Exact likelihood inference for Laplace distribution based on Type-II censored samples

We develop exact inference for the location and scale parameters of the Laplace (double exponential) distribution based on their maximum likelihood estimators from a Type-II censored sample. Based on some pivotal quantities, exact confidence intervals and tests of hypotheses are constructed. Upon conditioning first on the number of observations that are below the population median, exact distributions of the pivotal quantities are expressed as mixtures of linear combinations and of ratios of linear combinations of standard exponential random variables, which facilitates the computation of quantiles of these pivotal quantities. Tables of quantiles are presented for the complete sample case.     

Modification of Tukey's additivity test

In this paper we discuss testing for an interaction in the two-way ANOVA with just one observation per cell. The known results are reviewed and a simulation study is performed to evaluate type I and type II risks of the tests. It is shown that the Tukey and Mandel additivity tests have very low power in case of more general interaction scheme. A modification of Tukey's test is developed to resolve this issue. All tests mentioned in the paper have been implemented in R package Additivity Tests.     

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A linear combination test for combining several tests of the correlation coefficient in the bivariate normal distribution is proposed. The linear combination test is compared with the well-known Fisher method of combining tests. It is shown by a Monte Carlo study that the linear combination test has a larger power.     

An alternative method for global and partial comparison of two diagnostic systems based on ROC curves

In this paper, an alternative method for the comparison of two diagnostic systems based on receiver operating characteristic (ROC) curves is presented. ROC curve analysis is often used as a statistical tool for the evaluation of diagnostic systems. However, in general, the comparison of ROC curves is not straightforward, in particular, when they cross each other. A similar difficulty is also observed in the multi-objective optimization field where sets of solutions defining fronts must be compared with a multi-dimensional space. Thus, the proposed methodology is based on a procedure used to compare the performance of distinct multi-objective optimization algorithms. In general, methods based on the area under the ROC curves are not sensitive to the existence of crossing points between the curves. The new approach can deal with this situation and also allows the comparison of partial portions of ROC curves according to particular values of sensitivity and specificity of practical interest. Simulations results are presented. For illustration purposes, considering real data from newborns with very low birthweight, the new method was applied in order to discriminate the better index for evaluating the risk of death.     

Bootstrap confidence bands for the CDF using ranked-set sampling

In ranked-set sampling (RSS), a stratification by ranks is used to obtain a sample that tends to be more informative than a simple random sample of the same size. Previous work has shown that if the rankings are perfect, then one can use RSS to obtain Kolmogorov–Smirnov type confidence bands for the CDF that are narrower than those obtained under simple random sampling. Here we develop Kolmogorov–Smirnov type confidence bands that work well whether the rankings are perfect or not. These confidence bands are obtained by using a smoothed bootstrap procedure that takes advantage of special features of RSS. We show through a simulation study that the coverage probabilities are close to nominal even for samples with just two or three observations. A new algorithm allows us to avoid the bootstrap simulation step when sample sizes are relatively small.     

Testing the equality among distribution functions from independent and right censored samples via Cramér–von Mises criterion

The traditional Cramér–von Mises criterion is used in order to develop a test to compare the equality of the underlying lifetime distributions in the presence of independent censoring times. Its asymptotic distribution is proved and a resampling plan, which is valid for unbalanced data situations, is proposed. Its statistical power is studied and compared with commonly used linear rank tests by Monte Carlo simulations and a real data analysis is also considered. It is observed that the new test is clearly more powerful than the traditional ones when there exists no uniform dominance among involved distributions and in the presence of late differences. Its statistical power is also good in the other considered scenarios.     

Accurate detection of excess over a standard based on a random sample

A known number N of packages each contain, in differing unknown amounts, both substances of no particular import and some substance of interest, the total weight of the latter substance for all N of the packages being an unknown quantity T. Based on the amounts of the substance of interest found in each of n (n ≦= N) randomly sampled packages one is to decide, with a very small probability of the error of wrongly deciding that T exceeds L, whether or not the quantity T exceeds a given amount L. An optimal way of doing this is presented in which the probability of the error of wrongly deciding that T exceeds L can be precisely bounded above as desired.     

Goodness of fit and homogeneity tests on the basis of N-distances

In this paper we propose an application of N-distance theory [Klebanov, L.B., 2005. N-distances and their applications. Karolinum, Prague] for testing simple hypotheses of goodness of fit and homogeneity. The asymptotic null distribution of test statistics is established and coincides with the distribution of infinite quadratic form of independent standard normal random variables. A construction of multivariate free-of-distribution homogeneity test is considered. The power of proposed criteria is compared with classical tests using Monte-Carlo simulations.     

Global and multiple test procedures using ordered p-values—a review

This paper reviews global and multiple tests for the combination ofn hypotheses using the orderedp-values of then individual tests. In 1987, Röhmel and Streitberg presented a general method to construct global level α tests based on orderedp-values when there exists no prior knowledge regarding the joint distribution of the corresponding test statistics. In the case of independent test statistics, construction of global tests is available by means of recursive formulae presented by Bicher (1989), Kornatz (1994) and Finner and Roters (1994). Multiple test procedures can be developed by applying the closed test principle using these global tests as building blocks. Liu (1996) proposed representing closed tests by means of “critical matrices” which contain the critical values of the global tests. Within the framework of these theoretical concepts, well-known global tests and multiple test procedures are classified and the relationships between the different tests are characterised.