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Time Series and System Analysis with Applications.

时间序列与系统分析及其应用

A comprehensive, applications-oriented treatment of time series analysis. Integrates time series theory with methods of systems analysis. Clearly explains the use of ARMA forecasts and includes a complete treatment of the Box/Jenkins approach to modelling. Provides worked examples.

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Modern Elementary Statistics.

现代基础统计学

Preface Chapter 1: Introduction 1.1 The Growth of Modern Statistics 1.2 Sources of Statistical Data 1.3 The Nature of Statistical Data Chapter 2: Summarizing Data: Listing and Grouping 2.1 Listing Numerical Data 2.2 Stem-and-Leaf Displays 2.3 Frequency Distribution 2.4 Graphical Presentations 2.5 Summarizing Two-Variable Data Chapter 3: Summarizing Data: Measures of Location 3.1 Population and Samples 3.2 The Mean 3.3 The Weighted Mean 3.4 The Median 3.5 Other Fractiles 3.6…

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Optimal Design of Interviewer Variance Experiments in Complex Surveys

复杂调查中访员方差实验的最优设计

Fellegi's (1974) improved method for estimating the interviewer component of correlated response variance is extended to l groups of k interviewer assignments for general multistage survey designs. Using a linear models approach suggestive of Hartley and Rao's (1978), the independence of the two estimators of interviewer variance is established and the forms of the variances of the estimators are derived. Then using 1980 census data to compute terms in the estimator…

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Nonparametric Estimation of Lifetime Distributions from a Record of Failures and Follow-ups

基于故障与随访记录的寿命分布非参数估计

This article deals with the estimation problem of the survival function of an industrial product in which the real operating time is different from its actual calendar time. In an observational study of the product, sometimes only the time until failure is observable from the repair requests made by the owner, but nonfailure times themselves are not. The generalized maximum likelihood estimator of the survival function is presented, and its consistency, asymptotic normality,…

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On the Bounded-Influence Regression Estimator of Krasker and Welsch

论 Krasker–Welsch 有界影响回归估计量

Recently, Krasker and Welsch (1982) considered a class of bounded-influence regression estimators. They showed that within this class the so-called Krasker—Welsch estimator is the only solution to a first-order necessary condition for strong optimality, that is, for minimizing, in the sense of positive definiteness, the asymptotic covariance matrix. However, whether any strongly optimal estimator in fact exists remained an open question. In this article, an example is given…

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Small-Sample Comparisons for the Power Divergence Goodness-of-Fit Statistics

幂散度拟合优度统计量的小样本比较

The small-sample properties of the power divergence family of goodness-of-fit statistics (Cressie and Read in press) are examined. The asymptotic χ2 and three alternative approximations are used to obtain appropriate test levels for comparison with the exact level. It is shown that if the χ2 approximation is to be used, then there are many preferable statistics to the log-likelihood ratio G 2 (including Pearson's χ2). Furthermore, exact power comparisons under specific…

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Hypothesis Tests for Markov Process Models Estimated from Aggregate Frequency Data

利用汇总频数数据估计的马尔可夫过程模型检验

When the only data available for estimating the transition probabilities of a Markov chain are state occupation frequencies (rather than interstate transition frequencies), a least squares estimation technique and an accompanying hypothesis-testing methodology are proposed. This general hypothesis-testing procedure is used to develop three tests for adequacy of the simple stationary model. Null hypotheses of a zero-order process, stationarity, and homogeneity are considered.…

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The Order of Differencing in ARIMA Models

ARIMA 模型的差分阶数

A Lagrange multiplier test is derived for testing for the order of differencing in an autoregressive integrated moving average (ARIMA) model. The procedure is illustrated with an example.

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Measures of Conditional Linear Dependence and Feedback between Time Series

时间序列之间条件线性依赖与反馈的度量

Measures of linear dependence and feedback for two multiple time series conditional on a third are defined. The measure of conditional linear dependence is the sum of linear feedback from the first to the second conditional on the third, linear feedback from the second to the first conditional on the third, and instantaneous linear feedback between the first and second series conditional on the third. The measures are non-negative and may be expressed in terms of measures of…

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Global Sensitivity Results for Generalized Least Squares Estimates

广义最小二乘估计的全局敏感性结果

The covariance matrix for the residuals of a regression process is written as the identity matrix plus a matrix V. The matrix V is bounded from above, and the corresponding set of generalized least squares estimates is identified. The extreme estimates in this set are functions of the usual t statistics; in particular the number ((T - k)/8)1/2/|t| measures the influence of reweighting extreme observations, where T - k gives the degrees of freedom, t is the t statistic, and…

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Approximate Inference in Location—Scale Regression Models

位置—尺度回归模型的近似推断

It is shown that χ2 and multivariate t distributions provide good approximations to posterior distributions arising in location-scale regression models. In the case of a linear regression model, Bayesian inferences based on an improper prior have conditional frequency, as well as fiducial/structural interpretation; so the results are also applicable in a non-Bayesian context. Numerical support for the approximations is presented for the case of a Weibull regression model and…

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Cross-Validated Spline Methods for the Estimation of Three-Dimensional Tumor Size Distributions from Observations on Two-Dimensional Cross Sections

由二维截面估计三维肿瘤尺寸分布的交叉验证样条方法

We study the problem of estimating the distribution of the three-dimensional radiuses of a collection of spheres, given measurements of the two-dimensional radiuses of a sample of planar cross sections. This problem arises in the estimation of the tumor size distribution of spherical microtumors induced in mouse livers following injection of a carcinogen. We first convert this problem to a form suitable for the application of cross-validated spline methods for the solution…

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Inference from Nonrandomly Missing Categorical Data: An Example from a Genetic Study on Turner's Syndrome

非随机缺失分类数据的推断:特纳综合征遗传研究示例

The process leading to partial classification with categorical data is sometimes nonrandom. A particular model accounting for incomplete data, which allows the probability of uncertain classification to depend on category identity, is utilized for an analysis of data obtained from a genetic study on Turner's syndrome. Estimates of population proportions are obtained from maximum likelihood. A method for handling nonrandomly missing data arrayed in contingency tables is…

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Linear Discriminant Analysis with Misallocation in Training Samples

训练样本错分下的线性判别分析

Linear discriminant analysis for a two-class case is studied in the presence of misallocation in training samples. A general approach to modeling of misallocation is formulated, and the mean vectors and covariance matrices of the mixture distributions are derived. The asymptotic distribution of the discriminant boundary is obtained, and the asymptotic first two moments of the error rates are given. Certain numerical results for the error rates are presented by considering…

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A Likelihood Ratio Test regarding Two Nested but Oblique Order-Restricted Hypotheses

两个嵌套但斜交的序约束假设的似然比检验

Cadoret, Woolson, and Winokur (1977) considered two theories regarding the genetic makeup of patients suffering from unipolar affective disorder. These two theories imply nested but oblique order restrictions on the parameters of a statistical model. A likelihood ratio test for these two restrictions is studied and found to be dominated by a test that neglects some of the information in the model.

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Least Median of Squares Regression

最小中位数平方回归

Classical least squares regression consists of minimizing the sum of the squared residuals. Many authors have produced more robust versions of this estimator by replacing the square by something else, such as the absolute value. In this article a different approach is introduced in which the sum is replaced by the median of the squared residuals. The resulting estimator can resist the effect of nearly 50% of contamination in the data. In the special case of simple…

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