On Some Nuisance Parameter Free Uniformly Most Powerful Tests

TAKEUCHI (1969) provides a uniformly most powerful (UMP) one side test for testing the location parameter of the two parameters exponential model when the scale parameter is unknown. The power of his similar size α test depends, however, on the unknown scale parameter. In this case and in more general situations when there exists a sufficient statistic for the nuisance parameter, the theory of generalized THOMPSON's distributions, more specifically, the Thompsonization of a test statistic, LAURENT (1959, 1972) provides a UMP test whose power does not depend on the nuisance parameter. Examples of application of the general nuisance parameter free test procedure include here the truncated exponential, the inverse Gaussian, and the geometric distributions.     

Influence of rainfall on sleeping site choice by a group of anubis baboons (Papio anubis)

For diurnal nonhuman primates, shifting among different sleeping sites may provide multiple benefits such as better protection from predators, reduced risk of parasitic infection, and closer proximity to spatially and temporally heterogeneous food and water. This last benefit may be particularly important in sleeping site selection by primates living in savanna‐woodlands where rainfall is more limited and more seasonally pronounced than in rainforests. Here, we examined the influence of rainfall, a factor that affects food and water availability, on the use of sleeping sites by anubis baboons (Papio anubis) over two 13‐month study periods that differed in rainfall patterns. We predicted that during wet periods, when food and water availability should be higher, the study group would limit the number of sleeping sites and would stay at each one for more consecutive nights than during dry periods. Conversely, we predicted that during dry periods the group would increase the number of sleeping sites and stay at each one for fewer consecutive nights as they searched more widely for food and water. We also predicted that the group would more often choose sleeping sites closer to the center of the area used during daytime (between 07:00 and 19:00) during wet months than during dry months. Using Global Positioning System data from collared individuals, we found that our first prediction was not supported on either monthly or yearly timescales, although past monthly rainfall predicted the use of the main sleeping site in the second study period. Our second prediction was supported only on a yearly timescale. This study suggests that baboons’ choice of sleeping sites is fluid over time while being sensitive to local environmental conditions, one of which may be rainfall.     

The Structure of Ellipsoidal Distributions I. Canonical Analysis

This study is concerned with the structure of variables having ellipsoidal distributions. In Part I it is shown that many normal-theory results in canonical analysis are exact for all ellipsoidal distributions under a specified model for sampling. In Part II similar conclusions are drawn regarding the use of principal components. These findings suggest using normal-theory procedures in canonical and principal components analyses as approximate large-sample procedures for distributions attracted to ellipsoidal stable laws.     

Analysis of Profiles Based on Ordinal Classification Functions and Rank Tests

In this article a test for the comparison of K groups of independent profiles is suggested. It is based on rank tests, in which the criterion is obtained by using a suitably chosen ordinal classification function. This function represents a specific view on the profiles. The test, which is easy to use, can be regarded as a generalisation of other well known tests and can be applied within a variety of situations. The relationships to other procedures for the analysis of profiles are described. Some properties are discussed.     

Application of Multiple Test Procedures to the Combination of Multivariate and Univariate Tests with Varying Variable Sets

The positive ascertainment of location differences in a multivariate comparison of two or more groups gives rise to the question for the contribution of the single variables or of subsets of variables to the multivariate difference. In this paper two methods are proposed to accomplish the original multivariate test by tests in variable subsets or in single variables using a closed test procedure and Holm's procedure, respectively. Both control the multiple level of the whole procedure.     

On Comparing Correlated Means in the Presence of Incomplete Data

Two statistics are proposed for testing the hypothesis of equality of the means of a bivariate normal distribution with unknown common variance and correlation coefficient when observations are missing on both variates. One of the statistics reduces to the one proposed by Bhoj (1978, 1984) when the unpaired observations on the variates are equal. The distributions of the statistics are approximated by well known distributions under the null hypothesis. The empirical powers of the tests are computed and compared with those of some known statistics. The comparison supports the use of one of the statistics proposed in this paper.     

Estimates of a Treatment Effect Based on Censored Data Rank Tests

Linear rank test statistics are applied to the problem of estimating a treatment effect if two sets of censored failure time data are compared and the distributions of the log-failure times of the two samples are assumed to differ only in location. Rank tests for this accelerated failure time model are reviewed and Hodges-Lehmann type estimates for the shift parameter are proposed. Properties of these estimates are investigated, computational aspects are discussed and an example is presented.     

A More Powerful Simultaneous Test Procedure in Configural Frequency Analysis

In the Configural Frequency Analysis (CFA) of KRAUTH and LIENERT (1973 a, b), overfrequented (or underfrequented) cells in multivariate contingency tables are identified by simultaneous binomial tests. As an alternative, finite and asymptotic tests are proposed, which are derived from the (exact conditional) generalized hypergeometrical distribution of the cell frequencies. These tests allow for considerably more powerful decisions than do the conservative binomial tests.     

On the Assessment of the Performance of Multiple Test Procedures

Based on the concept of the multiple level of significance two criteria for assessing the performance of multiple tests are proposed: The simultaneous power is defined as the probability of rejecting all false null hypotheses. The probability of a correct decision is defined as the probability of correctly rejecting all false null hypotheses and accepting all true ones. Both criteria are discussed for nonstagewise and stagewise procedures in case of independent test statistics. For the example of 5 independently and normally distributed test statistics the values of the two criteria are calcutated under reasonably simple alternatives.