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根据边界穿越点估计两个构造板块的相对旋转AI 解读

Let η1, …, ηs be unknown vectors on the sphere and Ao be an unknown rotation. Suppose that uij are estimates of points lying on the great circle normal to ηi and υik are estimates of points lying on the great circle normal to Aoηi . This article discusses a method to construct a confidence region for Ao . This problem arises in the reconstruction of the relative motion of two tectonic plates on opposing sides of a rift. The boundary on each side is represented by a…

判定时间序列非平稳性的图形方法AI 解读

Integrated processes as models for time series data have proved to be an important component of the highly flexible class of ARIMA(p, d, q) models. Determining the amount of differencing, d, has been a difficult task: too little and the process is not yet second-order stationary; too much and the process is more variable than it need be. It is shown that by introducing the notion of generalized covariances, developed by Matheron (1973) for spatial processes, the amount of…

半参数模型中的极小极大估计AI 解读

The statistical analysis of multidimensional data has been greatly influenced by the widespread use of computer-intensive smoothing techniques. These techniques allow one to look at the dependency of a response on several covariates without actually specifying the exact form of that dependency. Nevertheless, when the response's dependency on some subset of the covariates can be assumed to be, say, linear, common sense dictates incorporating this assumption into the…

非参数回归估计的统一方法AI 解读

There exists a variety of nonparametric regression estimators, with cubic smoothing splines, k-nearest-neighbor (k-NN) estimators, and various types of kernel estimators among the most popular. A class of kernel estimators with local bandwidth depending on the density of the design points is introduced, where the degree of design adaptation may be expressed by a single parameter α in [0, 1]. The adaptation to the design is such that the bandwidth is made larger, to a degree…

高维模型的递归回归及其在生长曲线与重复测量中的应用AI 解读

A fixed-effects formulation of repeated-measures and growth-curve problems usually leads to an unwieldy linear model, so mixed models are widely used for inference that the conditional linear error model could otherwise support with weaker distributional assumptions. Very high-dimensional regressions (not necessarily arising this way) can be fitted by the proposed alternating algorithm, which partitions the design matrix into singly manageable strips and recursively calls a…

利用局部影响进行回归变换诊断AI 解读

Following Box and Cox (1964), the use of transformations in regression analysis is now common; recently there has been emphasis on diagnostic methods for transformation, much of which has involved deletion of data cases. Summaries were given by Cook and Weisberg (1982) and Atkinson (1985). This article obtains diagnostics for the estimated regression parameter of the Box-Cox transformation of the response variable in the linear model. Instead of deleting cases, the more…

一类新的多元分布及其在蒙特卡洛研究中的应用AI 解读

We consider a new class of multivariate probability distributions having representation X = RLY (p), where R is distributed as √χ 2 (p), L is the Choleski factorization of the scaling matrix Σ, and Y (p) represents an arbitrary distribution on the p-dimensional unit hypersphere. If Y (p) is uniform, then X has a multivariate normal distribution with mean 0 and covariance matrix Σ. The use of classical spherical distributions or other nonuniform distributions for Y (p) leads…

引入协变量的随机化回答模型AI 解读

The randomized response technique (RRT) is a survey procedure that requires respondents to decide randomly whether to respond to a sensitive question in its positive or negative form (Warner 1965) or respond to a sensitive question and an unrelated question (Greenberg, Abul-Ela, Simmons, and Horvitz 1969). Although RRT results in larger standard errors than direct questioning or anonymous questionnaires, there is empirical evidence that RRT results in less underreporting of…

三种简单稳健估计量的 Student t 近似AI 解读

Suppose that Tn is an estimator of a location parameter θ, Sn is an estimator of its standard error, and both are based on a random sample of size n. Then, approximations of (Tn – θ)/Sn in terms of Student's t are convenient and useful in confidence-interval estimation and tests of hypotheses of θ. In this article some moment-based t approximations of studentized trimmed means, the trimean, and Gastwirth's estimator are constructed at the normal and several near-normal…

多变量缺失数据的完全随机缺失检验AI 解读

A common concern when faced with multivariate data with missing values is whether the missing data are missing completely at random (MCAR); that is, whether missingness depends on the variables in the data set. One way of assessing this is to compare the means of recorded values of each variable between groups defined by whether other variables in the data set are missing or not. Although informative, this procedure yields potentially many correlated statistics for testing…

密度反卷积的最优收敛速度AI 解读

Suppose that the sum of two independent random variables X and Z is observed, where Z denotes measurement error and has a known distribution, and where the unknown density f of X is to be estimated. One application is the estimation of a prior density for a sequence of location parameters. A second application arises in the errors-in-variables problem for nonlinear and generalized linear models, when one attempts to model the distribution of the true but unobservable…

