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Suppose that the maximum of a random sample from a distribution F(x) may be obtained in each of k equally spaced observation periods. This paper proposes a test to determine the domain of attraction of F(x), and investigates the properties when the sample size is very large and perhaps unknown and k is fixed and small. The test statistic is a function of the spacings between the order statistics based on the sequence of maxima and is suggested by reference to one studied previously when inference was based on the largest k observations of a random sample. A Monte Carlo study shows that the proposed test is more powerful than its main competitor. The test is illustrated by two examples. 相似文献
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Patrick J. Farrell Sarjinder Singh 《Australian & New Zealand Journal of Statistics》2005,47(3):375-383
In survey sampling, interest often centres on inference for the population total using information about an auxiliary variable. The variance of the estimator used plays a key role in such inference. This study develops a new set of higher‐order constraints for the calibration of estimators of variance for various estimators of the population total. The proposed strategy requires an appropriate model for describing the relationship between the response and auxiliary variable, and the variance of the auxiliary variable. It is therefore referred to as a model‐assisted approach. Several new estimators of variance, including the higher‐order calibration estimators of the variance of the ratio and regression estimators suggested by Singh, Horn & Yu and Sitter & Wu are special cases of the proposed technique. The paper presents and discusses the results of an empirical study to compare the performance of the proposed estimators and existing counterparts. 相似文献
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This paper asks whether or not the efficient L-estimator of scale corresponding to the least informative distribution in ε-contamination and Kol-mogorov neighbourhoods of certain distributions possesses the saddlepoint property. This is of interest since the saddlepoint property implies the mini-max property, namely, that the supremum of the relative asymptotic variance of an L-estimator is minimized by the efficient estimator corresponding to that member of the distributional class with minimum Fisher information for scale. Our findings are negative in all cases investigated. 相似文献
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Murray Hannah Niels Becker Jacob Rich Charles Castle 《Australian & New Zealand Journal of Statistics》1989,31(2):253-267
For the planning of community tuberculosis, prophylaxis one must know the prevalence of tuberculosis (TB) infection as a function of response to the Mantoux intradermal tuberculin test; the standard test for indicating Mycobacterium TB infection. The skin induration size used to select individuals for prophylaxis must be chosen carefully, in view of the costs associated with carrying out and supervising such prophylaxis. The Mantoux test was used to obtain measurements on adolescents in metropolitan Victoria and on a small sample of adolescents with clinical TB. These data are employed to obtain estimates and to construct upper confidence bounds for the conditional probability of TB infection, given the level of Mantoux response. Two conservative methods are presented; one is ‘nonparametric’, the other ‘semiparametric’. The analyses indicate that for responses up to and including 13 mm, the probability of TB infection is less than.07 with ninety-five percent confidence. 相似文献
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《统计学通讯:理论与方法》2013,42(8-9):1903-1920
This paper was motivated by the problem of the determination of the change points of the failure rate of a mixture of two gamma distributions. For certain values of the parameters the existing methods are not applicable since, in this case, there are two turning points of the failure rate. Thus, we extend the results to models having two or more turning points of the failure rates. The extended procedure helps us to identify failure rates of more complex forms. Finally, the mixture gamma case is completely resolved employing theoretical, graphical and numerical techniques wherever necessary. 相似文献
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《统计学通讯:理论与方法》2013,42(8-9):1497-1506
Since Rao introduced the Quadratic Entropy (QE) in 1982, results on mathematical and statistical properties of the QE and its applications in data analysis and population indices have been published in the literature. In this paper, we study the asymptotic efficiency of the analysis of Rao's quadratic entropy (ANOQE) which is a generalization of the classical analysis of variance (ANOVA). Based on the results of Liu and Rao [1]and Liu [2]on asymptotic distribution and the bootstrap of the ANOQE, we derive the Bahadur's asymptotic efficiency of the ANOQE and compare efficiency of ANOQE tests based on different QE's. 相似文献
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QUANTILES OF SUMS AND EXPECTED VALUES OF ORDERED SUMS 总被引:1,自引:0,他引:1
