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稀疏函数型数据的主成分模型AI 解读

The elements of a multivariate dataset are often curves rather than single points. Functional principal components can be used to describe the modes of variation of such curves. If one has complete measurements for each individual curve or, as is more common, one has measurements on a fine grid taken at the same time points for all curves, then many standard techniques may be applied. However, curves are often measured at an irregular and sparse set of time points which can…

Recently, the concepts of population and individual bioequivalence have been proposed for assessing the bioequivalence of two drug formulations. Moment-based and probability-based measures of bioequivalence have led to criteria for deciding whether two formulations should be regarded as bioequivalent or not. The US Food and Drug Administration (1997) guidance recommended the use of bootstrap percentile intervals for this purpose. In this paper, we discuss theoretical…

带时间变换的 Copula 中的关联性AI 解读

We consider estimation of the cross ratio in Clayton's (1978) copula in which covariates are incorporated into the marginal distributions via semiparametric accelerated life regression models. Generalisations of Oakes' (1982, 1986) concordance estimating equations yield a closed form for the association parameter under right censoring. Joint inferences about covariate effects in the marginal models and the cross ratio are obtained with U-statistics, martingales and a…

非线性协方差分析的非参数模型与方法AI 解读

A fully nonparametric model for nonlinear analysis of covariance is proposed. The term nonlinear means that the covariate influences the response in a possibly nonlinear and nonpolynomial fashion, while the term fully nonparametric implies that the distributions for each factor level combination and covariate value are not restricted to comply with any parametric or semiparametric model. The possibility of different shapes of covariate effect in different factor level…

泊松回归模型中的自相关AI 解读

This paper develops a practical approach to diagnosing the existence of a latent stochastic process in the mean of a Poisson regression model. The asymptotic distribution of standard generalised linear model estimators is derived for the case where an autocorrelated latent process is present. Simple formulae for the effect of autocovariance on standard errors of the regression coefficients are also provided. Methods for adjusting for the severe bias in previously proposed…

等间隔高斯相关观测的精确高斯最大似然与模拟AI 解读

For regularly-spaced observations with the Gaussian autocorrelation function, the finite and infinite autoregressive and moving-average representations can be obtained theoretically. This allows exact Gaussian maximum likelihood to be performed very accurately, and gives a simple exact simulation method.

周期时间序列的一种改进状态空间表示AI 解读

We consider a commonly used two-state model for a cyclical time series and show how a particular specification of its observation vector allows maximum generality of the range of model spectra.

杂论：Fieller 问题的贝叶斯因子AI 解读

This paper considers point null hypothesis testing when the sampling distribution belongs to a particular class, defined in Gleser & Hwang (1987). We discuss the drawbacks of frequentist and likelihood solutions and we show how proper Bayesian analysis encounters relatively similar difficulties. We explore the performance of several noninformative Bayesian approaches to testing, namely asymptotic approximations of Bayes factors and default Bayes factors. We argue that in a…

杂论：二项回归误分类率的极大似然估计AI 解读

Binomial regression is commonly used to construct a binary classification rule from a set of observable covariates. The accuracy of the rule is summarised by empirical type 1 and type 2 misclassification rates as the threshold of the rule varies. However, the empirical misclassification rates are not the maximum likelihood estimators of the true rates if the binomial regression model is assumed true. We give a simple algorithm for the maximum likelihood estimators of the…

利用渐近展开与自助校准推断罕见审计差错AI 解读

The number of items in error in an audit population is usually quite small, whereas the error distribution is typically highly skewed to the right. For applications in statistical auditing, where line-item sampling is appropriate, a new upper confidence limit for the total error amount in an audit population is obtained. Our method involves an empirical Cornish-Fisher expansion in the first stage; in the second stage we employ the bootstrap to calibrate the coverage…

周期函数的非参数估计AI 解读

Motivated by applications to brightness data on periodic variable stars, we study nonparametric methods for estimating both the period and the amplitude function from noisy observations of a periodic function made at irregularly spaced times. It is shown that nonparametric estimators of period converge at parametric rates and attain a semiparametric lower bound which is the same if the shape of the periodic function is unknown as if it were known. Also, first-order…

利用循环对称性刻画无明显标志点的对象AI 解读

Grenander & Miller (1994) describe a model for representing amorphous two-dimensional objects with no obvious landmark. Each object is represented by n vertices around its perimeter, and is described by deforming an n-sided regular polygon using edge transformations. A multivariate normal distribution with a block circulant covariance matrix is used to model these edge transformations. The purpose of this paper is to describe in detail the statistical properties of this…

短论：无高斯成分的 Lévy 过程表示AI 解读

We consider Lévy processes without Gaussian components, known as pure jump processes, with a view to simulating such a process in order to implement full Bayesian nonparametric analyses involving the modelling of continuous time stochastic processes. In particular, from practical and theoretical perspectives, we investigate a recent representation of Wolpert & Ickstadt (1998).

