Bringing game theory to hypothesis testing: Establishing finite sample bounds on inference

Small sample properties are of fundamental interest when only limited data is avail-able. Exact inference is limited by constraints imposed by speci.c nonrandomizedtests and of course also by lack of more data. These e¤ects can be separated as we propose to evaluate a test by comparing its type II error to the minimal type II error among all tests for the given sample. Game theory is used to establish this minimal type II error, the associated randomized test is characterized as part of a Nash equilibrium of a .ctitious game against nature.We use this method to investigate sequential tests for the di¤erence between twomeans when outcomes are constrained to belong to a given bounded set. Tests ofinequality and of noninferiority are included. We .nd that inference in terms oftype II error based on a balanced sample cannot be improved by sequential sampling or even by observing counter factual evidence providing there is a reasonable gap between the hypotheses.

Some hypothesis tests for the covariance matrix when the dimension is large compared to the sample size

This paper analyzes whether standard covariance matrix tests work whendimensionality is large, and in particular larger than sample size. Inthe latter case, the singularity of the sample covariance matrix makeslikelihood ratio tests degenerate, but other tests based on quadraticforms of sample covariance matrix eigenvalues remain well-defined. Westudy the consistency property and limiting distribution of these testsas dimensionality and sample size go to infinity together, with theirratio converging to a finite non-zero limit. We find that the existingtest for sphericity is robust against high dimensionality, but not thetest for equality of the covariance matrix to a given matrix. For thelatter test, we develop a new correction to the existing test statisticthat makes it robust against high dimensionality.

Exact and approximate stepdown methods for multiple hypothesis testing

Consider the problem of testing k hypotheses simultaneously. In this paper,we discuss finite and large sample theory of stepdown methods that providecontrol of the familywise error rate (FWE). In order to improve upon theBonferroni method or Holm's (1979) stepdown method, Westfall and Young(1993) make eective use of resampling to construct stepdown methods thatimplicitly estimate the dependence structure of the test statistics. However,their methods depend on an assumption called subset pivotality. The goalof this paper is to construct general stepdown methods that do not requiresuch an assumption. In order to accomplish this, we take a close look atwhat makes stepdown procedures work, and a key component is a monotonicityrequirement of critical values. By imposing such monotonicity on estimatedcritical values (which is not an assumption on the model but an assumptionon the method), it is demonstrated that the problem of constructing a validmultiple test procedure which controls the FWE can be reduced to the problemof contructing a single test which controls the usual probability of a Type 1error. This reduction allows us to draw upon an enormous resamplingliterature as a general means of test contruction.

Experimental support for the make-up hypothesis in nestling tawny owls (Strix aluco)

Body condition can affect coloration of traits used in sexual selection and parent-offspring communication by inducing rapid internal changes in pigment concentration or aggregation, thickness of collagen arrays, or blood flux. The recent "makeup hypothesis" proposes an alternative honesty-reinforcing mechanism, with behaviorally mediated deposition of substances on body surfaces ("cosmetics") generating covariation between body condition and coloration. In birds, the uropygial gland wax is actively spread on feathers using the bill and changes in its deposition rate may cause rapid changes in bill and plumage coloration. Using tawny owl nestlings, we tested 3 predictions of the makeup hypothesis, namely that 1) quantity of preen wax deposited accounts for variation in bill coloration, 2) an immune stimulation (induced by injection of a lipopolysaccharide [LPS]) impairs uropygial gland wax production, and 3) different intensities of immune stimulations (strong vs. weak stimulations induced by injections of either LPS or phytohemagglutinin [PHA], respectively) and high versus low food availabilities result in different bill colorations. We found that 1) preen wax reduced bill brightness, 2) a challenge with LPS impaired uropygial gland development, and 3) nestlings challenged with LPS had a brighter bill than PHA-injected nestlings, whereas diet manipulation had no significant effect. Altogether, these results suggest that a strong immune challenge may decrease preen wax deposition rate on the bill of nestling birds, at least by impairing gland wax production, which causes a change in bill coloration. Our study therefore highlights that cosmetic colors might signal short-term variation in immunological status.

The V-region disease hypothesis: evidence from autoimmune encephalomyelitis.

Experimental allergic encephalomyelitis has been shown to have an immunological basis. In fact, the disease can be induced by T cells specific for myelin basic protein, a molecule found in abundance in the central nervous system. In this article, Ellen Heber-Katz and Hans Acha-Orbea discuss the T-cell receptor (TCR) repertoire of the encephalitogenic T-cell response, and show that a limited V gene pool, in fact a single V beta and two V alpha families, are being used by the PL/J and B10.PL mice and by every rat strain examined, even though the antigenic determinants and the major histocompatibility complex (MHC) molecules are different in all cases. This extraordinary finding suggests that the TCR is involved in encephalitogenicity in a way that not only involves the recognition of antigen in association with MHC, but also as an effector molecule that results in encephalitis. If this is true, it implies that TCRs, in general, play more than one role in mammalian physiology.

The economic effects of the Protestant Reformation: Testing the Weber hypothesis in the German Lands

Many theories, most famously Max Weber s essay on the Protestant ethic, have hypothesizedthat Protestantism should have favored economic development. With their considerablereligious heterogeneity and stability of denominational affiliations until the 19th century, theGerman Lands of the Holy Roman Empire present an ideal testing ground for this hypothesis.Using population figures in a dataset comprising 272 cities in the years 1300 1900, I find no effectsof Protestantism on economic growth. The finding is robust to the inclusion of a varietyof controls, and does not appear to depend on data selection or small sample size. In addition,Protestantism has no effect when interacted with other likely determinants of economic development.I also analyze the endogeneity of religious choice; instrumental variables estimates ofthe effects of Protestantism are similar to the OLS results.

