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多元广义分位数回归的置信带AI 解读

We focus on the construction of confidence corridors for multivariate nonparametric generalized quantile regression functions. This construction is based on asymptotic results for the maximal deviation between a suitable nonparametric estimator and the true function of interest, which follow after a series of approximation steps including a Bahadur representation, a new strong approximation theorem, and exponential tail inequalities for Gaussian random fields. As a byproduct…

比较回归曲线的最优设计AI 解读

We consider the optimal design problem for a comparison of two regression curves, which is used to establish the similarity between the dose response relationships of two groups. An optimal pair of designs minimizes the width of the confidence band for the difference between the two regression functions. Optimal design theory (equivalence theorems, efficiency bounds) is developed for this non-standard design problem and for some commonly used dose response models optimal…

检测时间序列模型中具有实质意义的变化AI 解读

Summary Most of the literature on change point analysis by means of hypothesis testing considers hypotheses of the form H0:θ1=θ2 versus H1:θ1≠θ2, where θ1 and θ2 denote parameters of the process before and after a change point. The paper takes a different perspective and investigates the null hypotheses of no relevant changes, i.e. H0:‖θ1−θ2‖⩽Δ, where ‖·‖ is an appropriate norm. This formulation of the testing problem is motivated by the fact that in many applications a…

用分位数检验多元经济限制：斯勒茨基矩阵负半定性AI 解读

This paper is concerned with testing a core economic restriction, negative semidefiniteness of the Slutsky matrix. We consider a system of nonseparable structural equations with infinite dimensional unobservables, and employ quantile regression methods because they allow us to utilize the entire distribution of the data. Difficulties arise because the restriction involves several equations, while the quantile is a univariate concept. We establish that we may use quantiles of…

相关误差回归中的最优设计AI 解读

This paper discusses the problem of determining optimal designs for regression models, when the observations are dependent and taken on an interval. A complete solution of this challenging optimal design problem is given for a broad class of regression models and covariance kernels. We propose a class of estimators which are only slightly more complicated than the ordinary least-squares estimators. We then demonstrate that we can design the experiments, such that…

贝叶斯 T 最优模型判别设计AI 解读

The problem of constructing Bayesian optimal discriminating designs for a class of regression models with respect to the $T$-optimality criterion introduced by Atkinson and Fedorov [Biometrika 62 (1975a) 57–70] is considered. It is demonstrated that the discretization of the integral with respect to the prior distribution leads to locally $T$-optimal discriminating design problems with a large number of model comparisons. Current methodology for the numerical construction of…

多元时间序列中多个结构断点的检测AI 解读

We propose a new nonparametric procedure (referred to as MuBreD) for the detection and estimation of multiple structural breaks in the autocovariance function of a multivariate (second-order) piecewise stationary process, which also identifies the components of the series where the breaks occur. MuBreD is based on a comparison of the estimated spectral distribution on different segments of the observed time series and consists of three steps: it starts with a consistent…

局部平稳过程中的渐进变化检测AI 解读

In a wide range of applications, the stochastic properties of the observed time series change over time. The changes often occur gradually rather than abruptly: the properties are (approximately) constant for some time and then slowly start to change. In many cases, it is of interest to locate the time point where the properties start to vary. In contrast to the analysis of abrupt changes, methods for detecting smooth or gradual change points are less developed and often…

关于基于 Copula 的回归的若干评论AI 解读

In a recent article, Noh, El Ghouch, and Bouezmarni proposed a new semiparametric estimate of a regression function with a multivariate predictor, which is based on a specification of the dependence structure between the predictor and the response by means of a parametric copula. This comment investigates the effect which occurs under misspecification of the parametric model. We demonstrate by means of several examples that even for a one or two-dimensional predictor the…

带活性对照的剂量探索研究最优设计AI 解读

Summary Dose finding studies often compare several doses of a new compound with a marketed standard treatment as an active control. In the past, however, research has focused mostly on experimental designs for placebo controlled dose finding studies. To the best of our knowledge, optimal designs for dose finding studies with an active control have not been considered so far. As the statistical analysis for an active controlled dose finding study can be formulated in terms of…

稳健的 T 最优模型判别设计AI 解读

This paper considers the problem of constructing optimal discriminating experimental designs for competing regression models on the basis of the $T$-optimality criterion introduced by Atkinson and Fedorov [Biometrika 62 (1975a) 57–70]. $T$-optimal designs depend on unknown model parameters and it is demonstrated that these designs are sensitive with respect to misspecification. As a solution to this problem we propose a Bayesian and standardized maximin approach to construct…

非线性回归设计的完备类与矩空间主表示AI 解读

In a recent paper Yang and Stufken [Ann. Statist. 40 (2012a) 1665–1685] gave sufficient conditions for complete classes of designs for nonlinear regression models. In this note we demonstrate that there is an alternative way to validate this result. Our main argument utilizes the fact that boundary points of moment spaces generated by Chebyshev systems possess unique representations.

