共查询到20条相似文献,搜索用时 78 毫秒
1.
Erhard Kremer 《Journal of multivariate analysis》1981,11(4):532-543
In previous papers [Approximate and local Bahadur efficiency of linear rank tests in the two-sample problem, Ann. Statist.7, 1246–1255, 1979; Local comparison of linear rank tests in the Bahadur sense, Metrika, 1979] the author developed for linear rank tests of the one-sample symmetry and the k-sample problem (k ≥ 2) a theory of local comparison, based on the concept of Bahadur efficiency. In the present article this theory is carried over to rank tests of the independence problem. 相似文献
2.
Madan L. Puri 《Annals of the Institute of Statistical Mathematics》1965,17(1):323-330
Summary In their paper [1], Ansari and Bradley discussed a two-sample rank test for dispersions and suggested the desirability of
extending their results to the problem of several samples. In this paper, besides generalizing their results, we provide a
few additional non-parametric tests, which include, among others, the multi-sample analogues of the two-sample normal scores
test of dispersion and the tests considered by Mood [6], Klotz [4], and Siegel and Tukey [10]. The asymptotic distributions
of the proposed test statistics are derived by an application of the author’s theorem [7]. The asymptotic efficiencies of
these tests relative to one another and theF test ([9], pp. 83–87) are computed in the standard fashion along the lines of the author’s paper [7].
The work represents results obtained at the Courant Institute of Mathematical Sciences, New York University, under Sloan Foundation
Grant for statistics and under U.S. Navy Contract Nonr-285 (38). 相似文献
3.
A class of affine-invariant test statistics, including a sign test and a related family of signed-rank tests, is proposed for randomized complete block designs with one observation per treatment. This class is obtained by using the transformation-retransformation approach of Chakraborty, Chaudhuri and Oja along with a directional transformation due to Tyler. Under the minimal assumption of directional symmetry of the underlying distribution, the null asymptotic distribution of the sign test statistic is shown to be chi-square with p-1 degrees of freedom. The same null distribution is also proved for the family of signed-rank statistics under the assumption of symmetry of the underlying distribution. The Pitman asymptotic relative efficiencies of the tests, relative to Hotelling-Hsu's T2 are established. Several score functions are discussed including a simple linear score function and the optimal normal score function. The test based on the linear score function is compared to the other members of this family and other statistics in the literature through efficiency calculations and Monte Carlo simulations. This statistic has an excellent performance over a wide range of distributions and for small as well as large dimensions. 相似文献
4.
Michael G. Akritas Richard A. Johnson 《Annals of the Institute of Statistical Mathematics》1992,44(4):745-753
Rank test statistics for the two-sample problem are based on the sum of the rank scores from either sample. However, a critical difference can occur when approximate scores are used since the sum of the rank scores from sample 1 is not equal to minus the sum of the rank scores from sample 2. By centering and scaling as described in Hajek and Sidak (1967, Theory of Rank Tests, Academic Press, New York) for the uncensored data case the statistics computed from each sample become identical. However such symmetrized approximate scores rank statistics have not been proposed in the censored data case. We propose a statistic that treats the two approximate scores rank statistics in a symmetric manner. Under equal censoring distributions the symmetric rank tests are efficient when the score function corresponds to the underlying model distribution. For unequal censoring distributions we derive a useable expression for the asymptotic variance of our symmetric rank statistics. 相似文献
5.
A local breakdown property of robust tests in linear regression 总被引:1,自引:0,他引:1
Xuming He 《Journal of multivariate analysis》1991,38(2)
The breakdown slope, as a useful summary measure of local stability for estimators and test statistics, has been studied recently by He, Simpson, and Protnoy (1990, J. Amer. Statist. Assoc., 85). It is shown here that all regression estimates based on residuals alone in linear models have zero breakdown slopes in contamination neighborhoods, even though they can have breakdown points as high as one-half. The breakdown functions of tests based on the S-estimation are investigated. It is also shown that the Generalized M-estimators can have better local breakdown robustness. One way to obtain regression estimators with desirable local and global breakdown properties is discussed. 相似文献
6.
7.