对模型不确定性稳健的投影型三水平主效应设计AI 解读

This paper is concerned with designing experiments under the assumption that an analysis strategy is used that considers interactions in addition to main effects. A criterion which averages an approximation to As-efficiency over lower-dimensional projections of the design is introduced to compare designs. A columnwise design procedure is used to construct three-level designs for six factors in 18 runs. The projection efficiencies of these designs are explored and compared…

这真的是最小二乘估计吗？AI 解读

It is shown that the sum of squares can have several local minima with a positive probability for any intrinsically nonlinear regression with infinite tails. Therefore, the availability of global criteria is crucial. The concept of the local convexity level for the sum of squares in nonlinear regression models is introduced. A general formula for this local convexity level is derived and it is shown that the local convexity level is equal to the minimum of the squared radius…

多元正态协方差矩阵广义线性模型的极大似然估计AI 解读

The positive-definiteness constraint is the most awkward stumbling block in modelling the covariance matrix. Pourahmadi's (1999) unconstrained parameterisation models covariance using covariates in a similar manner to mean modelling in generalised linear models. The new covariance parameters have statistical interpretation as the regression coefficients and logarithms of prediction error variances corresponding to regressing a response on its predecessors. In this paper, the…

近似狄利克雷与贝塔双参数过程层级模型中的 MCMCAI 解读

We present some easy-to-construct random probability measures which approximate the Dirichlet process and an extension which we will call the beta two-parameter process. The nature of these constructions makes it simple to implement Markov chain Monte Carlo algorithms for fitting nonparametric hierarchical models. For the Dirichlet process, we consider a truncation approximation as well as a weak limit approximation based on a mixture of Dirichlet processes. The same type of…

用于贝叶斯计算的广义 Gibbs 抽样与多重网格蒙特卡洛AI 解读

Although Monte Carlo methods have frequently been applied with success, indiscriminate use of Markov chain Monte Carlo leads to unsatisfactory performances in numerous applications. We present a generalised version of the Gibbs sampler that is based on conditional moves along the traces of groups of transformations in the sample space. We explore its connection with the multigrid Monte Carlo method and its use in designing more efficient samplers. The generalised Gibbs…

删失数据下的医疗费用估计AI 解读

Incompleteness of follow-up data is a common problem in estimating medical costs. Native analysis using summary statistics on the collected data can result in severely misleading statistical inference. This paper focuses on the problem of estimating the mean medical cost from a sample of individuals whose medical costs may be right censored. A class of weighted estimators which account appropriately for censoring are introduced. Our estimators are shown to be consistent and…

多种稀有特征流行比例的有效估计AI 解读

We consider a population with multiple traits of interest, where our goal is to estimate the proportions of individuals with the traits. When traits are rare, group testing can improve efficiency. Previous work of Hughes-Oliver & Swallow (1994) developed an adaptive two-stage design for group testing of only one trait. We extend this work to the multi-trait case. We derive the optimum group sizes using compound D-optimum design theory. Estimation is based on maximum…

形状双侧对称性的统计评估AI 解读

SUMMARY This paper formulates the problem of measuring bilateral symmetry of objects analytically for landmark data, and develops various new testing procedures and exploratory data analyses. The development is linked with the fundamental biological problem of measuring directional asymmetry and fluctuating asymmetry. We distinguish two types of symmetry, object symmetry and matching symmetry, and provide tests under assumptions of isotropic landmark variability as well as…

含噪声观测的点过程模型AI 解读

Consider a pair of point processes, X and Y, where X is regarded as a 'true' point process and Y is an imperfect observation of X. For the transformation from X to Y, we consider a number of disturbance mechanisms covering random thinning, displacement, censoring of the displaced points and superposition of extra points. We present the conditional likelihood of Y given X. When both point processes are observed the likelihood may be used for inference about the disturbance…

杂论：结合参数似然与经验似然AI 解读

Imbens & Lancaster (1994) pointed out that census reports can be interpreted as providing nearly exact knowledge of moments of the marginal distribution of economic variables. In this paper we show that empirical likelihood can effectively incorporate auxiliary information like this as long as it can be summarised as unbiased estimating equations. By combining empirical and parametric likelihoods, we show that the combined likelihood can produce valid inferences for the…

多元回归的失拟检验AI 解读

We study lack-of-fit tests based on orthogonal series estimators. A common feature of these tests is that they are functions of score statistics that employ data-driven model dimensions. The criteria used to select the dimension are score-based versions of AIC and BIC. The tests can be applied in a wide variety of settings, including both continuous and discrete data. With two or more covariates, a model sequence, i.e. a path in the alternative models space, has to be…