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二元Copula模型中的回归AI 解读

We consider a bivariate regression model in which the error structure is arbitrary, except for equality of its marginal distributions. Two simple but inefficient approaches to analysis are (i) to work with the differences between the two components of each response and (ii) to derive working independence estimators as if the two component responses were independent. The former strategy does well if the explanatory variables are balanced over pairs and the correlation between…

基于拟似然的多变点拟合及其 DNA 序列分段应用AI 解读

We consider situations where a step function with a variable number of steps provides an adequate model for a regression relationship, while the variance of the observations depends on their mean. This model provides for discontinuous jumps at changepoints and for constant means and error variances in between changepoints. The basic statistical problem consists of identification of the number of changepoints, their locations and the levels the function assumes in between. We…

非平稳布尔模型的平滑估计及覆盖过程应用AI 解读

Kernel smoothing methods are applied to nonparametric estimation for nonstationary Boolean models. In many applications only exposed tangent points of the models are observable rather than full realisations. Several methods are developed for estimating the distribution of the underlying Boolean model from observation of the exposed tangent points. In particular, estimation methods for coverage processes are studied in detail and applied to neurobiological data.

点过程强度函数中极点的估计AI 解读

Motivated by spatial data on earthquake epicentres, we consider the problem of estimating properties of poles in point-process intensity functions. Our methods are semiparametric, requiring only 'asymptotic' models for the intensity. They produce estimates of the locations and strengths of poles. Strength is expressed in terms of an exponent of regular variation, and is simply related to the correlation dimension of the underlying point process. It is argued that existing…

面板数据半参数模型的统计推断AI 解读

In a longitudinal study, suppose that, for each subject, repeated measurements of the response variable and covariates are collected at a set of distinct, irregularly spaced time points. We consider a semiparametric model which relates the mean of the response variable at each time point proportionally to a function of a time-dependent covariate vector to analyse such panel data. Inference procedures for regression parameters are proposed without involving any nonparametric…

一类双重删失现时状态模型的非参数极大似然估计及伴侣研究应用AI 解读

The California Partners' Study is an ongoing investigation of heterosexual HIV transmission in partners of infected index cases (Padian, et al., 1987; Shiboski & Jewell, 1990). In addition to the HIV-status of the partner at the recruiting time one also observes the initial time of the partnership and a lower bound for the infection time of the index case. Following Jewell, Malani & Vittinghoff (1994) we assume that the infection time of the index case is uniformly…

复杂抽样调查数据的 Cox 比例风险模型拟合AI 解读

Binder (1992) proposed a method of fitting Cox's proportional hazards to models to survey data with complex sampling designs. He defined the regression parameter of interest as the solution to the partial likelihood score equation based on all the data values of the survey population under study, and developed heuristically a procedure to estimate the regression parameter and the corresponding variance. In this paper, we provide a formal justification of Binder's method.…

现状数据的不可识别性与非信息性删失AI 解读

The event times and examination times that produce current status data are typically assumed to be independent. Here, an increasing sequence of nested models is considered for current status data, namely independence models, 'constant sum' models and models for which the conditional probability of the occurrence of the event prior to the examination time, given the examination time, is nondecreasing in the examination time. In the class of constant sum models, the…

概率统计史札记：Pizzetti 于1891年对正态观测分析的贡献AI 解读

Pizzetti's work is considered as bridging the gap between Helmert and Fisher. By means of an orthonormal transformation Pizzetti decomposed the total sum of squares in the linear normal model into its constituent and independent parts, thus providing the theoretical basis for the analysis of variance in the fixed effects model. He calculated a table of the χ2 distribution, which he used for finding probability limits for s/σ. He derived the estimates of the components of…

相关残差下单因子模型的识别AI 解读

A necessary and sufficient condition for the identification of a single-factor model with correlated residuals is derived by studying the zero elements of their concentration matrix. In particular the new condition is expressed in terms of the complementary graph of the residuals. This graphical condition can be simply checked by means of an efficient algorithm. An example is also given showing that sometimes the single-factor model with correlated residuals can be sued to…

向量自回归谱的渐近同时置信带AI 解读

Asymptotic simultaneous confidence bands for all ω in [0, 0.5] are obtained for each scalar function in a spectral density matrix, as well as for the logarithm of the autospectra, the squared coherence and the phase spectra. The bands are illustrated using a simulation study and surface elevation data.

加权比例的非参数估计及粒径测量应用AI 解读

Weighted proportions arise naturally in particle size measurement where one is interested in estimating the proportion of the total volume or surface corresponding to specific particle diameters. The particles are assumed to be spherical, and observations consist of the particle diameters. We consider the weighted proportion as a nonparametric functional of the diameter distribution, and investigate how well this functional can be estimated. It is shown that the commonly…

插补估计量的统计推断AI 解读

We derive an estimator of the asymptotic variance of both single and multiple imputation estimators. We assume a parametric imputation model but allow for non- and semiparametric analysis models. Our variance estimator, in contrast to the estimator proposed by Rubin (1987), is consistent even when the imputation and analysis models are misspecified and incompatible with one another.