David M. Mason 《Journal of multivariate analysis》1984,14(2):181-200
One and two sample rank statistics are shown in general to be more efficient in the Bahadur sense than their sequential rank statistic analogues as defined by Mason (1981, Ann. Statist.9 424–436) and Lombard (1981, South African Statist. J.15 129–152), even though the two families of statistics (those based on full ranks and those based on sequential ranks) have the same Pitman efficiency against local alternatives. In the process, general results on large deviation probabilities and laws of large numbers for statistics based on sequential ranks are obtained. 相似文献
8.
Willem Albers 《Annals of the Institute of Statistical Mathematics》1992,44(2):335-356
Stein's two-stage procedure produces a t-test which can realize a prescribed power against a given alternative, regardless of the unknown variance of the underlying normal distribution. This is achieved by determining the size of a second sample on the basis of a variance estimate derived from the first sample. In the paper we introduce a nonparametric competitor of this classical procedure by replacing the t-test by a rank test. For rank tests, the most precise information available are asymptotic expansions for their power to order n
-1, where n is the sample size. Using results on combinations of rank tests for sub-samples, we obtain the same level of precision for the two-stage case. In this way we can determine the size of the additional sample to the natural order and moreover compare the nonparametric and the classical procedure in terms of expected additional numbers of observations required. 相似文献
9.
V. E. Bening 《Journal of Mathematical Sciences》1996,78(1):18-27
In this paper an analogue of the formulas [D. M. Chibisov,Teor. Veroyatn. Primen.,30, 269–288 (1985);Izv. Akad. Nauk UzSSR,6, 23–30 (1982)] for the difference between the power of a given asymptotically efficient test and that of the most powerful
test is justified for one-sample L-and R-tests, i.e., tests based on linear combinations of order statistics and linear rank
statistics. This formula directly yields the Hodges-Lehmann deficiency of corresponding tests. A general theorem is stated
which is applied to L-and R-tests. The explicit expressions given by this formula for L- and R-tests are also presented. The
expression related to R-tests agrees with the one obtained in [W. Albers, P. J. Bickel, and W. R. Van Zwet,Ann. Statist.,4, 108–156 (1976);6, 1170–1171 (1978)]. We present here a nontechnical (heuristic) proof of these results.
Supported by the Russian Foundation for Fundamental Research (grant No. 93-011-1446).
Proceedings of the XVI Seminar on Stability Problems for Stochastic Models, Part II, Eger, Hungary, 1994. 相似文献
10.
Taka-Aki Shiraishi 《Annals of the Institute of Statistical Mathematics》1985,37(1):519-527
Summary Local powers of two- andk-sample rank tests under alternatives of contaminated distributions are investigated. It is shown that the rank tests based
on normal scores and Wilcoxon scores are superior to thet-test or theF-test for many choices of alternatives of contaminated distributions and that the values of the asymptotic relative efficiency
of the rank test based on Wilcoxon scores with respect to the normal scores are about one in all the investigated cases. 相似文献
11.
The limiting (as the significance level approaches 0) Pitman efficiency of a new “regression-based” rank test of independence to Kendall's tau and Spearman's rho is derived. The result is based on a version of [17], Ann. Statist.4 1003–1011) on coincidence of the limiting Pitman efficiency and the local (as the alternative approaches the hypothesis) approximate Bahadur efficiency. [7], Trans. Amer. Math. Soc.87, 173–186) result is applied to verify the main assumption of Wieand's paper. This approach is shown to be useful in some other situations, also. 相似文献
12.
M. A. Arcones 《Mathematical Methods of Statistics》2007,16(3):177-201
We present two tests for multivariate normality. The presented tests are based on the Lévy characterization of the normal
distribution and on the BHEP tests. The tests are affine invariant and consistent. We obtain the asymptotic null distribution
of the test statistics using some results about generalized one-sample U-statistics, which are of independent interest.
相似文献
13.
