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失效原因缺失的线性变换竞争风险模型：回归系数的半参数估计AI 解读

We consider the problem of estimating the regression coefficients in a competing risks model, where the relationship between the cause-specific hazard for the cause of interest and covariates is described using linear transformation models and when cause of failure is missing at random for a subset of individuals. Using the theory of Robins et al. (1994) for missing data problems and the approach of Chen et al. (2002) for estimating regression coefficients for linear…

曲线样本结构均值的非参数最大似然估计AI 解读

A random sample of curves can be usually thought of as noisy realisations of a compound stochastic process X(t) = Z{W(t)}, where Z(t) produces random amplitude variation and W(t) produces random dynamic or phase variation. In most applications it is more important to estimate the so-called structural mean μ(t) = E{Z(t)} than the crosssectional mean E{X(t)}, but this estimation problem is difficult because the process Z(t) is not directly observable. In this paper we propose…

回归模型残差分析的对称诊断方法AI 解读

Typical alternative hypotheses in the analysis of residuals of a standard regression model are considered, and for each one a Bayesian diagnostic based on a symmetric form of the Kullback–Leibler divergence is determined. The results include an explicit expression for the diagnostic when the alternative hypothesis is that the errors are generated by an unknown distribution function with a Dirichlet process prior. This expression is immediately interpretable, exactly…

紧致黎曼流形上分布拟合优度的 Sobolev 检验AI 解读

Classes of coordinate-invariant omnibus goodness-of-fit tests on compact Riemannian manifolds are proposed. The tests are based on Giné’s Sobolev tests of uniformity. A condition for consistency is given. The tests are illustrated by an example on the rotation group SO(3).

存在工具变量时的非参数推断方法AI 解读

We suggest two nonparametric approaches, based on kernel methods and orthogonal series to estimating regression functions in the presence of instrumental variables. For the first time in this class of problems, we derive optimal convergence rates, and show that they are attained by particular estimators. In the presence of instrumental variables the relation that identifies the regression function also defines an ill-posed inverse problem, the “difficulty” of which depends…

模型与设计联合推断的两阶段框架AI 解读

We establish a mathematical framework that formally validates the two-phase “super-population viewpoint” proposed by Hartley and Sielken [Biometrics 31 (1975) 411–422] by defining a product probability space which includes both the design space and the model space. The methodology we develop combines finite population sampling theory and the classical theory of infinite population sampling to account for the underlying processes that produce the data under a unified…

含固定与非正态潜变量的相关样本分析AI 解读

A general structural equation model is fitted on a panel data set that consists of I correlated samples. The correlated samples could be data from correlated populations or correlated observations from occasions of panel data. We consider cases in which the full pseudo-normal likelihood cannot be used, for example, in highly unbalanced data where the participating individuals do not appear in consecutive years. The model is estimated by a partial likelihood that would be the…

非高斯线性混合模型的部分观测信息与推断AI 解读

In mixed linear models with nonnormal data, the Gaussian Fisher information matrix is called a quasi-information matrix (QUIM). The QUIM plays an important role in evaluating the asymptotic covariance matrix of the estimators of the model parameters, including the variance components. Traditionally, there are two ways to estimate the information matrix: the estimated information matrix and the observed one. Because the analytic form of the QUIM involves parameters other than…

多类型分枝过程的识别AI 解读

We solve the problem of constructing an asymptotic global confidence region for the means and the covariance matrices of the reproduction distributions involved in a supercritical multitype branching process. Our approach is based on a central limit theorem associated with a quadratic law of large numbers performed by the maximum likelihood or the multidimensional Lotka–Nagaev estimator of the reproduction law means. The extension of this approach to the least squares…

时变自回归过程的递归估计AI 解读

This paper focuses on recursive estimation of time varying autoregressive processes in a nonparametric setting. The stability of the model is revisited and uniform results are provided when the time-varying autoregressive parameters belong to appropriate smoothness classes. An adequate normalization for the correction term used in the recursive estimation procedure allows for very mild assumptions on the innovations distributions. The rate of convergence of the pointwise…

线性过程的分布无关拟合优度检验AI 解读

This article proposes a class of goodness-of-fit tests for the autocorrelation function of a time series process, including those exhibiting long-range dependence. Test statistics for composite hypotheses are functionals of a (approximated) martingale transformation of the Bartlett Tp-process with estimated parameters, which converges in distribution to the standard Brownian motion under the null hypothesis. We discuss tests of different natures such as omnibus, directional…

