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.

HACEK infective endocarditis: characteristics and outcomes from a large, multi-national cohort.

The HACEK organisms (Haemophilus species, Aggregatibacter species, Cardiobacterium hominis, Eikenella corrodens, and Kingella species) are rare causes of infective endocarditis (IE). The objective of this study is to describe the clinical characteristics and outcomes of patients with HACEK endocarditis (HE) in a large multi-national cohort. Patients hospitalized with definite or possible infective endocarditis by the International Collaboration on Endocarditis Prospective Cohort Study in 64 hospitals from 28 countries were included and characteristics of HE patients compared with IE due to other pathogens. Of 5591 patients enrolled, 77 (1.4%) had HE. HE was associated with a younger age (47 vs. 61 years; p<0.001), a higher prevalence of immunologic/vascular manifestations (32% vs. 20%; p<0.008) and stroke (25% vs. 17% p = 0.05) but a lower prevalence of congestive heart failure (15% vs. 30%; p = 0.004), death in-hospital (4% vs. 18%; p = 0.001) or after 1 year follow-up (6% vs. 20%; p = 0.01) than IE due to other pathogens (n = 5514). On multivariable analysis, stroke was associated with mitral valve vegetations (OR 3.60; CI 1.34-9.65; p<0.01) and younger age (OR 0.62; CI 0.49-0.90; p<0.01). The overall outcome of HE was excellent with the in-hospital mortality (4%) significantly better than for non-HE (18%; p<0.001). Prosthetic valve endocarditis was more common in HE (35%) than non-HE (24%). The outcome of prosthetic valve and native valve HE was excellent whether treated medically or with surgery. Current treatment is very successful for the management of both native valve prosthetic valve HE but further studies are needed to determine why HE has a predilection for younger people and to cause stroke. The small number of patients and observational design limit inferences on treatment strategies. Self selection of study sites limits epidemiological inferences.

Robust response transformations based on optimal prediction

Nonlinear regression problems can often be reduced to linearity by transforming the response variable (e.g., using the Box-Cox family of transformations). The classic estimates of the parameter defining the transformation as well as of the regression coefficients are based on the maximum likelihood criterion, assuming homoscedastic normal errors for the transformed response. These estimates are nonrobust in the presence of outliers and can be inconsistent when the errors are nonnormal or heteroscedastic. This article proposes new robust estimates that are consistent and asymptotically normal for any unimodal and homoscedastic error distribution. For this purpose, a robust version of conditional expectation is introduced for which the prediction mean squared error is replaced with an M scale. This concept is then used to develop a nonparametric criterion to estimate the transformation parameter as well as the regression coefficients. A finite sample estimate of this criterion based on a robust version of smearing is also proposed. Monte Carlo experiments show that the new estimates compare favorably with respect to the available competitors.

Constant coefficient tests for random coefficient regression

Random coefficient regression models have been applied in differentfields and they constitute a unifying setup for many statisticalproblems. The nonparametric study of this model started with Beranand Hall (1992) and it has become a fruitful framework. In thispaper we propose and study statistics for testing a basic hypothesisconcerning this model: the constancy of coefficients. The asymptoticbehavior of the statistics is investigated and bootstrapapproximations are used in order to determine the critical values ofthe test statistics. A simulation study illustrates the performanceof the proposals.

Phase II study of imatinib in patients with recurrent gliomas of various histologies: a European Organisation for Research and Treatment of Cancer Brain Tumor Group Study.

