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形状的典型成分与主成分AI 解读

Canonical components of shape, discriminant functions of shape and principal components of shape are defined from log shape vectors. Several results relate these components to the corresponding components of log measurement and to a particular size variable referred to as residual log size. The latter variable accounts for the variation which cannot be attributed to shape. Canonical components of shape are determined for Anderson's data for three species of iris, as well as…

非参数回归中若干带宽选择方法的渐近非等价性AI 解读

SUMMARY The bandwidth selection problem in nonparametric kernel regression is considered. Bandwidth selectors based on cross-validation and on Akaike's information criterion, atc, and his finite prediction error, FBE, are among those compared. It is seen that they are not necessarily asymptotically equivalent. Conditions are given under which the equivalence holds and modifications are suggested which make the selectors equivalent.

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…

椭圆总体下协方差矩阵特征根与特征向量检验的渐近分布AI 解读

The asymptotic expansion under an elliptical population is obtained for the probability density function of the sample covariance matrix and for the power functions of the likelihood ratio criteria for testing latent roots and latent vectors appropriate to a normal population.

移动平均过程创新表示的收敛速度AI 解读

SUMMARY 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(l/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,…

扩散过程及其在布朗运动漂移变化检测中的应用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…

方差与协方差分量模型中的变换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.

Logistic 回归影响度量的另一种视角AI 解读

Several measures of influence for logistic regression have been suggested. These measures have been developed for the purpose of identifying observations which are influential relative to the estimation of the regression coefficients vector and the deviance. We propose measures for detecting influence relative to the determination of probabilities and the classification of future observations. The relationships among measures are indicated.

具有时间不变协变量的二元纵向数据分析AI 解读

This paper considers extensions of logistic regression to the case where the binary outcome variable is observed repeatedly for each subject. We propose two working models that lead to consistent estimates of the regression parameters and of their variances under mild assumptions about the time dependence within each subject's data. The efficiency of the proposed estimators is examined. An analysis of stress in mothers with infants is presented to illustrate the proposed…

非线性回归中的残差AI 解读

We employ a quadratic expansion to investigate the behaviour of the ordinary residuals in nonlinear regression. These residuals can produce misleading results when used in diagnostic methods analogous to those for linear regression. We suggest a new type of residual that overcomes many of the potential shortcomings of the ordinary residuals.

对称分布中异常值对位置 L 估计量的影响AI 解读

The effect is studied of an outlier which has the same symmetric distribution as the other observations except for a change in location and a possible increase in scale. We show that the median is the most bias-resistant estimator, in the class of L-statistics with symmetric nonnegative coefficients that add up to one, for a class of distributions which includes the normal, double-exponential and logistic distributions.

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.

列联表数量很大时观测优势比的加权平均AI 解读

When estimating the common odds ratio in a set of 2 × 2 tables, we show that, except in the special case of matched pairs, no weighted average of the observed odds ratios is asymptotically efficient as the number of tables goes to infinity with the numbers of observations per table uniformly bounded.

通过修正经验 logit 降低简单线性逻辑斯蒂回归的偏差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.

经验 logit 的偏差、方差估计、偏度和峰度对加权最小二乘分析的影响AI 解读

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…

估计响应面斜率的二阶与三阶极小极大设计AI 解读

Designs for estimating the slope of a response surface are considered. Minimization of the variance of the estimated slope maximized over all points in the factor space is taken as the optimality criterion. Optimal designs under the minimax criterion are derived for second- and third-order polynomial regression over spherical regions.

使分布对称的幂变换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中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：多元正态且协方差相等的情形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…

比例风险回归的影响函数AI 解读

Influence functions for the regression parameters in the proportional hazards model are presented. It is suggested that empirical influence functions, computed for each observation and each covariate, can be useful in an informal way to identify influential observations. This is illustrated on the Stanford heart transplant data and two other examples.

协方差选择模型的改进似然比统计量AI 解读

The expected value of the likelihood ratio statistic for covariance selection models, when this statistic has a closed form, is derived correct to terms of order n−2, n being the sample size. Then a Bartlett-type correction factor is available for such statistics. By simulation, the practical use of such a correction factor is illustrated, and is compared with an alternative correction factor in a special case. The null density of the corrected statistic is also considered.

基于有效得分的异质性检验AI 解读

For cases in which a parameter may be estimated from several independent data sets, Mather (1935) proposed a heterogeneity test based on the efficient scores for the individual data sets evaluated at the overall maximum likelihood estimator. Following Fisher (1946), a modification of the heterogeneity score test is presented wherein a consistent but inefficient estimator of the parameter of interest is substituted for the overall maximum likelihood estimator. The modified…