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线性系统的递归估计AI 解读

The estimation of parameters for a scalar linear system with rational transfer function is considered, the estimates being updated each time a new data point comes to hand. Two well-known algorithms are compared by simulation with a method related to the three-stage algorithm of Hannan & Rissanen (1982); a computation scheme using Givens transformations is proposed which makes the three-stage recursive algorithm economical. A central limit theorem is proved for the…

多元时间序列的降秩模型AI 解读

This paper is concerned with the investigation of reduced rank coefficient models for multiple time series. In particular, autoregressive processes which have a structure to their coefficient matrices similar to that of classical multivariate reduced rank regression are studied in detail. The estimation of parameters and associated asymptotic theory are derived. The exact correspondence between the reduced rank regression procedure for multiple autoregressive processes and…

含变点泊松过程的贝叶斯分析AI 解读

A Bayesian approach to estimation and hypothesis testing for a Poisson process with a change-point is developed, and an example given.

删失数据的估计方程AI 解读

General estimating equations based on independent identically distributed random variables which may be right-censored are considered. The equations which appear to be natural analogues of the uncensored equations require full distributional assumptions, and a distribution-free modification based on the product-limit estimator is suggested. It follows from self-consistency that the resulting estimating functions are simply means obtained from the product-limit estimator. The…

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非参数 t 临界值表的界AI 解读

A simple inequality for bounding the tail probabilities of normalized sums of independent, symmetric random variables is used to produce bounds on the tail probabilities of the usual Student t statistic under the same hypothesis. The relative difference between the resulting t scores and the usual ones is shown to be asymptotically negligible as the sample size increases and the tail probability decreases to zero. As an example, a table of upper 0·025 cutoff bounds is given…

线性模型中两个异常值的检验AI 解读

The detection of two outliers in a linear model is considered. The case of two outliers in the same direction is studied in detail. The first Bonferroni inequality is used to obtain nominal upper percentage points. For a random sample from a normal distribution, the proposed statistic reduces to the well known Murphy's test statistic. Similarly, for two outliers on either direction, our statistic reduces to the studentized range statistic. An approximate relationship between…

调查抽样中最优模型预测量的刻画AI 解读

This paper presents the necessary and sufficient conditions for the optimality of an arbitrary linear predictor of the total of a finite population in survey sampling under a general linear model with a symmetric and positive-definite covariance matrix. Results of the paper extend and unify earlier work on robust estimation in survey sampling under more restrictive conditions.

抽样设计对关联比较的影响AI 解读

A family of measures of association designed to compare the inherent association in two r×c contingency tables was proposed by Altham (1970). Under simple random sampling the measures are asymptotically distributed as noncentral chi-squared random variables. In this paper we show that under complex sampling this distribution changes to a mixture and that ignoring the design may lead to misleading results. We derive measures of the misestimation and measures of association…

双变量泊松分布的偶数点估计AI 解读

Estimation of the parameters in the bivariate Poisson distribution by the methods of maximum likelihood, moments and double zero proportion was considered by Holgate (1964). An alternative estimation procedure, the even points method, is studied, asymptotic efficiencies are examined and comparisons with moment estimators are given.

分数差分时间序列建模AI 解读

Aspects of model building using fractionally differenced autoregressive-moving average processes are discussed. An algorithm for approximate maximum likelihood estimation is outlined and the large-sample distribution of the maximum likelihood estimates is derived. The large-sample distribution of the residual autocorrelations is also derived and a modified portmanteau test statistic is obtained for checking model adequacy.

匹配病例对照研究中的交叉乘积估计量AI 解读

This paper is devoted to a study of the unmatched cross-product estimator of relative risk in a I : M matched case-control study. It is shown that this estimator is consistent for the ‘case-adjusted relative risk’ in rare disease settings. The cross-product estimator has a much wider range of applicability than the classical matched methods, which require a conditionally independent binomial model with a common odds ratio. In general, the methods estimate different…

小样本中的异常值抵抗性AI 解读

This paper presents a new measure of outlier resistance based on Huber's maximum bias. After standardizing by the maximum bias of the median for the same situation, outlier resistance seems to be essentially independent of n and depends on the fraction of contamination. The advantages over alternative measures of resistance involve this relative stability with the sample size, and the ability to measure resistance to a large fraction of outliers. As an example, this method…

单位球面或超球面随机变量的相关系数AI 解读

A coefficient to measure association between two random variables, each distributed on the surface of the unit sphere in p-dimensional space, is proposed, analogous to an existing correlation coefficient for circular data. The sample estimate is studied in detail for the case p = 3, and comparisons are made with other statistics in current use. Some applications are given to studying remanent magnetization in rock samples.

大量秩相关系数的显著性评估AI 解读

A recent Poisson limit theorem for dissociated random variables is shown to apply to rank correlation coefficients which have been calculated from independently distributed vectors. This allows the asymptotic distribution of the largest of the rank correlations to be derived. Simulations show that the asymptotic approximations are close in the tails of the distributions. An example indicates how these approximations can be used to assess the significance of the large…

高阶交叉的渐近方差及其快速白噪声检验应用AI 解读

The rate of decrease in the variance of higher order crossings is obtained for stationary m-dependent Gaussian sequences. This result provides a quick approximation to the variance of the number of axis-crossings of m-dependent processes, and is applied in determining approximate probability limits for the higher order crossings of white noise. The limits are used in testing for white noise in simulated and also real data examples.

Bootstrap 在功率谱密度估计中的应用AI 解读

A shortcoming in the use of autoregressive spectral estimation has been the lack of methods for placing confidence intervals or bands on estimated spectral density. The bootstrap method is applied to obtain nonparametric confidence bands and intervals. It is the aim of this paper to indicate how this can be done and to report on the outcome of some Monte Carlo studies of the properties of the resulting procedures. Some asymptotic theory concerning the properties of the…

使用广义线性模型分析纵向数据AI 解读

This paper proposes an extension of generalized linear models to the analysis of longitudinal data. We introduce a class of estimating equations that give consistent estimates of the regression parameters and of their variance under mild assumptions about the time dependence. The estimating equations are derived without specifying the joint distribution of a subject's observations yet they reduce to the score equations for niultivariate Gaussian outcomes. Asymptotic theory…

时间序列回归模型的高效估计与预测AI 解读

For a time series regression model with correlated residuals we show how to compute efficiently the likelihood, predict future values and interpolate missing values. As an illustration we consider a regression model with autoregressive moving average residuals.

The asymptotic distribution of residual autocorrelations in multivariate autoregressive index models is derived. Generalization of the classical portmanteau statistic for checking model adequacy is discussed.

依赖数据下的优势比推断AI 解读

When data can be presented as a series of k 2×2 tables with cell counts (xi ,ni−xi, yi, mi−yi), it is often assumed that xi and yi are binomially distributed. This paper deals with inference for the common odds ratio Ψ when the binomial assumption is invalid. When k increases, the consistency and asymptotic normality of the Mantel & Haenszel (1959) estimator is derived. The conditional maximum likelihood estimator is shown to be inconsistent and the asymptotic bias is…

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存在相关测量误差的线性结构关系估计AI 解读

Maximum likelihood estimators for model parameters in linear structural relationships having correlated measurement errors are presented. Comparisons between asymptotic mean squared errors of least squares and maximum likelihood estimators of the slope parameter indicate that the least squares estimator is only preferable when the slope parameter is sufficiently small relative to the ratio of error standard deviations; however, unlike structural relationships having…

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