John Orban

Bio: John Orban is an academic researcher from Binghamton University. The author has contributed to research in topics: Rank (linear algebra) & Sample size determination. The author has an hindex of 2, co-authored 2 publications receiving 81 citations.

A Class of Distribution-Free Two-Sample Tests Based on Placements

Abstract: We consider a class of two-sample distribution-free tests that are appropriate for situations where one of the sample sizes is large relative to the other. These procedures are based on the placements of the observations in the smaller sample among the ordered observations in the larger sample, and this class of tests generalizes the Mann-Whitney (1947) procedure in much the same way that the class of linear rank tests generalizes the equivalent Wilcoxon (1945) rank sum form. Optimality criteria for choosing a test from this class are discussed and limiting distributions for the associated class of test statistics are determined for the case where only one of the sample sizes goes to infinity.

Properties of a distribution-free two-stage two-sample median test

Abstract: In this paper we consider a class of distribution-free two-stage two-sample median tests. These procedures are based on a fixed size sample from one population, while the observations from the second population are collected in a truncated sequential fashion. Necessary tables are provided enabling us to select a particular member from the class such that arbitrarily preset power levels are approximately obtained. We also present asymptotic expressions and tables for the expected number of observations from the second population. Finally, comparisons between the asymptotic version of this two-stage median test and the binomial sequential probability ratio test due to Wald (1947) are discussed.

Nonparametric Control Charts: An Overview and Some Results

Abstract: The literature on nonparametric or distribution-free control charts for univariate variables data is examined. The advantages of these charts have over more traditional distribution-based control charts are demonstrated. Constructive criticism of the li..

Robust Rank Procedures for the Behrens-Fisher Problem

Abstract: The problem of testing for equality of the medians of two populations is considered. The standard distribution-free tests for this problem require that the two populations have the same shape to maintain their nominal significance level under the null hypothesis. A method is given to modify many of these tests so they can be used to test for equality of the medians with fewer assumptions on the shapes of the two populations. The method is demonstrated using the Mann-Whitney-Wilcoxon statistic.

Rank-based multiple test procedures and simultaneous confidence intervals

Abstract: We study simultaneous rank procedures for unbalanced designs with independent observations. The hypotheses are formulated in terms of purely nonparametric treatment effects. In this context, we derive rank-based multiple contrast test procedures and simultaneous confidence intervals which take the correlation between the test statistics into account. Hereby, the individual test decisions and the simultaneous confidence intervals are compatible. This means, whenever an individual hypothesis has been rejected by the multiple contrast test, the corresponding simultaneous confidence interval does not include the null, i.e. the hypothetical value of no treatment effect. The procedures allow for testing arbitrary purely nonparametric multiple linear hypotheses (e.g. many-to-one, all-pairs, changepoint, or even average comparisons). We do not assume homogeneous variances of the data; in particular, the distributions can have different shapes even under the null hypothesis. Thus, a solution to the multiple nonparametric Behrens-Fisher problem is presented in this unified framework.

Distribution-Free Quality Control Charts Based on Signed-Rank-Like Statistics

Abstract: In this article we propose three distribution-free (or nonparametric) statistical quality control charts for monitoring a process center when an in-control target center is not specified. These charts are of the Shewhart-type, the exponentially moving average-type, and the cumulative sum-type. The constructions of the proposed charts require the availability of an initial reference sample taken when the process was operating in-control to calculate an estimator for the unknown in-control target process center. This estimated center is then used in the calculation of signed-rank-like statistics based on grouped observations taken periodically from the process output. As long as the in-control process underlying distribution is continuous and symmetric, the proposed charts have a constant in-control average run length and a constant false alarm rate irrespective of the process underlying distribution. Other advantages of the proposed distribution-free charts include their robustness against outliers and the...

Affine Invariant Multivariate Sign and Rank Tests and Corresponding Estimates: a Review

Abstract: The paper reviews recent contributions to the statistical inference methods, tests and estimates, based on the generalized median of Oja. Multivariate analogues of sign and rank concepts, affine invariant one-sample and two-sample sign tests and rank tests, affine equivariant median and Hodges–Lehmann-type estimates are reviewed and discussed. Some comparisons are made to other generalizations. The theory is illustrated by two examples.