多个竞争回归模型的最优判别设计AI 解读

The problem of constructing optimal discriminating designs for a class of regression models is considered. We investigate a version of the $T_{p}$-optimality criterion as introduced by Atkinson and Fedorov [Biometrika 62 (1975a) 289–303]. The numerical construction of optimal designs is very hard and challenging, if the number of pairwise comparisons is larger than 2. It is demonstrated that optimal designs with respect to this type of criteria can be obtained by solving…

分位数回归模型的最优设计AI 解读

Despite their importance, optimal designs for quantile regression models have not been developed so far. In this article, we investigate the D-optimal design problem for nonlinear quantile regression analysis. We provide a necessary condition to check the optimality of a given design and use it to determine bounds for the number of support points of locally D-optimal designs. The results are illustrated, determining locally, Bayesian and standardized maximin D-optimal…

局部平稳过程的平稳性度量及检验应用AI 解读

In this article we investigate the problem of measuring deviations from stationarity in locally stationary time series. Our approach is based on a direct estimate of the L2-distance between the spectral density of the locally stationary process and its best approximation by a spectral density of a stationary process. An explicit expression of the minimal distance is derived, which depends only on integrals of the spectral density of the locally stationary process and its…

Pickands 依赖函数的新估计量与极值依赖检验AI 解读

We propose a new class of estimators for Pickands dependence function which is based on the concept of minimum distance estimation. An explicit integral representation of the function A*(t), which minimizes a weighted L2-distance between the logarithm of the copula C(y1−t, yt) and functions of the form A(t)log(y) is derived. If the unknown copula is an extreme-value copula, the function A*(t) coincides with Pickands dependence function. Moreover, even if this is not the…

局部最优设计中的 de la Garza 现象札记AI 解读

The celebrated de la Garza phenomenon states that for a polynomial regression model of degree p−1 any optimal design can be based on at most p design points. In a remarkable paper, Yang [Ann. Statist. 38 (2010) 2499–2524] showed that this phenomenon exists in many locally optimal design problems for nonlinear models. In the present note, we present a different view point on these findings using results about moment theory and Chebyshev systems. In particular, we show that…

相关观测回归模型最优设计的几何刻画AI 解读

Summary We consider the problem of optimal design of experiments for random-effects models, especially population models, where a small number of correlated observations can be taken on each individual, whereas the observations corresponding to different individuals are assumed to be uncorrelated. We focus on c-optimal design problems and show that the classical equivalence theorem and the famous geometric characterization of Elfving from the case of uncorrelated data can be…

相关观测线性模型最优设计的新方法AI 解读

We consider the problem of designing experiments for regression in the presence of correlated observations with the location model as the main example. For a fixed correlation structure approximate optimal designs are determined explicitly, and it is demonstrated that under the model assumptions made by Bickel and Herzberg (1979) for the determination of asymptotic optimal design, the designs derived in this article converge weakly to the measures obtained by these authors.…

异方差回归中 c 最优设计的几何刻画AI 解读

We consider the common nonlinear regression model where the variance, as well as the mean, is a parametric function of the explanatory variables. The c-optimal design problem is investigated in the case when the parameters of both the mean and the variance function are of interest. A geometric characterization of c-optimal designs in this context is presented, which generalizes the classical result of Elfving [Ann. Math. Statist. 23 (1952) 255–262] for c-optimal designs. As…

多元时间序列频域检验的自助法：谱密度比较应用AI 解读

Summary We propose a general bootstrap procedure to approximate the null distribution of non-parametric frequency domain tests about the spectral density matrix of a multivariate time series. Under a set of easy-to-verify conditions, we establish asymptotic validity of the bootstrap procedure proposed. We apply a version of this procedure together with a new statistic to test the hypothesis that the spectral densities of not necessarily independent time series are equal. The…

用于模型判别的最优设计AI 解读

We consider the problem of constructing optimal designs for model discrimination between competing regression models. Various new properties of optimal designs with respect to the popular T-optimality criterion are derived, which in many circumstances allow an explicit determination of T-optimal designs. It is also demonstrated, that in nested linear models the number of support points of T-optimal designs is usually too small to estimate all parameters in the extended…

剂量探索研究的最优设计AI 解读

Understanding and properly characterizing the dose–response relationship is a fundamental step in the investigation of a new compound, be it a herbicide or fertilizer, a molecular entity, an environmental toxin, or an industrial chemical. In this article we investigate the problem of deriving efficient designs for the estimation of target doses in the context of clinical dose finding. We propose methods to determine the appropriate number and actual levels of the doses to be…

不交叉分位数曲线的非参数估计AI 解读

Summary Since the introduction by Koenker and Bassett, quantile regression has become increasingly important in many applications. However, many non-parametric conditional quantile estimates yield crossing quantile curves (calculated for various p ∈ (0, 1)). We propose a new non-parametric estimate of conditional quantiles that avoids this problem. The method uses an initial estimate of the conditional distribution function in the first step and solves the problem of…