Watson & Gordon (1986) investigated the relationship between the quantiles of a sum of independent continuous random variables and the sum of the individual quantiles. In this note some further results are obtained. Also corresponding relationships are developed for the expected values of the order statistics of a sum, and for the sum of the expected values of the individual order statistics. 相似文献
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N. I. Fisher 《Australian & New Zealand Journal of Statistics》1986,28(2):213-219
Robust methods are proposed for testing whether several directional distributions on the unit p-sphere have comparable dispersions. The families of distributions considered are the Langevin for random vectors, and the Generalised Scheidegger-Watson for random axes, with specific interest in the Fisher and Watson distributions on the sphere. The methods are analogues of Levene's procedure for comparing variances of normal distributions. 相似文献
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TESTING THE LARGEST OF A SET OF CORRELATION COEFFICIENTS 总被引:1,自引:0,他引:1
P. A. P. Moran 《Australian & New Zealand Journal of Statistics》1980,22(3):289-297
A previous paper which studied the distribution of the smallest distance between N independent random points on the surface of a sphere is generalised to higher dimensions in order to study the distribution of the largest sample correlation coefficient between a set of independent normally distributed variables. Inclusion-exclusion arguments provide accurate bounds for the tail of this distribution, and by another argument more exact bounds are also found, one of which is an improvement on the result in the previous paper. Bounds are also found for the power of the test against the alternative hypothesis that one only of the population correlation coefficients is non-zero. The test is also shown to be the likelihood ratio test against the latter alternative. 相似文献
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An expression for the exact distribution of the Bell-Doksum test of independence based upon the use of order statistics from normally distributed random samples is derived and a table of critical values is provided. Two extensions of the theory are considered and possible applications to Poisson processes and queueing theory are noted. 相似文献
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We consider the problem of semi-parametric regression modelling when the data consist of a collection of short time series for which measurements within series are correlated. The objective is to estimate a regression function of the form E[Y(t) | x] =x'ß+μ(t), where μ(.) is an arbitrary, smooth function of time t, and x is a vector of explanatory variables which may or may not vary with t. For the non-parametric part of the estimation we use a kernel estimator with fixed bandwidth h. When h is chosen without reference to the data we give exact expressions for the bias and variance of the estimators for β and μ(t) and an asymptotic analysis of the case in which the number of series tends to infinity whilst the number of measurements per series is held fixed. We also report the results of a small-scale simulation study to indicate the extent to which the theoretical results continue to hold when h is chosen by a data-based cross-validation method. 相似文献
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Paul S. F. Yip Ray Watson K. S. Chan Eric H. Y. Lau Feng Chen Ying Xu Liqun Xi Derek Y. T. Cheung Brian Y. T. Ip Danping Liu 《Australian & New Zealand Journal of Statistics》2010,52(1):17-26
It is of interest to estimate the size of a crowd in a demonstration. We propose a practical method to obtain an estimate of the size of the crowd and its standard error. This method has been implemented in practice and, compared with other counting methods, is found to be more efficient, more timely and have less scope for bias. The method described in this paper was motivated by the annual 1 July demonstrations in Hong Kong, and data from the 2006 demonstration are used as an example of the proposed method. 相似文献
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Let x1 x2 , x3 ,be a sequence of independent Bernoulli trials with common success probability p . We consider the problem of estimation of p using a sequential Bayes theoretic approach when the cost per observation is c , and the loss of estimation is squared error loss. A heuristic procedure is suggested, a bound on its Bayes risk is computed, and asymptotic results are exhibited. 相似文献
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P. J. Diggle N. I. Fisher A. J. Lee 《Australian & New Zealand Journal of Statistics》1985,27(1):53-59
A comparison is made af three tests of uniformity for spherical vector data, and of the corresponding tests of uniformity for spherical axial data. 相似文献
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AnantM. Kshirsagar Joanna Chung-inCheng 《Australian & New Zealand Journal of Statistics》1996,38(1):83-89
This paper proposes a new measure of rotatability of a response surface design. It is based on a comparison between the design moments of a given design and the design moments of a rotatable design closest to the given design in the least squares sense. This measure is easier to calculate than Khur?s measure. An alternative easier non-geometrical way of deriving Khuri's measure is also presented. Both measures are calculated to illustrate some designs considered by Khuri. 相似文献