Hypothesis on immigration and welfare

The number of hypothesis trying to explain which are the reasons behind the decision to migrate to work into a developed country are diverse and at the same time, difficult to test due to the multiplicity of factors which affect it. This papers attempts to move forward trying to disentangle which are the socio-economic factors that explain the differences in the figures of immigrants in the OECD countries. We show empirical evidence about the determinants of the migratory flows to 17 OECD countries from 65 countries in the 1980-2000 period. Our results reveal the importance to differentiate the inflows composition by at least income in the origin countries. Thus, regarding inflows from non-high-income countries, the results suggest that there is a pull effect from monetary and not real income, and then, the welfare magnets hypothesis should be rejected. This group reacts more to the migratory policy than the inflows coming from high-income countries, although those policies designed to slow down the inflows have not been able, in the aggregate, to reduce them.

The quasi-judicial role of large retailers: An efficiency hypothesis of their relation with suppliers

The paper explores an efficiency hypothesis regarding the contractual process between large retailers, such as Wal-Mart and Carrefour, and their suppliers. The empirical evidence presented supports the idea that large retailers play a quasi-judicial role, acting as "courts of first instance" in their relationships with suppliers. In this role, large retailers adjust the terms of trade to on-going changes and sanction performance failures, sometimes delaying payments. A potential abuse of their position is limited by the need for re-contracting and preserving their reputations. Suppliers renew their confidence in their retailers on a yearly basis, through writing new contracts. This renovation contradicts the alternative hypothesis that suppliers are expropriated by large retailers as a consequence of specific investments.

Comparing and validating hypothesis test procedures: Graphical and numerical tools

When the behaviour of a specific hypothesis test statistic is studied by aMonte Carlo experiment, the usual way to describe its quality is by givingthe empirical level of the test. As an alternative to this procedure, we usethe empirical distribution of the obtained \emph{p-}values and exploit itsinformation both graphically and numerically.

The fixation of locally beneficial alleles in a metapopulation.

Extinction, recolonization, and local adaptation are common in natural spatially structured populations. Understanding their effect upon genetic variation is important for systems such as genetically modified organism management or avoidance of drug resistance. Theoretical studies on the effect of extinction and recolonization upon genetic variance started appearing in the 1970s, but the role of local adaptation still has no good theoretical basis. Here we develop a model of a haploid species in a metapopulation in which a locally adapted beneficial allele is introduced. We study the effect of different spatial patterns of local adaptation, and different metapopulation dynamics, upon the fixation probability of the beneficial allele. Controlling for the average selection pressure, we find that a small area of positive selection can significantly increase the global probability of fixation. However, local adaptation becomes less important as extinction rate increases. Deme extinction and recolonization have a spatial smoothing effect that effectively reduces spatial variation in fitness.

Occurrence and molecular diversity of the Fit insect toxin locus in plant-beneficial pseudomonads

The application of plant-beneficial pseudomonads provides a promising alternative to chemical pest management in agriculture. The fact that Pseudomonas fluorescens CHA0 and Pf-5, both well-known biocontrol agents of fungal root diseases, exhibit also potent insecticidal activity is of particular interest, as these plant-beneficial bacteria naturally colonize the rhizosphere of important crop plants. Insecticidal activity in these strains depends on a novel locus encoding the production of a protein toxin termed Fit (for P. fluorescens insecticidal toxin). To gain a better understanding of the ecological relevance of the Pseudomonas anti-insect activity, we have begun to investigate the occurrence and molecular diversity of the Fit toxin genes among root-associated pseudomonads. To this end, we have screened a large world-wide collection of fluorescent Pseudomonas sp. isolated from the roots of different plant species using molecular fingerprinting techniques. The strains are already well characterized for exoproduct patterns and disease-suppressive ability and are currently being tested for insecticidal activity in a greater wax moth larvae assay system.

Whose DNA is this? How relevant a question? (a note for forensic scientists).

This communication seeks to draw the attention of researchers and practitioners dealing with forensic DNA profiling analyses to the following question: is a scientist's report, offering support to a hypothesis according to which a particular individual is the source of DNA detected during the analysis of a stain, relevant from the point of view of a Court of Justice? This question relates to skeptical views previously voiced by commentators mainly in the judicial area, but is avoided by a large majority of forensic scientists. Notwithstanding, the pivotal role of this question has recently been evoked during the international conference "The hidden side of DNA profiles. Artifacts, errors and uncertain evidence" held in Rome (April 27th to 28th, 2012). Indeed, despite the fact that this conference brought together some of the world's leading forensic DNA specialists, it appeared clearly that a huge gap still exists between questions lawyers are actually interested in, and the answers that scientists deliver to Courts in written reports or during oral testimony. Participants in the justice system, namely lawyers and jurors on the one hand and forensic geneticists on the other, unfortunately talk considerably different languages. It thus is fundamental to address this issue of communication about results of forensic DNA analyses, and open a dialogue with practicing non-scientists at large who need to make meaningful use of scientific results to approach and help solve judicial cases. This paper intends to emphasize the actuality of this topic and suggest beneficial ways ahead towards a more reasoned use of forensic DNA in criminal proceedings.