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典型分析在时间序列模型识别中的应用AI 解读

The second-order moment structure of time series models is used to derive a canonical analysis in time series modelling. Consistency properties of certain canonical correlations and the corresponding eigenvectors are shown. Based on these properties, a canonical correlation approach for tentative order determination in building autoregressive-moving average models is proposed. This approach can handle directly nonstationary as well as stationary processes and it also…

It is shown that any test of normality computed from autoregressive residuals has the same limiting null distribution as for the standard case of independent, identically distributed observations with estimated parameters. Some numerical results are given to indicate that this approximation is acceptable for sample size 20 in first- and second-order models. Limited numerical results are also given to explore the effect of incorrectly specifying the order.

用于评估依赖关系的 χ 图AI 解读

This paper presents a graphical method to be used, in conjunction with a scatterplot, to investigate possible association of two variates as manifested in a sample of bivariate measurements. The method is designed so that the plot is approximately horizontal under independence, and under various forms of association it produces corresponding characteristic patterns. Examples given include application to study of regression residuals, dependence of two spatial point…

方差与协方差分量模型的变量变换AI 解读

Variance component models make various independence assumptions and typically assume effects are normally distributed. Here we assume that the data, possibly after suitable transformation, satisfy such a model. An analysis of transformations for balanced variance component models is presented, components of covariance being incorporated in the multivariate case. An analysis of some blood pressure data is discussed.

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抽样检验中的经验贝叶斯估计AI 解读

This paper considers an empirical Bayes approach to estimating the number of defectives in a hypergeometric distribution. It involves application of an empirical Bayes identity which has proved useful in providing simple Bayes estimates for various other models. Data on the reliability of coding the answers to questions from a household survey illustrate how an empirical Bayes estimate can be computed without knowledge of the prior distribution of the number of defectives.

序约束推断中层级概率的近似：简单树序AI 解读

Distribution theory for the likelihood ratio statistics for the comparison of several treatments with a control is discussed. These test statistics account for prior information that the treatments are at least as effective as the control. Their null distributions are mixtures of chi-squared or beta distributions and the mixing coefficients, which are ‘level probabilities’, are intractable for even a moderate number of treatments and unequal weights, which are typically the…

随机过程有限样本估计的基础AI 解读

The Gauss-Markov theorem on least squares for linear models derives its general applicability because it depends on the underlying distribution only through the first two moments. In this paper, a similar theorem is established within the context of stochastic processes. Various problems of finite sample estimation are solved by application of this theorem.

临床试验两期交叉设计中不完整数据的分析AI 解读

A procedure for analysing a simple two-period crossover design is proposed when some observations at the second treatment period are missing. Using all available data, the maximum likelihood estimators of the parameters are obtained and approximate tests proposed under the assumption that the data come from bivariate normal populations. The performances of these tests are compared with those of Grizzle's tests which require complete pairs of observations, using Monte Carlo…

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移动平均过程新息表示的收敛速度AI 解读

A moving average process of order q can be written as a linear combination of the (q+1) most recent innovations. We show that if the moving average polynomial has roots on the unit circle, then the coefficients of the innovations tend to the true moving average coefficients, the difference between the two being O (1/t), where t is the number of observations we consider. The results are extended to mixed autoregressive moving average models and multivariate models.

平稳二维随机过程的一般模型类AI 解读

A parametric family of spectral density-covariance function pairs for stationary spatial processes is introduced. The spectral densities are rational functions of elliptic forms along with factors in the numerator that may be of mixed hyperbolic, parabolic or elliptic form. The resulting covariance functions are linear combinations of modified Bessel functions of the second kind, which have been shown to be the natural basis for two-dimensional covariance functions (Whittle,…

扩散过程及其在检测布朗运动漂移变化中的应用AI 解读

The classical cusum procedure of Page (1954) and a competitor suggested independently by Shiryayev (1963) and Roberts (1966) for detecting a change in distribution are systematically compared, when the change point v = 0 and when v is large. The specific model considered is that of detecting a change in the drift of Brownian motion, for which diffusion theory yields certain explicit results that seem impossible to compute in discrete time. The Shiryayev-Roberts process turns…

排序理论中的解释与估计AI 解读

A simple probabilistic interpretation is given to the expected ranks of k objects ordered by randomly generated observers. The result is shown to yield naturally an estimation procedure in a parametric model for the distribution of permutations. The resulting estimators, in contrast to those suggested by previous authors using approximate likelihood, are consistent for the parameters.

Papadakis 估计量在一维与二维田间试验中的作用AI 解读

Field trials when observations are correlated with those in neighbouring or nearby plots in one dimension are examined. The relationships between maximum likelihood solutions and the well-known Papadakis estimator are clarified and it is shown that the Papadakis estimator is appropriate under one covariance assumption but not others.

关于指定中位数的对称性检验：渐近临界值AI 解读

We examine the asymptotic distribution and give asymptotic critical values for a statistic suggested by Hill & Rao (1977) for testing the symmetry of a continuous distribution about a specified median.

通过修正经验 Logit 降低简单线性逻辑回归的偏差AI 解读

The effect on the bias of Berkson's minimum logit chi-squared estimator of adding a constant to each observed count before forming the empirical logit is examined as a function of the number of design points. It is shown that the ‘best’ constant for reducing bias is essentially a linear function of the reciprocal of the number of design points.

The bias and first four cumulants of the empirical logit transformation of a binomial variate are studied by means of asymptotic expansions and exact computation. The covariance of the empirical logit and its estimated variance is derived. Neither the +½ correction of Haldane (1955) and Anscombe (1956) nor the −½ suggested by Cox (1970) for weighted logit regression is universally effective in reducing bias. Other corrections are considered. The distribution of the empirical…

可分解与仿射可分解的方差平衡设计AI 解读

This paper introduces the notion of affine (μ1, …, μ1)-resolvability and explores the interrelations between: (a) affine (μ1…, μ1)-resolvability, (b) variance-balance, and (c) the relation b = v+t−1, where b is the number of blocks. It is seen that, while (a) and (b) imply (c), and (b) and (c) imply (a), the relation (a) and (c) imply (b) is not in general true. A necessary and sufficient condition under which (a) and (c) imply (b) has been derived and certain nonexistence…

实现分布对称性的幂变换AI 解读

Power transformations for achieving distributional symmetry are discussed. Estimates of the transformation power are based on general measures of symmetry. They are shown to be consistent and asymptotically normal. Use of the skewness coefficient as a measure of symmetry is shown to be optimal in an important special case. The methods are compared to the likelihood methods of Box & Cox (1964) and alternative methods of Hinkley (1975, 1977). The Box-Cox method or a robust…

不等式约束下矩结构分析检验统计量的渐近分布AI 解读

The analysis of moment structural models has become an important tool of investigation in behavioural, educational and economic studies. The chi-squared large-sample test is routinely employed to assess the goodness of fit of the model considered. However, in order to invoke the standard asymptotic distribution theory certain regularity conditions have to be met. Here we consider the case where the population value of the parameter vector is a boundary point of the feasible…

判别分析中的区间估计：多元正态等协方差情形AI 解读

A general approach to discrimination problems is described which emphasizes the viewpoint of individual cases and expresses the uncertainty with which individual decisions are made. It is applied to the particular case of two multivariate normal distributions with a common covariance matrix. An affine transformation, to which the key quantities are invariant, simplifies discussion of the distribution of the estimated log odds ratio and suggests a practically useful plot…

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