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平滑样条高斯回归：通过有效近似实现更可扩展的计算AI 解读

Summary Smoothing splines via the penalized least squares method provide versatile and effective nonparametric models for regression with Gaussian responses. The computation of smoothing splines is generally of the order O(n3), n being the sample size, which severely limits its practical applicability. We study more scalable computation of smoothing spline regression via certain low dimensional approximations that are asymptotically as efficient. A simple algorithm is…

脑成像中重复非均匀点模式的空间强度建模AI 解读

Summary Pharmacological experiments in brain microscopy study patterns of cellular activ- ation in response to psychotropic drugs for connected neuroanatomic regions. A typical ex- perimental design produces replicated point patterns having highly complex spatial variability. Modelling this variability hierarchically can enhance the inference for comparing treatments. We propose a semiparametric formulation that combines the robustness of a nonparametric kernel method with…

混合回归模型中的假设检验AI 解读

Summary We establish asymptotic theory for both the maximum likelihood and the maximum modified likelihood estimators in mixture regression models. Moreover, under specific and reasonable conditions, we show that the optimal convergence rate of n−1/4 for estimating the mixing distribution is achievable for both the maximum likelihood and the maximum modified likelihood estimators. We also derive the asymptotic distributions of two log-likelihood ratio test statistics for…

Summary Multivariate failure time data arise when data consist of clusters in which the failure times may be dependent. A popular approach to such data is the marginal proportional hazards model with estimation under the working independence assumption. In some contexts, however, it may be more reasonable to use the marginal additive hazards model. We derive asymptotic properties of the Lin and Ying estimators for the marginal additive hazards model for multivariate failure…

稀疏聚类数据的复合条件似然AI 解读

Summary Sparse clustered data arise in finely stratified genetic and epidemiologic studies and pose at least two challenges to inference. First, it is difficult to model and interpret the full joint probability of dependent discrete data, which limits the utility of full likelihood methods. Second, standard methods for clustered data, such as pairwise likelihood and the generalized estimating function approach, are unsuitable when the data are sparse owing to the presence of…

局部多项式回归与模拟外推AI 解读

Summary The paper introduces a new local polynomial estimator and develops supporting asymptotic theory for nonparametric regression in the presence of covariate measurement error. We address the measurement error with Cook and Stefanski's simulation–extrapolation (SIMEX) algorithm. Our method improves on previous local polynomial estimators for this problem by using a bandwidth selection procedure that addresses SIMEX's particular estimation method and considers higher…

“删除等于替换”在线性混合模型方差分量删除诊断中的应用AI 解读

Summary ‘Delete = replace’ is a powerful and intuitive modelling identity. This paper extends previous work by stating and proving the identity in more general terms and extending its application to deletion diagnostics for estimates of variance components obtained by restricted maximum likelihood estimation for the linear mixed model. We present a new, fast, transparent and approximate computational procedure, arising as a by-product of the fitting process. We illustrate…

检测标记点过程中的标记与位置依赖AI 解读

Summary We introduce two characteristics for stationary and isotropic marked point proces- ses, E(h) and V(h), and describe their use in investigating mark–point interactions. These quantities are functions of the interpoint distance h and denote the conditional expectation and the conditional variance of a mark respectively, given that there is a further point of the process a distance h away. We present tests based on E and V for the hypothesis that the values of the marks…

基于球面小波的空间自适应全球温度场估计AI 解读

Summary The paper considers the problem of estimating the entire temperature field for every location on the globe from scattered surface air temperatures observed by a network of weather-stations. Classical methods such as spherical harmonics and spherical smoothing splines are not efficient in representing data that have inherent multiscale structures. The paper presents an estimation method that can adapt to the multiscale characteristics of the data. The method is based…

时变协变量与依赖删失下的重复事件分析AI 解读

Summary Recurrent events models have had considerable attention recently. The majority of approaches show the consistency of parameter estimates under the assumption that censoring is independent of the recurrent events process of interest conditional on the covariates that are included in the model. We provide an overview of available recurrent events analysis methods and present an inverse probability of censoring weighted estimator for the regression parameters in the…

错误发现率的强控制、保守点估计与同时保守一致性：统一方法AI 解读

Summary The false discovery rate (FDR) is a multiple hypothesis testing quantity that describes the expected proportion of false positive results among all rejected null hypotheses. Benjamini and Hochberg introduced this quantity and proved that a particular step-up p-value method controls the FDR. Storey introduced a point estimate of the FDR for fixed significance regions. The former approach conservatively controls the FDR at a fixed predetermined level, and the latter…

单一方差分量线性混合模型中的似然比检验AI 解读

Summary We consider the problem of testing null hypotheses that include restrictions on the variance component in a linear mixed model with one variance component and we derive the finite sample and asymptotic distribution of the likelihood ratio test and the restricted likelihood ratio test. The spectral representations of the likelihood ratio test and the restricted likelihood ratio test statistics are used as the basis of efficient simulation algorithms of their null…

