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平滑秩估计量的标准误与协方差矩阵AI 解读

A ‘pseudo-Bayesian’ interpretation of standard errors yields a natural induced smoothing of statistical estimating functions. When applied to rank estimation, the lack of smoothness which prevents standard error estimation is remedied. Efficiency and robustness are preserved, while the smoothed estimation has excellent computational properties. In particular, convergence of the iterative equation for standard error is fast, and standard error calculation becomes…

平滑中位数与自助法AI 解读

Even in one dimension the sample median exhibits very poor performance when used in conjunction with the bootstrap. For example, both the percentile‐t bootstrap and the calibrated percentile method fail to give second‐order accuracy when applied to the median. The situation is generally similar for other rank‐based methods, particularly in more than one dimension. Some of these problems can be overcome by smoothing, but that usually requires explicit choice of the smoothing…

正态得分、正态概率图与正态性检验AI 解读

In this article we develop new plotting positions for normal plots. The use of the plots usually centers on detecting irregular tail behavior or outliers. Along with the normal plot, we develop tests for various departures from normality, especially for skewness and heavy tails. The tests can be considered as components of a Shapiro-Wilk type test that has been decomposed into different sources of nonnormality. Convergence to the limiting distributions is slow, so finite…

具有回降影响函数的正则秩估计AI 解读

A study is made of some unusual location estimates first proposed in 1977 by J. S. Maritz, M. Wu, and R. G. Staudte, Jr., who established some strong robustness properties of these estimates, such as redescending influence functions and, in some cases, full efficiency at the Cauchy model. It is further shown here that the estimates, called M-W-S estimates, are derivable from a rank-based scheme founded on convex functions and hence are regular, are unique, and have…

正则的回降秩估计AI 解读

A study is made of some unusual location estimates first proposed in 1977 by J. S. Maritz, M. Wu, and R. G. Staudte, Jr., who established some strong robustness properties of these estimates, such as redescending influence functions and, in some cases, full efficiency at the Cauchy model. It is further shown here that the estimates, called M-W-S estimates, are derivable from a rank-based scheme founded on convex functions and hence are regular, are unique, and have…

圆周拟合优度检验的分组修正AI 解读

SUMMARY Simple corrections are outlined for the application to grouped seasonal data of Watson's and Maag's tests. These tests are circular or seasonal analogues of one-sample and k- (≥2) sample tests, of Cramér–von Mises type, and have several natural advantages over their competitors. The provision of simple grouping corrections may enhance the use of these tests, which otherwise have very good features. The corresponding grouping corrections are also presented for…

若干二元符号检验与中位数的性质AI 解读

Brown and Hettmansperger proposed an affine invariant bivariate analogue of the sign test, the OS test, based on the generalized median of Oja. On the other hand, Oja and Nyblom introduced a family of locally most powerful affine invariant sign tests. In the case of elliptic distributions, the locally most powerful Blumen's test and the OS test are shown to be asymptotically equivalent. Formulas for calculating asymptotic relative efficiencies of the OS test and the Oja…

多参数线性化定理AI 解读

SUMMARY A linearization theorem represents an estimating equation for an unknown parameter as approximately linear in the neighbourhood of the true parameter point, and can provide a convenient approach to asymptotic theory. A multiparameter version of a standard linearization theorem is proved, and applied to two examples: M-estimates in multiple regression, and the spherical median.

空间中位数的统计用途AI 解读

SUMMARY The spatial median, called the mediancentre in an earlier paper by J. C. Gower, is defined as the bivariate location measure to minimize the sum of absolute distances to observations. its asymptotic efficiency relative to the sample mean vector with normal data is shown to exceed the usual univariate 2/π = 0.637. its estimating equations have an angular aspect and are used to develop “angle tests”, which are analogues of sign tests in one dimension.

正稳定分布的高效率估计AI 解读

A moment method based on the sample averages of X -t and X -2t (with suitably chosen t) is suggested for estimating the index a and scale parameter c 1/α of the positive stable distribution with Laplace transform E exp(-ΛX) = exp(-cΛα). The corresponding Cramér-Rao lower bounds are computed by using a new and simple Fourier technique, which is based on an idea of Jarrett. It is found that the asymptotic efficiencies of the proposed estimators exceed .97 for all values of α…

对称分位数平均及相关估计量AI 解读

The average of two complementary order statistics is termed a symmetric quantile average. In addition to having quite good efficiency, robustness and computational properties, exact nonparametric confidence intervals for location can be derived from it. A related type of estimator called a combined quantile average is introduced; it is slightly more difficult to compute than the symmetric quantile average, but can have better efficiency and robustness properties. In fact the…

对称分位数平均及相关估计量AI 解读

The average of two complementary order statistics is termed a symmetric quantile average. In addition to having quite good efficiency, robustness and computational properties, exact nonparametric confidence intervals for location can be derived from it. A related type of estimator called a combined quantile average is introduced; it is slightly more difficult to compute than the symmetric quantile average, but can have better efficiency and robustness properties. In fact the…

缩减 U 统计量与 Hodges–Lehmann 估计量AI 解读

A reduced $U$-statistic (of order 2) is defined as the sum of terms $f(X_i, X_j),$ where $f$ is a symmetric function, $(X_1, \cdots, X_N)$ are independent and identically distributed (i.i.d.) random variables (rv's), and $(i,j)$ are drawn from a restricted, though balanced, set of pairs. (A $U$-statistic corresponds to summation over all $(i, j)$ pairs.) A limit normal distribution is found for the reduced $U$-statistic, and it follows that estimates based on reduced $U$-stat…

利用残差的异常值简便检验AI 解读

The differences between the numbers of positive and negative residuals in each row and column of a two-way analysis of variance are used to define an approximate chi-squared statistic which can be used to test for the presence of outlying observations. The chi-squared approximation rests on a Central Limit Theorem for the number of positive residuals in the two-way table. Extensions to other classifications are also discussed.

利用残差快速检验异常观测AI 解读

The differences between the numbers of positive and negative residuals in each row and column of a two-way analysis of variance are used to define an approximate chi-squared statistic which can be used to test for the presence of outlying observations. The chi-squared approximation rests on a Central Limit Theorem for the number of positive residuals in the two-way table. Extensions to other classifications are also discussed.