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用于时变谱分析的平滑样条 ANOVAAI 解读

In this article we propose a smoothing spline ANOVA model (SS-ANOVA) to estimate and to make inference on the time-varying log-spectrum of a locally stationary process. The time-varying spectrum is assumed to be smooth in both time and frequency. This assumption essentially turns a time-frequency spectral estimation problem into a 2-dimensional surface estimation problem. A smooth localized complex exponential (SLEX) basis is used to calculate the initial periodograms, and a…

校准自由度：自动数据平滑与有效曲线检验AI 解读

Curve fitting and curve checking based on the local polynomial regression technique are commonly used data-analytic methods in statistics. This article examines, in nonparametric settings, both the asymptotic expressions and empirical formulas for degrees of freedom (DF), a notion introduced by Hastie and Tibshirani, of linear smoothers. The asymptotic results give useful insights into the nonparametric modeling complexity. Meanwhile, by substituting the exact DFs by the…

长周期彗星轨道的本征分布与选择偏差AI 解读

A question that arises in the study of cometary orbits is whether or not the directed normals to the orbits are uniformly distributed on the celestial sphere. Previous studies by statisticians have not taken selection effects into account and have tended to reject uniformity. Here a plausible selection mechanism is proposed that gives rise to a one-parameter family of distributions on the sphere. Data on long-period comets are analyzed using this one-parameter family. A…

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核苷酸序列沿线系统发育变异的推断AI 解读

We develop a Bayesian multiple changepoint model to infer spatial phylogenetic variation (SPV) along aligned molecular sequence data. SPV occurs in sequences from organisms that have undergone biological recombination or when evolutionary rates and selective pressures vary along the sequences. This Bayesian approach permits estimation of uncertainty regarding recombination, the crossing-over locations, and all other model parameters. The model assumes that the sites along…

受试者工作特征曲线下面积的半参数回归AI 解读

Medical advances continue to provide new and potentially better means for detecting disease. Such is true in cancer, for example, where biomarkers are sought for early detection and where improvements in imaging methods may pick up the initial functional and molecular changes associated with cancer development. In other binary classification tasks, computational algorithms such as neural networks, support vector machines, and evolutionary algorithms have been applied to…

多元自适应样条模型中线性方向的识别AI 解读

Identifying linear directions in multivariate regression has been a statistical challenge and has attracted particular attention since projection pursuit was developed. To this end, we propose and investigate the use of linear discriminant analysis and projection Hessian directions in conjunction with multivariate adaptive regression splines. Simulation studies in a variety of settings demonstrate the usefulness of our approach in revealing both the functional forms and the…

基于多元自由结点回归样条的广义非线性建模AI 解读

A Bayesian method is presented for the nonparametric modeling of univariate and multivariate non-Gaussian response data. Data-adaptive multivariate regression splines are used where the number and location of the knot points are treated as random. The posterior model space is explored using a reversible-jump Markov chain Monte Carlo sampler. Computational difficulties are partly alleviated by introducing a random residual effect in the model that leaves many of the posterior…

多元回归降秩的无预设模型检验AI 解读

We propose a test of dimension in multivariate regression. This test is in the spirit of tests on the rank of the coefficient matrix in a multivariate linear model, but it does not require a prespecified model. The test may be particularly useful at the outset of an analysis before a multivariate model is posited, because it can lead to low-dimensional summary plots that are inferred to contain all of the sample information on the multivariate mean function.

未记录有效投票选票的重新计票AI 解读

The vote recount in the 2000 Presidential election (Broward, Miami-Dade and Palm Beach Counties, Florida) is examined for evidence of bias. A precinct-level dataset is constructed, incorporating the machine-vote tally, the recount vote tally, voter registration demographics, and the ballot review by media sources. A new multivariate beta-logit model is introduced that allows joint modeling of multivariate unobserved latent probabilities. A simple two-step estimator is…

从数据统计到知识统计AI 解读

Increasingly, datasets are so large they must be summarized in some fashion so that the resulting summary dataset is of a more manageable size, while still retaining as much knowledge inherent to the entire dataset as possible. One consequence of this situation is that the data may no longer be formatted as single values such as is the case for classical data, but rather may be represented by lists, intervals, distributions, and the like. These summarized data are examples…

简单线性回归的序贯监测AI 解读

This article considers an important aspect of the general sequential analysis problem where a process is in control up to some unknown point i = ν − 1, after which the distribution from which the observations are generated changes. An extensive sequential analytic literature assumes that the change in distribution is abrupt, for example, from N(0,1) to N(μ,1). There is also an extensive literature that deals with a gradual change in the case where the decision (whether or…

利用贝叶斯模型选择识别微阵列中的差异表达基因AI 解读

DNA microarrays open up a broad new horizon for investigators interested in studying the genetic determinants of disease. The high throughput nature of these arrays, where differential expression for thousands of genes can be measured simultaneously, creates an enormous wealth of information, but also poses a challenge for data analysis because of the large multiple testing problem involved. The solution has generally been to focus on optimizing false-discovery rates while…

含删失生存数据的临床试验样本量再估计AI 解读

A flexible design with updating of sample size in clinical trials is proposed for censored survival data. Patients enter trials serially and are subject to random loss to follow-up. The statistical inference is based on a weighted average of the linear rank statistics, where the weight function at each look depends on prior observed data. A stopping rule is devised to allow early termination and acceptance of the null hypothesis when the experimental treatment offers no…

具有状态依赖方差的非线性状态空间模型AI 解读

Nonlinear state-space models with state-dependent variances (SDVs) are commonly used in financial time series. Important examples include stochastic volatility (SV) and affine term structure models. We propose a methodology for state smoothing in this class of models. Our smoothing technique is simulation based and uses an auxiliary mixture model. Key features of the auxiliary mixture model are the use of state-dependent weights and efficient block sampling algorithms to…

采用平方损失的提升方法AI 解读

This article investigates a computationally simple variant of boosting, L2Boost, which is constructed from a functional gradient descent algorithm with the L2-loss function. Like other boosting algorithms, L2Boost uses many times in an iterative fashion a prechosen fitting method, called the learner. Based on the explicit expression of refitting of residuals of L2Boost, the case with (symmetric) linear learners is studied in detail in both regression and classification. In…

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