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图形辅助回归：应用统计的进阶课程AI 解读

1. Variable Distributions 2. Bivariate Regression Analysis 3. Basics of Multiple Regression 4. Regression Criticism 5. Fitting Curves 6. Robust Regressions 7. Logit Regression 8. Principle Components and Factor Analysis

线性回归分析导论AI 解读

Preface. Introduction. Simple Linear Regression. Multiple Linear Regression. Model Adequacy Checking. Transformations and Weighting to Correct Model Inadequacies. Diagnostics for Leverage and Influence. Polynomial Regression Models. Indicator Variables. Variable Selection and Model Building. Multicollinearity. Robust Regression. Introduction to Nonlinear Regression. Generalized Linear Models. Other Topics in the Use of Regression Analysis. Validation of Regression Models.…

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用于验证混合分布分析的信息比率AI 解读

Determining the number of components in a mixture of distributions is an important but difficult problem. This article introduces a procedure called minimum information ratio estimation and validation (MIREV), which is based on a ratio of Fisher information matrices. The smallest eigenvalue of the information ratio matrix is used to determine the number of components. A measure of uncertainty may be obtained using a bootstrap technique. Simulations illustrate the…

复杂抽样调查中仅使用入样概率的条件一致估计量AI 解读

Predictive regression estimators using functions of the probability of selection π i , as covariates are studied as an alternative to classical p-weighting estimators for the finite population mean in complex sample surveys. Variance estimators are developed based on the relationship var(y i | π i ), where y, is the response and π i is the probability of selection. Extensions to cluster sample designs are outlined, and an example is given from the National Educational…

误设回归模型中线性约束预检验的最优检验水平AI 解读

When the choice of estimator for the coefficients in a linear regression model is determined by the outcome of a prior test of the validity of restrictions on the model, it is well known that a minimax (risk) regret criterion leads to the simple rule that the optimal critical value for the preliminary test is approximately two in value, regardless of the degrees of freedom. We show that this result no longer holds in the (likely) event that relevant regressors are excluded…

大自由度多项模型的正态拟合优度检验AI 解读

Goodness-of-fit tests for independent multinomials with parameters to be estimated are usually based on Pearson's X 2 or the likelihood ratio G 2. Both are included in the family of power-divergence statistics SD λ. For increasing sample sizes each SD λ has an asymptotic X 2 distribution, provided that the number of cells remains fixed. We are dealing with an increasing-cells approach, where the number J of independent multinomials increases while the number of classes for…

贝叶斯网络中的参数更新AI 解读

A Bayes network is a directed acyclic graph in which the links are quantified by fixed conditional probabilities and the nodes represent random variables. The primary use of the network is to provide an efficient method for updating conditional probabilities in the graph. We consider the consequences of using the network as the computational device for updating parameter estimates in the dynamic linear model, a discrete time Bayesian model. We show that using the network…

多元失效时间观测的线性回归分析AI 解读

In this article we consider the case that each patient in a longitudinal study may experience two or more distinct failures. The corresponding failure times, which are possible censored, are recorded for each patient. The logarithm of each marginal failure time is assumed to be linearly related to its covariates; however, the distributional form of the error term in the model does not have to be specified in the analysis. Furthermore, no specific structure of dependence…

线性平滑器的频域诊断AI 解读

Frequency domain analysis is used to examine estimates from linear smoothers operating on realizations of random fields over space and/or time. The estimates are expressed in terms of the Fourier transforms of the dependent variable and of the smoother weights. The latter is referred to as the equivalent transfer function. The data do not need to be evenly spaced to perform this analysis. The modulus of the equivalent transfer function characterizes the spectral content of…

非线性回归中的击穿AI 解读

The breakdown point is considered an important measure of the robustness of a linear regression estimator. This article addresses the concept of breakdown in nonlinear regression. Because it is not invariant to nonlinear reparameterization, the usual definition of the breakdown point in linear regression is inadequate for nonlinear regression. The original definition of breakdown due to Hampel is more suitable for nonlinear problems but may indicate breakdown when the fitted…

