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厚尾与偏度的贝叶斯建模AI 解读

We consider a Bayesian analysis of linear regression models that can account for skewed error distributions with fat tails.The latter two features are often observed characteristics of empirical data sets, and we will formally incorporate them in the inferential process.A general procedure for introducing skewness into symmetric distributions is rst proposed.Even though this allows for a great deal of exibility in distributional shape, tail behaviour is not aected.In…

具有相关随机误差的平滑样条模型AI 解读

Spline-smoothing techniques are commonly used to estimate the mean function in a nonparametric regression model. Their performances depend greatly on the choice of smoothing parameters. Many methods of selecting smoothing parameters such as generalized maximum likelihood (GML), generalized cross-validation (GCV), and unbiased risk (UBR), have been developed under the assumption of independent observations. They tend to underestimate smoothing parameters when data are…

稳健二元非参数回归的贝叶斯方法AI 解读

This article presents a Bayesian approach to binary nonparametric regression that assumes that the argument of the link is an additive function of the explanatory variables and their multiplicative interactions. The article makes the following contributions. First, a comprehensive approach is presented in which the function estimates are smoothing splines with the smoothing parameters integrated out and the estimates are made robust to outliers. Second, the approach can…

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Triogram 三角剖分样条模型AI 解读

In this article we introduce the Triogram method for function estimation using piecewise linear, bivariate splines based on an adaptively constructed triangulation. We illustrate the technique for bivariate regression and log-density estimation and indicate how our approach can be applied directly to model bivariate functions in the broader context of an extended linear model. The entire estimation procedure is invariant under affine transformations and is a natural approach…

估计从未发生事件的概率：你的一票何时具有决定性？AI 解读

Researchers sometimes argue that statisticians have little to contribute when few realizations of the process being estimated are observed. We show that this argument is incorrect even in the extreme situation of estimating the probabilities of events so rare that they have never occurred. We show how statistical forecasting models allow us to use empirical data to improve inferences about the probabilities of these events. Our application is estimating the probability that…

时间序列分析在天文学和气象学中的应用AI 解读

Part 1 Time series - theory and methodology: A short history of time series, M.B. Priestley Frequency estimation, E.J. Hannan et al Asymptotic expansion of estimators for diffusions with small noises, N. Yoshida Spatial-temporal spectral analysis with random sampling, I-Shang Chow, Ken-Shin Lii Detection of periodicities, M.B. Priestley Spectral and multivariate probability density estimation of continuous time stationary processes from randomly sampled data, Elias Masry…

形状的统计理论AI 解读

1 Introduction.- 1.1 Background of Shape Theory.- 1.2 Principles of Allometry.- 1.3 Defining and Comparing Shapes.- 1.4 A Few More Examples.- 1.4.1 A Simple Example in One Dimension.- 1.4.2 Dinosaur Trackways From Mt. Tom, Massachusetts.- 1.4.3 Bronze Age Post Mold Configurations in England.- 1.5 The Problem of Homology.- 1.6 Notes.- 1.7 Problems.- 2 Background Concepts and Definitions.- 2.1 Transformations on Euclidean Space.- 2.1.1 Properties of Sets.- 2.1.2 Affine…

有放回抽样中预测函数与未见物种数量的估计AI 解读

A sample of N units is taken from a population consisting of an unknown number of species. We are interested in estimating the number of species and the prediction function for future sampling. The prediction function is defined as the expected number of new species that will be found if an additional sample of size tN is taken for any positive real number t. In this paper we point out that an estimator suggested by Efron and Thisted lacks some essential properties of the…

更有能力判定均值符号的置信区间：两端约束均值AI 解读

We present two new families of two-sided nonequivariant confidence intervals for the mean θ of a continuous, unimodal, symmetric random variable. Compared with the conventional symmetric equivariant confidence interval, they are shorter when the observation is small, and restrict the sign of θ for smaller observations. One of the families, a modification of Pratt's construction of intervals with minimal expected length when θ = 0, is longer than the conventional symmetric…