PURPOSE: To evaluate the safety and the efficacy of imatinib in recurrent malignant gliomas. PATIENTS: AND METHODS: This was a single-arm, phase II study. Eligible patients had recurrent glioma after prior radiotherapy with an enhancing lesion on magnetic resonance imaging. Three different histologic groups were studied: glioblastomas (GBM), pure/mixed (anaplastic) oligodendrogliomas (OD), and low-grade or anaplastic astrocytomas (A). Imatinib was started at a dose of 600 mg/d with dose escalation to 800 mg in case of no toxicity; during the trial this dose was increased to 800 mg/d with escalation to 1,000 mg/d. Trial design was one-stage Fleming; both an objective response and 6 months of progression-free survival (PFS) were considered a successful outcome to treatment. RESULTS: A total of 112 patients (51 patients with GBM, 25 patients with A, and 36 patients with OD) were enrolled. Imatinib was in general well tolerated. The median number of cycles was 2.0 (range, 1 to 43 cycles). Five patients had an objective partial response, including three patients with GBM; all had 6 months of PFS. The 6-month PFS rate was 16% (95% CI, 8.0% to 34.0%) in GBM, 4.0% (95% CI, 0.3% to 15.0%) in OD, and 9% (95% CI, 2.0% to 25.0%) in A. The exposure to imatinib was significantly lower in patients using enzyme-inducing antiepileptic drugs. The presence of ABCG2 point mutations were not correlated with pharmacokinetic findings. No somatic activating mutations of KIT or platelet-derived growth factor receptor-A or -B were found. CONCLUSION: In the dose range of 600 to 1,000 mg/d, single-agent imatinib is well tolerated but has limited antitumor activity in patients with recurrent gliomas.

Statistics in archaeology: New directions

Connections between Statistics and Archaeology have always appeared veryfruitful. The objective of this paper is to offer an outlook of somestatistical techniques that are being developed in the most recentyears and that can be of interest for archaeologists in the short run.

Weighted Kernel regression

In the fixed design regression model, additional weights areconsidered for the Nadaraya--Watson and Gasser--M\"uller kernel estimators.We study their asymptotic behavior and the relationships between new andclassical estimators. For a simple family of weights, and considering theIMSE as global loss criterion, we show some possible theoretical advantages.An empirical study illustrates the performance of the weighted estimatorsin finite samples.

Exact tests for correlation and for the slope in simple linear regressions without making assumptions

We present an exact test for whether two random variables that have known bounds on their support are negatively correlated. The alternative hypothesis is that they are not negatively correlated. No assumptions are made on the underlying distributions. We show by example that the Spearman rank correlation test as the competing exact test of correlation in nonparametric settings rests on an additional assumption on the data generating process without which it is not valid as a test for correlation.We then show how to test for the significance of the slope in a linear regression analysis that invovles a single independent variable and where outcomes of the dependent variable belong to a known bounded set.

Trade credit: Suppliers as debt collectors and insurance providers

There are two fundamental puzzles about trade credit: why does it appearto be so expensive,and why do input suppliers engage in the business oflending money? This paper addresses and answers both questions analysingthe interaction between the financial and the industrial aspects of thesupplier-customer relationship. It examines how, in a context of limitedenforceability of contracts, suppliers may have a comparative advantageover banks in lending to their customers because they hold the extrathreat of stopping the supply of intermediate goods. Suppliers may alsoact as lenders of last resort, providing insurance against liquidityshocks that may endanger the survival of their customers. The relativelyhigh implicit interest rates of trade credit result from the existenceof default and insurance premia. The implications of the model areexamined empirically using parametric and nonparametric techniques on apanel of UK firms.

Forecasting with missing data: Application to a real case

This paper presents a comparative analysis of linear and mixed modelsfor short term forecasting of a real data series with a high percentage of missing data. Data are the series of significant wave heights registered at regular periods of three hours by a buoy placed in the Bay of Biscay.The series is interpolated with a linear predictor which minimizes theforecast mean square error. The linear models are seasonal ARIMA models and themixed models have a linear component and a non linear seasonal component.The non linear component is estimated by a non parametric regression of dataversus time. Short term forecasts, no more than two days ahead, are of interestbecause they can be used by the port authorities to notice the fleet.Several models are fitted and compared by their forecasting behavior.

