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基于竞争模型L²距离的混合分布同质性检验AI 解读

Ascertaining the number of components in a mixture distribution is an interesting and challenging problem for statisticians. Chen, Chen, and Kalbfleisch recently proposed a modified likelihood ratio test (MLRT), which is distribution-free and locally most powerful, asymptotically. In this article we present a new method for testing whether a finite mixture distribution is homogeneous. Our method, the D test, is based on the L2 distance between a fitted homogeneous model and…

通过边际密度分解进行有限混合模型的贝叶斯选择AI 解读

We consider the problem of estimating the number of components d and the unknown mixing distribution in a finite mixture model, in which d is bounded by some fixed finite number N. Our approach relies on the use of a prior over the space of mixing distributions with at most N components. By decomposing the resulting marginal density under this prior, we discover a weighted Bayes factor method for consistently estimating d that can be implemented by an iid generalized…

广义线性模型中的置信带AI 解读

Generalized linear models (GLM) include many useful models. This paper studies simultaneous confidence regions for the mean response function in these models. The coverage probabilities of these regions are related to tail probabilities of maxima of Gaussian random fields, asymptotically, and hence, the so-called tube formula is applicable without any modification. However, in the generalized linear models, the errors are often nonadditive and non-Gaussian and may be…

均匀分布对单调密度备择的检验AI 解读

The paper is concerned with testing uniformity versus a monotone den-sity. This problem arises in two important contexts, after transformations, testing whether a sample is a simple random sample or a biased sample, and testing whether the intensity function of a nonhomogeneous Poisson process is constant against monotone alternatives. A penalized likelihood ratio test ($P$-test) and a Dip likelihood test ($D$-test) are developed. The $D$-test is analogous to Hartigan and…

异方差误差下线性回归的同时置信带AI 解读

The Scheffé method may be used to construct simultaneous confidence bands for a regression surface for the whole predictor space. When the bands need only hold for a subset of that space, previous authors have described how the bands can be appropriately narrowed while still maintaining the desired level of confidence. Data with heteroscedastic errors occur often, and unless some transformation is feasible, there is no obvious way to construct bands using the current…

异方差误差下线性回归的同时置信带AI 解读

The Scheffé method may be used to construct simultaneous confidence bands for a regression surface for the whole predictor space. When the bands need only hold for a subset of that space, previous authors have described how the bands can be appropriately narrowed while still maintaining the desired level of confidence. Data with heteroscedastic errors occur often, and unless some transformation is feasible, there is no obvious way to construct bands using the current…

线性回归与平滑的同时置信带AI 解读

Suppose we observe $Y-i = f(x_i) + \varepsilon_i, i = 1, \ldots, n$. We wish to find approximate $1 - \alpha$ simultaneous confidence regions for $\{f(x), x \in \mathscr{X}\}$. Our regions will be centered around linear estimates $\hat{f}(x)$ of nonparametric or nonparametric $f(x)$. There is a large amount of previous work on this subject. Substantial restrictions have been usually placed on some or all of the dimensionality of $x,$ the class of functions $f$ that can be…