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通过维度扩展建模非平稳空间过程AI 解读

In this article, we propose a novel approach to modeling nonstationary spatial fields. The proposed method works by expanding the geographic plane over which these processes evolve into higher-dimensional spaces, transforming and clarifying complex patterns in the physical plane. By combining aspects of multidimensional scaling, group lasso, and latent variable models, a dimensionally sparse projection is found in which the originally nonstationary field exhibits…

通过交叉验证选择似然权重AI 解读

The (relevance) weighted likelihood was introduced to formally embrace a variety of statistical procedures that trade bias for precision. Unlike its classical counterpart, the weighted likelihood combines all relevant information while inheriting many of its desirable features including good asymptotic properties. However, in order to be effective, the weights involved in its construction need to be judiciously chosen. Choosing those weights is the subject of this article in…

设计性缺失数据下的贝叶斯多变量空间插值AI 解读

Summary In a network of s g sites, responses like levels of airborne pollutant concentrations may be monitored over time. The sites need not all measure the same set of response items and unmeasured items are considered as data missing by design. We propose a hierarchical Bayesian approach to interpolate the levels of, say, k responses at s u other locations called ungauged sites and also the unmeasured levels of the k responses at the gauged sites. Our method involves two…

摘要暂缺

基于线性模型估计方程的自助法AI 解读

This paper presents a method of bootstrap estimation for the linear model. Rather than resampling from the original sample, as is conventional, the proposed method resamples summands in an estimating function used to produce the original estimate. The method is computationally simpler then existing competitors. However, its main advantage lies in the robustness to heteroscedasticity of the estimators it produces. These estimators are shown to have desirable asymptotic…

二项分布试验次数的估计方法比较AI 解读

Estimating the number, n, of trials, given a sequence of independent success counts obtained by replicating the n-trial experiment is less studied and a considerably harder problem than estimating p for the binomial distribution. Both the method of moments and the maximum likelihood estimators of n are considered. When p is unknown and small, while n is large, both estimators become highly unstable. Stabilized versions of these estimators are proposed, and their performance…

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非平稳泊松过程强度函数的贝叶斯线性估计AI 解读

A Bayesian approach is taken to the problem of estimating the intensity function of a nonstationary Poisson process. The intensity function, Λ(t), − T < t < T, is a priori a second-order stochastic process. Estimators are found which minimize among, respectively, the class of step functions, the class of moving averages, and a class of linear estimators. An approximation for large T to the last estimator is found. These estimators are compared in a numerical example…

非平稳泊松过程强度函数的贝叶斯线性估计AI 解读

A Bayesian approach is taken to the problem of estimating the intensity function of a nonstationary Poisson process. The intensity function, Λ(t), − T < t < T, is a priori a second-order stochastic process. Estimators are found which minimize among, respectively, the class of step functions, the class of moving averages, and a class of linear estimators. An approximation for large T to the last estimator is found. These estimators are compared in a numerical example…

摘要暂缺

独立泊松总体均值的同时估计AI 解读

A procedure is derived for simultaneously estimating the means of Poisson populations using independent samples. The total loss is the sum of component, standardized squared error losses. The derived procedure is minimax, generalized Bayes, admissible relative to a large class, and better than using the sample means as estimators of the corresponding population means. The latter procedure is compared with the derived procedure, both numerically and asymptotically.