共同均值估计与加权均值统计量AI 解读

Measurements made by several laboratories may exhibit nonnegligible between-laboratory variability, as well as different within-laboratory variances. Also, the number of measurements made at each laboratory often differ. Questions of fundamental importance in the analysis of such data are how to form a best consensus mean, and what uncertainty to attach to this estimate. An estimation equation approach due to Mandel and Paule is often used at the National Institute of…

一类动态非线性统计模型的估计与预测AI 解读

A class of nonlinear state-space models, characterized by a single source of randomness, is introduced. A special case, the model underpinning the multiplicative Holt-Winters method of forecasting, is identified. Maximum likelihood estimation based on exponential smoothing instead of a Kalman filter, and with the potential to be applied in contexts involving non-Gaussian disturbances, is considered. A method for computing prediction intervals is proposed and evaluated on…

广义帕累托分布的数据拟合AI 解读

The generalized Pareto distribution (GPD) was introduced by Pickands to model exceedances over a threshold. It has since been used by many authors to model data in several fields. The GPD has a scale parameter ([sgrave] > 0) and a shape parameter (−∞ < k < ∞). The estimation of these parameters is not generally an easy problem. When k > 1, the maximum likelihood estimates do not exist, and when k is between 1/2 and 1, they may have problems. Furthermore, for k ≤ −1/2, second…

仿射不变的多元单样本符号秩检验AI 解读

Brown and Hettmansperger introduced affine-invariant bivariate analogs of the sign, rank, and signed-rank tests based on the Oja median. In this article affine-invariant k-variate extensions of the one-sample signed-rank test and the Hodges-Lehmann estimate are considered. The necessary distribution theory is developed, and asymptotic Pitman efficiencies with respect to Hotelling's T 2 test under multivariate t distributions are tabulated. An application of the signed-rank…

标准化影响矩阵及其应用AI 解读

In this article we introduce the standardized influence matrix (SIM) of parameter estimators as a conjugate of the sample covariance matrix of standardized influence functions (SIFs) evaluated at the data points. We propose principal component analysis for the SIM and its complement (SIM analysis) as a diagnostic tool for regression or other statistical inference, and provide theoretical insight to the local influence defined by Cook. We show that SIM analysis reveals the…

用于偏最小二乘回归的加性样条AI 解读

This article introduces a generalization of the partial least squares regression (PLS). Transforming the predictors by means of spline functions is a useful way to extend PLS into nonlinearity and to obtain a multiresponse additive model. We describe both statistical and computational aspects of this new method, termed additive splines partial least squares (ASPLS). The performance of ASPLS compared with other PLS methods is illustrated with chemical and physiological…

非参数二元回归的贝叶斯方法AI 解读

This article outlines a general Bayesian approach to estimating a bivariate regression function in a nonparametric manner. It models the function using a bivariate regression spline basis with many terms. Binary indicator variables corresponding to these terms are introduced to explicitly model the uncertainty of whether or not the terms provide a significant contribution to the regression. The regression function is estimated using an estimate of its posterior mean,…

基于无穷小方法的稳健设计AI 解读

We introduce an infinitesimal approach to the construction of robust designs for linear models. The resulting designs are robust against small departures from the assumed linear regression response and/or small departures from the assumption of uncorrelated errors. Subject to satisfying a robustness constraint, they minimize the determinant of the mean squared error matrix of the least squares estimator at the ideal model. The robustness constraint is quantified in terms of…

利用 Voronoi 剖分非参数极大似然估计空间点过程特征AI 解读

This article addresses the problem of estimating the support domain of a bounded point process in presence of background noise. This situation occurs, for example, in the detection of a minefield from aerial observations. A maximum likelihood estimator for a mixture of uniform point processes is derived using a natural partition of the space defined by the data themselves: the Voronoi tessellation. The methodology is tested on simulations and compared to a model-based…

基于随机扫描分区的空间扫描统计量AI 解读

This article develops a spatial scan statistic for homogeneity analysis of point processes that utilizes stochastic scan partitions. The derivation of the sampling distribution for the statistic yields an exact test. This test has the potential for improved power over conventional alternatives when the point process is embedded in an underlying continuous random field and is recommended in situations for which the location of subregions of nonhomogeneity in the point process…