惩罚三角网模型：二维平滑的全变差正则化AI 解读

Summary Hansen, Kooperberg and Sardy introduced a family of continuous, piecewise linear functions defined over adaptively selected triangulations of the plane as a general approach to statistical modelling of bivariate densities and regression and hazard functions. These triograms enjoy a natural affine equivariance that offers distinct advantages over competing tensor product methods that are more commonly used in statistical applications. Triograms employ basis functions…

改善正态近似的幂变换及其应用AI 解读

Summary Random variables which are positive linear combinations of positive independent random variables can have heavily right-skewed finite sample distributions even though they might be asymptotically normally distributed. We provide a simple method of determining an appropriate power transformation to improve the normal approximation in small samples. Our method contains the Wilson–Hilferty cube root transformation for χ2 random variables as a special case. We also…

有限混合模型中两组分假设的检验AI 解读

Summary We consider a finite mixture model with k components and a kernel distribution from a general one-parameter family. The problem of testing the hypothesis k=2 versusk⩾3 is studied. There has been no general statistical testing procedure for this problem. We propose a modified likelihood ratio statistic where under the null and the alternative hypotheses the estimates of the parameters are obtained from a modified likelihood function. It is shown that estimators of the…

双重自回归模型的估计与平稳性检验AI 解读

Summary The paper considers the double-autoregressive model yt = φyt−1+ɛt with ɛt =ηt√(ω+αyt−12). Consistency and asymptotic normality of the estimated parameters are proved under the condition E ln |φ +√αηt|<0, which includes the cases with |φ|=1 or |φ|>1 as well as E(εt2)=∞. It is well known that all kinds of estimators of φ in these cases are not normal when ɛt are independent and identically distributed. Our result is novel and surprising. Two tests are proposed for…

Summary We suggest two new methods, which are applicable to both deconvolution and regression with errors in explanatory variables, for nonparametric inference. The two approaches involve kernel or orthogonal series methods. They are based on defining a low order approximation to the problem at hand, and proceed by constructing relatively accurate estimators of that quantity rather than attempting to estimate the true target functions consistently. Of course, both techniques…

多路径模型中逗留时间分布的非参数估计AI 解读

Summary We use a multipath (multistate) model to describe data with multiple end points. Statistical inference based on the intermediate end point is challenging because of the problems of nonidentifiability and dependent censoring. We study nonparametric estimation for the path probability and the sojourn time distributions between the states. The methodology proposed can be applied to analyse cure models which account for the competing risk of death. Asymptotic properties…

自由结点多项式样条及其置信区间AI 解读

Summary We construct approximate confidence intervals for a nonparametric regression function, using polynomial splines with free-knot locations. The number of knots is determined by generalized cross-validation. The estimates of knot locations and coefficients are obtained through a non-linear least squares solution that corresponds to the maximum likelihood estimate. Confidence intervals are then constructed based on the asymptotic distribution of the maximum likelihood…

多周期函数解卷积的非参数方法AI 解读

Summary Multiperiodic functions, or functions that can be represented as finite additive mixtures of periodic functions, arise in problems related to stellar radiation. There they represent the overall variation in radiation intensity with time. The individual periodic components generally correspond to different sources of radiation and have intrinsic physical meaning provided that they can be ‘deconvolved’ from the mixture. We suggest a combination of kernel and orthogonal…

利用粒子滤波进行隐马尔可夫模型的在线推断AI 解读

Summary We consider the on-line Bayesian analysis of data by using a hidden Markov model, where inference is tractable conditional on the history of the state of the hidden component. A new particle filter algorithm is introduced and shown to produce promising results when analysing data of this type. The algorithm is similar to the mixture Kalman filter but uses a different resampling algorithm. We prove that this resampling algorithm is computationally efficient and…

因果模型中对百分位不变性随机偏离的处理AI 解读

Summary Consider a clinical trial in which participants are randomized to a single-dose treatment or a placebo control and assume that the adherence level is accurately recorded. If the treatment is effective, then good adherers in the treatment group should do better than poor adherers because they received more drug; the treatment group data follow a dose–response curve. But, good adherers to the placebo often do better than poor adherers, so the observed…

量子统计推断AI 解读

Summary Interest in problems of statistical inference connected to measurements of quantum systems has recently increased substantially, in step with dramatic new developments in experimental techniques for studying small quantum systems. Furthermore, developments in the theory of quantum measurements have brought the basic mathematical framework for the probability calculations much closer to that of classical probability theory. The present paper reviews this field and…

使用广义结构均值模型进行因果推断AI 解读

Summary We estimate cause–effect relationships in empirical research where exposures are not completely controlled, as in observational studies or with patient non-compliance and self-selected treatment switches in randomized clinical trials. Additive and multiplicative structural mean models have proved useful for this but suffer from the classical limitations of linear and log-linear models when accommodating binary data. We propose the generalized structural mean model to…