线性移动平均模型对门限移动平均模型的检验AI 解读

This paper investigates the (conditional) quasi-likelihood ratio test for the threshold in MA models. Under the hypothesis of no threshold, it is shown that the test statistic converges weakly to a function of the centred Gaussian process. Under local alternatives, it is shown that this test has nontrivial asymptotic power. The results are based on a new weak convergence of a linear marked empirical process, which is independently of interest. This paper also gives an…

纵向数据的函数型线性回归分析AI 解读

We propose nonparametric methods for functional linear regression which are designed for sparse longitudinal data, where both the predictor and response are functions of a covariate such as time. Predictor and response processes have smooth random trajectories, and the data consist of a small number of noisy repeated measurements made at irregular times for a sample of subjects. In longitudinal studies, the number of repeated measurements per subject is often small and may…

针对分数积分扰动的Durbin–Watson检验有限样本功效AI 解读

We consider the finite-sample power of various tests against serial correlation in the disturbances of a linear regression model when these disturbances follow certain stationary long-memory processes. It emerges that the power depends on the form of the regressor matrix and that, for the Durbin--Watson test and many other tests that can be written as ratios of quadratic forms in the disturbances, the power can drop to zero as the long-memory parameter approaches the…

存在趋势突变时基于残差的块自助法单位根检验AI 解读

In this paper, we build on the "residual-based block bootstrap unit root testing" (RBB) method, proposed by Paparoditis and Politis (2003). We develop an extension of this method to allow for bootstrap unit root testing in a model defined by an augmented Dickey--Fuller (ADF) equation that contains linear combinations of arbitrary dummies as its deterministic part. The main application of such an extension is that it allows for unit root testing in the presence of arbitrary…

GARCH均值模型中的人工回归检验AI 解读

The issue of finite-sample inference in Generalised Autoregressive Conditional Heteroskedasticity (GARCH)-like models has seldom been explored in the theoretical literature, although its potential relevance for practitioners is obvious. In some cases, asymptotic theory may provide a very poor approximation to the actual distribution of the estimators in finite samples. The aim of this paper is to propose the application of the so-called double length regressions (DLR) to…

某些基于广义逆的渐近检验统计量的任意性AI 解读

Under appropriate conditions, some asymptotic test statistics based on generalized inverses (g-inverses) are shown to be arbitrary in the sense that any desired numerical value for a statistic can be obtained by appropriately choosing a g-inverse of an estimator. Examples of statistics based on g-inverses include score-type and Hausman-type statistics. Some versions of these statistics considered in the literature can be viewed as polar cases in the sense that their…

This paper derives second‐order expansions for the distributions of the Whittle and profile plug‐in maximum likelihood estimators of the fractional difference parameter in the ‘Autoregressive Fractionally Integrated Moving Average of order (0, d, 0)’ with unknown mean and variance. Both estimators are shown to be second‐order pivotal. This extends earlier findings of Lieberman and Phillips (2004a, Econometric Theory, 20, 464–84), who derived expansions for the Gaussian…

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行政数据中存在测量误差的二元治疗变量插补AI 解读

Administrative systems—specifically, cancer registries—can be a valuable data source for studies of health care; however, provision of adjuvant chemotherapy or radiation therapy is often underreported in such databases. In a study of colorectal cancer in California, a relatively small physician follow-back survey allowed us to model the probability of underreporting. We then wished to model the relationship of true treatment status to covariates in the full database. We…

多变量观测的线性解混AI 解读

In many fields of science there are multivariate observations that may be assumed to be generated by a (physical) linear mixing process of contributions from different sources. If the compositions of the sources are constant for different observations, then these observations are, up to a random error term, nonnegative linear combinations of a fixed set of so-called “source profiles” that characterize the sources. The goal of linear unmixing is to recover both the source…

存在辅助协变量时的一元非参数回归AI 解读

This article addresses the problem of finding a relationship between the univariate predictor and the response when regression errors, created in part by known auxiliary covariates, are too large for a reliable regression estimation. A typical example is a controlled random design experiment with a large number of covariates, where the statistician is interested in the effect of a particular covariate and this effect is blurred by a large regression noise created by other…

聚类数据广义部分线性模型的稳健估计AI 解读

In this article we consider robust generalized estimating equations for the analysis of semiparametric generalized partial linear models (GPLMs) for longitudinal data or clustered data in general. We approximate the nonparametric function in the GPLM by a regression spline, and use bounded scores and leverage-based weights in the estimating equation to achieve robustness against outliers. We show that the regression spline approach avoids some of the intricacies associated…