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191.
Abstract. This is probably the first paper which discusses likelihood inference for a random set using a germ‐grain model, where the individual grains are unobservable, edge effects occur and other complications appear. We consider the case where the grains form a disc process modelled by a marked point process, where the germs are the centres and the marks are the associated radii of the discs. We propose to use a recent parametric class of interacting disc process models, where the minimal sufficient statistic depends on various geometric properties of the random set, and the density is specified with respect to a given marked Poisson model (i.e. a Boolean model). We show how edge effects and other complications can be handled by considering a certain conditional likelihood. Our methodology is illustrated by analysing Peter Diggle's heather data set, where we discuss the results of simulation‐based maximum likelihood inference and the effect of specifying different reference Poisson models. 相似文献
192.
Kallappa M. Koti 《统计学通讯:理论与方法》2013,42(10):3671-3676
Some inequalities are established in P1(r, s) and P1(r+1, s), where P1(r, s) is the confidence coefficient of Wilks’ (1962) outer confidence interval (X(r) X(s)) for the quantile interval (ξp1, ξp2). An inequality concerning incomplete beta functions is also presented and it is shown to be an improved version of one of Koti's (1989) inequalities. 相似文献
193.
This paper reviews recent developments in the stochastic comparison of order statistics. The results discussed are basically: (l) Stochastic comparisons of linear combinations of order statistics from distributions F and G where G?1 F is convex or starshaped. (2) Stochastic comparisons of individual order statistics and of vectors of order statistics from underlying heterogeneous distributions by the use of majorization and Schur function theory. (3) Stochastic comparison of random processes. Applications to reliability problems are presented illustrating the use and value of the theoretical results described 相似文献
194.
J. N. Adichie 《统计学通讯:理论与方法》2013,42(11):985-997
For the problem of testing the equality of slopes of several regression lines against the alternative that the slopes are in increasing (decreasing) order of magnitude, two types of tests are proposed. These are the likelihood ratio test and a test that depends on suitable linear combination of one group statistics. Rank analogues of the two tests are also examined. 相似文献
195.
Ronald J. Bosch 《统计学通讯:理论与方法》2013,42(11):3075-3083
When cubic smoothing splines are used to estimate the conditional quantile function, thereby balancing fidelity to the data with a smoothness requirement, the resulting curve is the solution to a quadratic program. Using this quadratic characterization and through comparison with the sample conditional quan-tiles, we show strong consistency and asymptotic normality for the quantile smoothing spline. 相似文献
196.
Marc Sobel 《统计学通讯:理论与方法》2013,42(11):3037-3051
On a multiple choice test in which each item has r alternative options, a given number c of which are correct, various scoring models have been proposed. In one case the test-taker is allowed to choose any size solution subset and he/she is graded according to whether the subset is small and according to how many correct answers the subset contains. In a second case the test-taker is allowed to select only solution subsets of a prespecified maximum size and is graded as above. The first case is analogous to the situation where the test-taker is given a set of r options with each question; each question calls for a solution which consists of selecting that subset of the r responses which he/she believes to be correct. In the second case, when the prespecified solution subset is restricted to be of size at most one, the resulting scoring model corresponds to the usual model, referred to below as standard. The number c of correct options per item is usually known to the test-taker in this case. Scoring models are evaluated according to how well they correctly identify the total scores of the individuals in the class of test-takers. Loss functions are constructed which penalize scoring models resulting in student scores which are not associated with the students true (or average) total score on the exam. Scoring models are compared on the basis of cross-validated assessments of the loss incurred by using each of the given models. It is shown that in many cases the assessment of the loss for scoring models which allow students the opportunity to choose more than one option for each question are smaller than the assessment of the loss for the standard scoring model. 相似文献
197.
Fernando Jiménez 《统计学通讯:理论与方法》2013,42(1):75-89
In this paper we give a class of row-column designs with the property that the i-th row and the j-th column have precisely r treatments in common. A conjecture that such designs are quasi-factorial is disproved by showing that the designs given in this paper are not quasi-factorial. It is also shown that the designs given here are nearly optimal. 相似文献
198.
J. John Petkau 《统计学通讯:理论与方法》2013,42(15):1523-1534
For a hypothesis testing problem involving the location and scale parameters of an exponential distribution, Perng (1977) proposed a test procedure based on the first r out of n observed failure times. In this paper the likelihood ratio test is determined, critical values are provided and the asymptotic null distribution is determined. An alternate test based on an F statistic is also proposed and the critical regions and power functions of the procedures are compared. 相似文献
199.
This paper presents an asymptotic equivalence result with a sharp rate of convergence forthe sample median and the Harrell-Davis median estimator. The consequences of this result are discussed. 相似文献
200.
Uditha Balasooriya 《统计学通讯:理论与方法》2013,42(2):711-720
In this paper, we present a test procedure to detect outliers in the one-parameter exponential distribution based on prediction. The distribution of the test statistic is obtained. The proposed test can be used to detect more than one outlier and the required percentage points can be easily determined. Furthermore, the test provides a simple procedure to detect whether a given set of data is free from outliers or spurious observations. 相似文献