T^2 Type Test Statistic and Simultaneous Confidence Intervals for Two Sub-mean Vectors

In this paper, we consider tests for sub-mean vectors and its simultaneous confidence intervals in two-sample problems. We give the T^2 type test statistic and the simultaneous confidence intervals by using two approximate upper percentiles of T^2 type test statistic. One of the approximate percentiles is obtained by normal approximation for a part of the T^2 type statistic, and the other is an approximation obtained by correcting the degrees of freedom of the F distribution. Finally, we investigate the asymptotic behavior of the approximate upper percentiles of T^2 type statistic by Monte Carlo simulation, and we give an example to illustrate the simultaneous confidence intervals.

A note on Asymptotical Efficiency of the Goodness of Fit Tests Based on disjoint k-spacings Statistic

In this paper Pitman's asymptotic efficiencies (AE) as well as Kallenberg's intermediate AE of the goodness-of-fit tests based on higher-order non-overlapping spacings is considered. We study log statistic as well as entropy type statistic based on k-spacings when k may tend to infinity as n approaches infinity. It certainly compliments the available results for fixed k and provides more general result. We show that both types of statistics based on higher ordered spacings have higher efficiencies in Pitman's sense compared to their counterparts based on simple spacings. It is also shown that the Kallenberg's intermediate AE of such test coincides with its Pitman's AE, the power of the tests are also discussed.

A Guttman-Based Approach to Identifying Cumulativeness Applied to Chimpanzee Culture

Human culture appears to build on itself—that is, to be to some extent cumulative. Whether this property is shared by culture in the common chimpanzee is controversial. The question previously has been approached, qualitatively (and inconclusively), by debating whether any chimpanzee culture traits have resulted from individuals building on one another’s work (“ratcheting”). The fact that the chimpanzees at different sites have distinctive repertoires of traits affords a different avenue of approach: determining whether the traits accumulate, site to site, in a structure more orderly than would be expected by chance. Here we use Guttman scalograms and a gamma-type statistic to bring the first quantitative evidence to bear on the question. We show that while traditional methods provide apparent support for a cumulative tendency, our more rigorous methods do not. This may be because cumulativeness requires human-like social-learning mechanisms, or because culture generally is not sufficiently unidimensional to scale well. A cumulative tendency would be expected, however, under rather weak assumptions; therefore it seems more likely that chimpanzee culture is cumulative, but this data set is simply too small to evidence it.