For continuous observations from time-sequential studies, suitable Cramér-von Mises and Kolmogorov-Smirnov types of (nonparametric) statistics (based on linear rank statistics) for testing hypotheses on some multiple-regression models are proposed and studied. The asymptotic theory of these tests is provided for both the null and (local) alternative hypotheses situations and is based on the weak convergence of suitable rank order processes (on the D[0, 1] space) to certain functions of Brownian motions. Bahadur efficiency results are also presented. Empirical values of the percentile points of the null distributions of the proposed test statistics, obtained through simulation studies, are also provided. 相似文献
14.
Recent results show that densities of convolutions can be estimated by local U-statistics at the root-n rate in various norms. Motivated by this and the fact that convolutions of normal densities are normal, we introduce new tests for normality which use as test statistics weighted L1-distances between the standard normal density and local U-statistics based on standardized observations. We show that such test statistics converge at the root-n rate and determine their limit distributions as functionals of Gaussian processes. We also address a choice of bandwidth. Simulations show that our tests are competitive with other tests of normality. 相似文献
15.
Let A, B be associative rings with identity, and (S, ≤) a strictly totally ordered commutative monoid which is also artinian. For any bimodule AMB , we construct a bimodule A[[S]]M[S]B[[S]] and prove that AMB defines a quasi-duality if and only if the bimodule A[[S]]M[S]B[[S]] defines a quasi-duality. As a corollary, it is shown that if a ring A has a quasi-duality then the ring A[[S]] of generalized power series over A has a quasi-duality. 相似文献
16.
Kaoru Fueda 《Annals of the Institute of Statistical Mathematics》1996,48(2):337-347
Critchlow (1992, J. Statist. Plann. Inference, 32, 325–346) proposed a method of a unified construction of a class of rank tests. In this paper, we introduce a convex sum distance and prove the limiting normality of the test statistics for the two-sample problem derived by his method. 相似文献
17.
B. M. Bennett 《Annals of the Institute of Statistical Mathematics》1965,17(1):55-61
Summary As a test for the hypothesis of equality of means in a sample ofn matched pairs of observations from a single bivariate population in(x, y), Wilcoxon ([4], [5]) proposed a signed rank sum testU involving the differencesz=x\t-y. Tables of valuesUs have been provided forn of 50 or less and four significance levelsε. The following paper considers some generalizations of the Wilcoxon test for the case of matched bivariate or trivariate populations.
These tests utilize certain properties of thep-variate normal distribution when integrated over certain regions for the cases:p=2,3. 相似文献
18.
Vilijandas Bagdonavičius Ruta Levuliene Mikhail Nikulin 《Comptes Rendus Mathematique》2004,339(6):425-428
We propose two tests to test the hypothesis of the equality of two survival functions against the alternative of crossing of these functions for right-censured data. The asymptotic laws of test statistics are given. The powers of the tests are calculated. To cite this article: V. Bagdonavi?ius et al., C. R. Acad. Sci. Paris, Ser. I 339 (2004). 相似文献
19.
Dumbgen L. 《Journal of multivariate analysis》1995,52(2)
A particular class of tests for the principal components of a scatter matrix Σ is proposed. In the simplest case one wants to test whether a given vector is an eigenvector of Σ corresponding to its largest eigenvalue. The test statistics are likelihood ratio statistics for the classical Wishart model, and critical values are obtained parametrically as well as nonparametrically without making any assumptions on the eigenvalues of Σ. Still, the tests have asymptotic properties similar to those of classical procedures and are asymptotically admissible and optimal in some sense. 相似文献
20.
P.M Robinson 《Journal of multivariate analysis》1973,3(2):141-160
Canonical correlation analysis is shown to be equivalent to the problem of estimating a linear regression matrix, B0, of less than full rank. After reparameterizing B0 some estimates of the new parameters, obtained by solving an eigenvalue problem and closely related to canonical correlations and vectors, are found to be consistent and efficient when the residuals are mutually independent. When the residuals are generated by an autocorrelated, stationary time series these estimates are still consistent and obey a central limit theorem, but they are no longer efficient. Alternative, more general estimates are suggested which are efficient in the presence of serial correlation. Asymptotic theory and iterative computational procedures for these estimates are given. A likelihoodratio test for the rank of B0 is seen to be an extension of a familiar test for canonical correlations. 相似文献