超逆 Wishart 矩阵的 Cholesky 分解AI 解读

The canonical parameter of a covariance selection model is the inverse covariance matrix [sum ]-1 whose zero pattern gives the conditional independence structure characterising the model. In this paper we consider the upper triangular matrix Φ obtained by the Cholesky decomposition [sum ]-1 = ΦTΦ. This provides an interesting alternative parameterisation of decomposable models since its upper triangle has the same zero structure as [sum ]-1 and its elements have an…

病例队列研究的加性风险回归AI 解读

The case-cohort design is a common means of reducing cost in large epidemiological cohort studies. Under this design, covariates are measured only on the cases and a subcohort randomly selected from the entire cohort. In this paper, we demonstrate how to use the case-cohort data to estimate the regression parameter of the additive hazards model, which specifies that the conditional hazard function given a set of covariates is the sum of an arbitrary baseline hazard function…

病例队列设计的竞争风险分析AI 解读

The case-cohort design has been put forward as an alternative design in epidemiological follow-up studies which is less expensive than a full-scale cohort study. In this design, all cases are assembled together with a randomly selected sub-cohort which is then used as a comparison group, one advantage being that the same sub-cohort may serve as a comparison group for a number of different case series. However, the fact that all case groups are compared with the same…

回归误差序列独立性的非参数检验AI 解读

A test for serial independence of regression errors is proposed that is consistent in the direction of serial dependence alternatives of first order. The test statistic is a function of a Hoeffding-Blum-Kiefer-Rosenblatt type of empirical process, based on residuals. The resultant statistic converges, surprisingly, to the same limiting distribution as the corresponding statistic based on true errors.

多项模型的残差AI 解读

Ordinary residuals from linear models are useful for diagnostic purposes. Unfortunately residuals from nonlinear models do not share the same useful properties, and Cook & Tsai (1985) introduced so-called projected residuals which overcome some of the problems. After setting up some second-order asymptotics, we briefly discuss various residuals used currently for multinomial models and introduce some new diagnostics including projected residuals. Two examples, from genetics…

通过混合建模开展因子实验的贝叶斯分析AI 解读

A Bayesian analysis for factorial experiments is presented, using finite mixture distributions to model the main effects and interactions. This allows both estimation and an analogue of hypothesis testing in a posterior analysis using a single prior specification. A detailed formulation based on this approach is provided for the case of the two-way model with replication, allowing interactions. Issues in formulating a suitable prior are discussed in detail, and, in the…

回归函数形状的比较AI 解读

Does a regression function follow a specified shape? Do two regression functions have the same shape? How can regression functions be grouped, based on shape? These questions can occur when investigating monotonicity, when counting local maxima or when studying variation in families of curves. One can address these questions by considering the rank correlation coefficient between two functions. This correlation is a generalisation of the rank correlation between two finite…

允许更新样本量的组序贯 t 检验AI 解读

If the maximum sample size for a group sequential t-test is calculated on the basis of a prior estimate of the variance, power at a fixed distance from the null hypothesis is not robust to misspecification of the variance. We propose a new group sequential t-test, based on Stein's (1945) two-stage test, in which we use internal estimates of the variance to update the maximum sample size, and allow early stopping to reject the null hypothesis through a Lan & DeMets (1983)…

杂论：不完整长程依赖数据的统计分析AI 解读

This paper addresses both theoretical and methodological issues related to the prediction of long-memory models with incomplete data. Estimates and forecasts are calculated by means of state space models and the influence of data gaps on the performance of short and long run predictions is investigated. These techniques are illustrated with a statistical analysis of the minimum water levels of the Nile river, a time series exhibiting strong dependency.

非正则情形的概率匹配先验AI 解读

We study probability matching priors in non-regular cases. Both one-parameter and multi-parameter cases are considered. The resulting priors are shown to satisfy certain differential equations. Several examples are discussed. It is observed that the reference prior in the sense of Bernardo is in many cases also probability matching. As a necessary tool for finding such priors, asymptotic expansion of posterior distributions for multi-parameter non-regular cases is also…

杂论：调查抽样中的影响诊断——条件偏差AI 解读

We propose a diagnostic to assess the influence of a unit ui in the sample s, selected from a finite population U={u1,....,uN} using a sampling design D, on θ̂(s) as an estimator of a population parameter θ=θ(Y1,...,YN). We adjust the definition of conditional bias (Muñoz-Picardo et al., 1995), in order to obtain an influence diagnostic in survey sampling. Conditional bias as an influence measure of unit ui (ui∈s) on θ̂(s), depends on Yi and on the sampling design, D. This…