通过条件化总渔获量估计渔具的体长选择性AI 解读

A conditional maximum likelihood model is used to estimate the size-selectivity of trawls, gillnets, and hooks when the data are obtained by simultaneous fishing with meshes or hooks of different size and/or shape. Size-selectivity is expressed here by the selection curve, r(l), the probability that a fish of length l, if contacting the gear, will be retained (caught). In many selectivity studies r(l) is fitted either by eye, by heuristic means, or by improper application of…

利用样条灵活分析生存数据：乳腺癌预后应用AI 解读

In this article some flexible methods for modeling censored survival data using splines are applied to the problem of modeling the time to recurrence of breast cancer patients. The basic idea is to use fixed knot splines with a fairly modest number of knots to model aspects of the data, and then to use penalized partial likelihood to estimate the parameters of the model. Test statistics are proposed which are analogs of those used in traditional likelihood analysis, and…

自变量缺失的回归分析：综述AI 解读

The literature of regression analysis with missing values of the independent variables is reviewed. Six classes of procedures are distinguished: complete case analysis, available case methods, least squares on imputed data, maximum likelihood, Bayesian methods, and multiple imputation. Methods are compared and illustrated when missing data are confined to one independent variable, and extensions to more general patterns are indicated. Attention is paid to the performance of…

线性出生死亡过程的刻画AI 解读

This research determined the manner of convergence of certain Markov processes to their steady state limiting distributions. This article looks at linear birth and death processes with birth rate at each state determined by the immigration constant a and the natural growth multiplier b; with death rate at each state determined by fixed execution constant c and the natural declination multiplier d. All parameters are nonnegative. There is a reflective barrier at state 0. It…

比率估计量的抗离群值替代方法AI 解读

Many techniques have been suggested to lower the impact of outliers on sample survey estimates. Outliers can be downweighted by winsorization; that is, by replacing extreme data points by a data-dependent or a predetermined value before calculating estimates. Another approach is to reduce the weight of outliers, from the inverse sampling fraction to 1, in the estimation of population characteristics. In this article the problem of estimating the population mean using…

有协变量时相关均值的排序与估计：贝叶斯方法AI 解读

Choosing the largest of several means can be a demanding problem, especially in the presence of a covariate. A hierarchical Bayesian approach to ranking and selection, as well as estimation of related means in the presence of a covariate, is considered. For the multiple slopes model we compute, in addition to the posterior means and standard deviations of the parameters, the posterior probabilities that each mean, at a given value of the covariate, is the largest. The vector…

具有二次方差函数的指数族共轭先验AI 解读

Consider a natural exponential family parameterized by θ. It is well known that the standard conjugate prior on θ is characterized by a condition of posterior linearity for the expectation of the model mean parameter μ. Often, however, this family is not parameterized in terms of θ but rather in terms of a more usual parameter, such at the mean μ. The main question we address is: Under what conditions does a standard conjugate prior on μ induce a linear posterior expectation…

多元ARMA模型中两个变量向量之间的因果性检验AI 解读

In the analysis of economic time series, a question often raised is whether a vector of variables causes another one in the sense of Granger. Most of the literature on this topic is concerned with bivariate relationships or uses finite-order autoregressive specifications. The purpose of this article is to develop a causality analysis in the sense of Granger for general vector autoregressive moving average (ARMA) models. We give a definition of Granger noncausality between…

含加性项的非参数回归模型诊断AI 解读

Recent developments of multivariate smoothing methods provide a rich collection of feasible models for nonparametric multivariate data analysis. Among the most interpretable are models with additive terms. Construction of various models and algorithms for computing the models have been the main concern of the existing literature in this area. Few results are available on the validation of computed fits, and many applications of nonparametric methods unfortunately end up…