the circle Part IV. Analysis of a Single Sample of Data: 4.1. Introduction 4.2.…

论条件自回归与内蕴自回归AI 解读

Gaussian conditional autoregressions have been widely used in spatial statistics and Bayesian image analysis, where they are intended to describe interactions between random variables at fixed sites in Euclidean space. The main appeal of these distributions is in the Markovian interpretation of their full conditionals. Intrinsic autoregressions are limiting forms that retain the Markov property. Despite being improper, they can have advantages over the standard…

回归误差相关性的置换检验AI 解读

This article is about tests for serial, spatial, or other correlation in e, the error vector in the linear model Y = Xβ + e. The errors need not come from a particular parametric distribution such as the normal. P values are computed using permutations of the regression residuals. In the special cases that Y = e or X is a vector of Is, the tests are valid and consistent. In general, regression residuals are not exchangeable, so the tests are only approximate. It is shown,…

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卫星影像贝叶斯分类中的信息性先验AI 解读

In the Bayesian classification of satellite images, a prior distribution is used that aims to model the belief of spatial homogeneity of the underlying region. We extend this prior distribution to model certain topographical features of the area such as the position of the roads, the slopes, and the aspects. We demonstrate the effectiveness of this prior distribution in a reconstruction algorithm by means of a simulation study in which the quality of the result is assessed…

观测值函数的密度估计AI 解读

Density estimates, such as histograms and more sophisticated versions, are important in applied and theoretical statistics. In applied statistics, a density estimate gives the data analyst a graphical overview of the shape of the distribution. This overview allows the data analyst to arrive immediately at a qualitative impression of the location, scale, and various aspects of the extremes of the distribution. In theoretical statistics, the shape of the density allows the…

空间数据一般统计量矩的非参数估计AI 解读

A statistic s(·) is computed on spatially indexed data {X i : i ∈ D}, where D is a finite subset of the integer lattice Z2. We propose a simple nonparametric method for estimating the moments (e.g., variance, skewness) of s(D), using only the observed data at hand. The method uses “replicates” of s(·) computed on smaller subsets of D. No explicit knowledge of the underlying spatial dependence mechanism is needed, and the marginal distribution of X i may also be unknown. The…

气象场的统计时空建模方法AI 解读

In this article we develop a random field model for the mean temperature over the region in the northern United States covering eastern Montana through the Dakotas and northern Nebraska up to the Canadian border. The readings are temperatures at the stations in the U.S. historical climatological network. The stochastic structure is modeled by a stationary spatial-temporal Gaussian random field. For this region, we find little evidence of temporal dependence while the spatial…

气象场时空统计建模方法：评论AI 解读

Abstract In this article we develop a random field model for the mean temperature over the region in the northern United States covering eastern Montana through the Dakotas and northern Nebraska up to the Canadian border. The readings are temperatures at the stations in the U.S. historical climatological network. The stochastic structure is modeled by a stationary spatial-temporal Gaussian random field. For this region, we find little evidence of temporal dependence while…

卫星图像贝叶斯分类中的信息先验AI 解读

In the Bayesian classification of satellite images, a prior distribution is used that aims to model the belief of spatial homogeneity of the underlying region. We extend this prior distribution to model certain topographical features of the area such as the position of the roads, the slopes, and the aspects. We demonstrate the effectiveness of this prior distribution in a reconstruction algorithm by means of a simulation study in which the quality of the result is assessed…

具有空间相关误差的回归模型AI 解读

In this article we consider regression models for two-dimensional spatial data when the errors follow a spatial unilateral first-order autoregressive moving average (ARMA) model studied by Basu and Reinsel. We give details on the convenient computation of the generalized least squares (GLS) estimator of the regression parameters in the presence of spatially correlated errors, and compare the GLS estimator to the ordinary least squares (OLS) estimator in some special cases.…

利用新古典消费者选择理论从购买数据构建市场图谱AI 解读

This article presents a new model for estimating the spatial representation of objects and preference vectors from actual choice behavior of individuals or households. It is based on neoclassical economic theory of consumer choice. The model integrates both decisions of which good(s) to buy and the quantity of purchase. Overall preference is decomposed into price effects and intrinsic preference for the good. A maximum likelihood method for estimating the model parameters is…

多维符号检验：基于数据点云几何的推断AI 解读

Multivariate sign tests attracted several statisticians in the past, and it is evident from recent nonparametric literature that they still continue to draw attention. One of the most important features of the univariate sign test is that it does not involve much technical assumptions or complicacy, and this makes it quite popular among statistics users. In this article we have come up with a new method for constructing multivariate sign tests that have reasonable…

通过最大稳定过程进行极端暴风雨的区域建模AI 解读

SUMMARY Asymptotic models for extremes of random processes often form the basis for estimating the extremal behaviour of environmental phenomena. Most such phenomena have a spatial dimension, and the aim of this paper is to develop a procedure for modelling in continuous space the spatial dependence within extreme events. A principal objective in the analysis—as with other current research on extremes—is to base inference on as much of the available data as possible. The…