含缺失数据的不平衡设计中的 Friedman 型统计量与一致多重比较AI 解读

A generalization of the Friedman test using the marginal likelihood principle (Kalbfleisch and Prentice 1973) is presented and its asymptotic power given. It allows use of a variety of score functions and handles ties and unbalanced designs. Some well-known statistics [including the tests of Kruskal and Wallis (1952), Prentice (1979), and Rinaman (1983)] are proven to be special cases, whereas others (e.g., Klotz 1980; Groggel and Skillings 1986; Rai 1987; Skillings and Mack…

随机删失配对数据的组合秩检验AI 解读

Many authors have dealt with the problem of extending ordinary two-sample rank tests to cases where censoring occurs. Albers and Akritas (1987) proposed simple tests for this purpose, based on the idea of making separate rankings for uncensored and censored observations and subsequently combining the resulting two rank statistics. Similarly, some papers appeared that studied the problem of censoring for the paired-data case rather than the two-sample case. This article…

二水平因子设计中抗趋势运行顺序的构造AI 解读

In experimental situations where a factorial design with all factors occurring at two levels is to be run in a time sequence, the usual advice given to the experimenter is that the order of runs should be randomized before the experiment is performed; however, randomization may lead to an undesirable run order. For example, in a factory experiment, there may be a certain learning process that occurs over time as a result of making level changes in the factors being studied,…

摘要暂缺

平滑样条的贝叶斯置信区间AI 解读

The frequency properties of Wahba's Bayesian confidence intervals for smoothing splines are investigated by a large-sample approximation and by a simulation study. When the coverage probabilities for these pointwise confidence intervals are averaged across the observation points, the average coverage probability (ACP) should be close to the nominal level. From a frequency point of view, this agreement occurs because the average posterior variance for the spline is similar to…

针对一阶序列依赖的随机性秩检验AI 解读

Optimal rank-based procedures were derived in Hallin, Ingenbleek, and Puri (1985, 1987) and Hallin and Puri (1988) for some fundamental testing problems arising in time series analysis. The optimality properties of these procedures are of an asymptotic nature, however, whereas much of the attractiveness of rank-based methods lies in their small-sample applicability and robustness features. Accordingly, the objective of this article is twofold: (a) a study of the…

共同趋势检验AI 解读

Cointegrated multiple time series share at least one common trend. Two tests are developed for the number of common stochastic trends (i.e., for the order of cointegration) in a multiple time series with and without drift. Both tests involve the roots of the ordinary least squares coefficient matrix obtained by regressing the series onto its first lag. Critical values for the tests are tabulated, and their power is examined in a Monte Carlo study. Economic time series are…

推广 Logistic 回归的代价AI 解读

Binary-response regression models in which the link function is a family defined by one or more unknown shape parameters are considered. Detailed attention is given to the two single-parameter families proposed by Aranda-Ordaz (1981) that incorporate the logistic, linear, and complementary log-log link functions as special cases. One model is a symmetric family of alternatives to the logistic shape and the second model is an asymmetric family. The increase in variance of…

协变量测量误差回归的近似修正AI 解读

The effect of covariate measurement error on maximum likelihood and maximum quasilikelihood estimates (MLE's or MQLE's) of regression parameters is considered. The naive estimates, obtained by ignoring error, are modified to account for it. The modified estimates can be computed explicitly from the naive ones, and have less bias for small error. They are particularly useful for Berkson error models. Examples illustrate their application to linear and nonlinear regression,…

截断对回归系数可识别性的影响AI 解读

When data are truncated and hence partly unobservable, parameters identifiable under the complete observation may not be identifiable. A class of distributions is characterized, under which regression coefficients are unidentifiable by truncation of a dependent variable in the regression model. In a class of strongly unimodal densities regression coefficients are shown to be unidentifiable only when the underlying distribution is proportional to the exponential distribution…

估计权重对加权最小二乘的影响AI 解读

In weighted least squares, it is typical that the weights are unknown and must be estimated. Most packages provide standard errors assuming that the weights are known. This is fine for sufficiently large sample sizes, but what about for small-to-moderate sample sizes? The investigation of this article into the effect of estimating weights proceeds under the assumption typical in practice—that one has a parametric model for the variance function. In this context, generalized…

线性回归中的贝叶斯变量选择AI 解读

This article is concerned with the selection of subsets of predictor variables in a linear regression model for the prediction of a dependent variable. It is based on a Bayesian approach, intended to be as objective as possible. A probability distribution is first assigned to the dependent variable through the specification of a family of prior distributions for the unknown parameters in the regression model. The method is not fully Bayesian, however, because the ultimate…

重复测量线性混合效应模型的 Newton–Raphson 与 EM 算法AI 解读

We develop an efficient and effective implementation of the Newton—Raphson (NR) algorithm for estimating the parameters in mixed-effects models for repeated-measures data. We formulate the derivatives for both maximum likelihood and restricted maximum likelihood estimation and propose improvements to the algorithm discussed by Jennrich and Schlüchter (1986) to speed convergence and ensure a positive-definite covariance matrix for the random effects at each iteration. We use…