Tests based on higher-order orm-step spacings have been considered in the literature for the goodness of fit problem. This paper studies the asymptotic distribution theory for such tests based on non-overlappingm-step...
Tests based on higher-order orm-step spacings have been considered in the literature for the goodness of fit problem. This paper studies the asymptotic distribution theory for such tests based on non-overlappingm-step spacings whenm, the length of the step, also increases with the sample sizen, to inifinity. By utilizing the asymptotic distributions under a sequence of close alternatives and studying their relative efficiencies, we try to answer a central question about the choice ofm in relation ton. Efficiency comparisons are made with tests based on overlappingm-step spacings, as well as corresponding chi-square tests.
作者：
Fisher, Nicholas I.Hall, PeterProgram Leader
Applied and Industrial Statistics Division of Mathematics and Statistics Commonwealth Scientific and Industrial Research Organisation Lindfield New South Wales 2070 Australia. Professor
Department of Statistics Australian National University Canberra Australian Capital Territory 2601 Australia
Methods are proposed for constructing bootstrap confidence regions for the mean direction of a random p-dimensional unit vector X with an arbitrary unimodal distribution on the p sphere. The approach of this article d...
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Methods are proposed for constructing bootstrap confidence regions for the mean direction of a random p-dimensional unit vector X with an arbitrary unimodal distribution on the p sphere. The approach of this article differs from that of other authors in that it is based on pivotal statistics. A general pivotal method is introduced that produces a wide variety of confidence regions on general p-dimensional spheres; included are confidence cones and likelihood-based regions. It can readily be modified to incorporate extra assumptions about the underlying distribution, such as rotational symmetry. The general method leads to confidence pictures, which present information about the estimated posterior likelihood of mean orientation by shading spherical surfaces. An application is given to a sample of spherical cross-bed measurements. The methods extend to the case where X has random length, and to calculation of confidence regions for reference directions of axial bipolar or girdle distributions. [ABSTRACT FROM AUTHOR]
Given symmetric generalized inverses of A χ x′ c , where χ is a vector with n components, we obtain formulae for the corresponding generalized inverses (symmetric) of A . An application of such formulae in linear m...
Given symmetric generalized inverses of A χ x′ c , where χ is a vector with n components, we obtain formulae for the corresponding generalized inverses (symmetric) of A . An application of such formulae in linear models is suggested.
In this paper, we consider what may be done when researchers anticipate that in the implementation of field experiments, random assignment to experimental and control groups is likely to be flawed. We then reanalyze d...
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Tests for the goodness-of-fit problem based on sample spacings, i.e., observed distances between successive order statistics, have been used in the literature. We propose a new test based on the number of “small” a...
Tests for the goodness-of-fit problem based on sample spacings, i.e., observed distances between successive order statistics, have been used in the literature. We propose a new test based on the number of “small” and “large” spacings. The asymptotic theory under close alternative sequences is also given thus enabling one to calculate the asymptotic relative efficiencies of such tests. A comparison of the new test and other spacings tests is given.
This paper discusses a sequential procedure to estimate an estimable parameter of the underlying unknown distribution function. The estimator is based on the corresponding U-statistic. Under appropriate regularity con...
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作者：
MCNICHOLS, RJDAVIS, CBRoger J. McNichols is a professor of industrial engineering at the University of Toledo (Department of Industrial Engineering
University of Toledo Toledo OH 43606). After receiving his Ph.D in industrial engineering from The Ohio State University he joined the faculty of Texas A and M University where he directed the Maintainability Engineering Graduate Program at Red River Army Depot. At UT he has served as associate dean of engineering and as chairman of the Systems engineering doctoral program. His research and consulting interests include reliability quality control manufacturing mathematical modeling and applied statistics. Charles B. Davis is an associate professor of mathematics at the University of Toledo (Department of Mathematics
University of Toledo Toledo OH 43606). After receiving his M.S. in mathematics and statistics and his Ph.D. in statistics from the University of New Mexico he joined the Mathematics Department at UT where he established the graduate program in statistics. His research and consulting interests include statistical modeling statistical computation simultaneous inference and data analysis.
Ground water monitoring presents interesting statistical challenges, including controlling the risk of entering compliance monitoring, incorporating all modes of inherent variability into the statistical model on whic...
Ground water monitoring presents interesting statistical challenges, including controlling the risk of entering compliance monitoring, incorporating all modes of inherent variability into the statistical model on which tests are based, and taming the detection limit problem, all while maintaining demonstrable sensitivity to real contamination. Some of these challenges exceed textbook statistics considerably, even when considered alone, and good solutions are scarce. When these challenges are combined, the task of developing good statistical procedures or good regulations can be formidable. This article presents a number of realities of ground water monitoring that should be considered when developing statistical procedures. Recommendations made for addressing these realities include the following: (1) the false positive rate should be controlled on a facility-wide basis, rather than per well or per parameter as required in the proposed regulation (40 CFR §264); (2) multiple comparisons with control procedures are preferable to analysis of variance (ANOVA) for controlling the overall false positive rate; (3) retests can be made an explicit part of the statistical procedure in order to increase power and decrease sensitivity to distribution shape assumptions; (4) commonly used simple methods of handling below detection limit data with parametric tests, including Cohen's procedure as implemented in the U.S. EPA's Technical Enforcement Guidance Document (TEGD), should probably be avoided; (5) the statistical properties of practical quantitation limits for non-naturally occurring compounds should be studied carefully; and (6) so long as the facility-wide false positive rate is controlled, better sensitivity to real contamination is obtained by monitoring fewer well-chosen parameters at a smaller number of well-chosen locations. An evaluation of the proposed revised §264 regulation with respect to these realities reveals that it seems to be a definite improvement over the
In applications, considerations on stochastic models often involve a Markov chain [formula omitted] with state space in R+, and a transition probability Q. For each x ε R+ the support of Q(x,) is [0, x]. This implies...
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The primary objective of this paper is to review several results available in the statistical literature pertaining to the problem of hierarchical estimation. Some relevant extensions are derived for the problem of re...
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The primary objective of this paper is to review several results available in the statistical literature pertaining to the problem of hierarchical estimation. Some relevant extensions are derived for the problem of reconstructing the globally optimal estimate based on local estimates transmitted by feeder nodes. Their utilisty is next demonstrated with characterizations and examples pertaining to common scenarios in decentralized estimation problems.
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