Cytochrome P450 2D6 genotype and methadone steady-state concentrations

A genetic polymorphism of cytochrome P450 2D6 has been described with the existence of poor (zero functional genes), extensive (one or two functional genes), and ultrarapid metabolizers (three or more functional genes). The authors measured the steady-state trough (R)- (i.e., the active enantiomer), (S)-, and (R,S)-methadone plasma levels in opiate-dependent patients receiving methadone maintenance treatment (MMT) and genotyped them for cytochrome P4502D6. The patients' medical records were reviewed to assess the outcome of the MMT with regard to the absence of illicit opiate consumption and to the absence of withdrawal complaints in ultrarapid and poor metabolizers. Of 256 patients included, 18 were found to be poor metabolizers, 228 to be extensive metabolizers, and 10 to be ultrarapid metabolizers. Significant differences were found between genotypes for (R)- (p = 0.024), (S)- (p = 0.033), and (R,S)-methadone (p = 0.026) concentrations to dose-to-weight ratios. For (R)-methadone, a significant difference was found between ultrarapid metabolizers and poor metabolizers (p = 0.009), with the median value in the former group being only 54% of the median value in the latter group. These results confirm the involvement of cytochrome P450 2D6 in methadone metabolism. Although the difference was nonsignificant (p = 0.103), 13 (72%) of the 18 poor metabolizers and only 4 (40%) of the 10 ultrarapid metabolizers were considered successful in their treatment. More studies are needed to examine the influence of the ultrarapid metabolizer status on the outcome of the MMT.

Morphological and physiological variation between queens and workers of Protonectarina sylveirae (de Saussure) (Hymenoptera, Vespidae, Epiponini)

Morphological and physiological variation between queens and workers of Protonectarina sylveirae (de Saussure) (Hymenoptera, Vespidae, Epiponini). The Neotropical swarm-founding wasps, Epiponini, range from the absence of morphological differentiation between castes to highly distinct castes. We measured eight body parts of females of two colonies of Protonectarina sylveirae (de Saussure, 1854). ANOVA and Discriminant Analysis evidenced significant differences between castes, as previously observed by other authors for other species of Epiponini. However, some females previously categorized as queens, were actually workers, supported by our statistic analyses. These individuals showed intermediate morphological features between queens and workers, having distinct patterns of hairs and clypeal spots. The castes of P. sylveirae are distinct, however intermediate individuals may be found in colonies promoting social flexibility.

Geographical deviations in foreign trade statistics: A study into European trade with Latin American Countries, 1925

We have analyzed the spatial accuracy of European foreign trade statistics compared to Latin American. We have also included USA s data because of the importance of this country in Latin American trade. We have developed a method for mapping discrepancies between exporters and importers, trying to isolate systematic spatial deviations. Although our results don t allow a unique explanation, they present some interesting clues to the distribution channels in the Latin American Continent as well as some spatial deviations for statistics in individual countries. Connecting our results with the literature specialized in the accuracy of foreign trade statistics; we can revisit Morgernstern (1963) as well as Federico and Tena (1991). Morgernstern had had a really pessimistic view on the reliability of this statistic source, but his main alert was focused on the trade balances, not in gross export or import values. Federico and Tena (1991) have demonstrated howaccuracy increases by aggregation, geographical and of product at the same time. But they still have a pessimistic view with relation to distribution questions, remarking that perhaps it will be more accurate to use import sources in this latest case. We have stated that the data set coming from foreign trade statistics for a sample in 1925, being it exporters or importers, it s a valuable tool for geography of trade patterns, although in some specific cases it needs some spatial adjustments.

Worst-case bounds for the logarithmic loss of predictors

We investigate on-line prediction of individual sequences. Given a class of predictors, the goal is to predict as well as the best predictor in the class, where the loss is measured by the self information (logarithmic) loss function. The excess loss (regret) is closely related to the redundancy of the associated lossless universal code. Using Shtarkov's theorem and tools from empirical process theory, we prove a general upper bound on the best possible (minimax) regret. The bound depends on certain metric properties of the class of predictors. We apply the bound to both parametric and nonparametric classes ofpredictors. Finally, we point out a suboptimal behavior of the popular Bayesian weighted average algorithm.

Minimum distance estimation of stationary and non-stationary ARFIMA processes

A new parametric minimum distance time-domain estimator for ARFIMA processes is introduced in this paper. The proposed estimator minimizes the sum of squared correlations of residuals obtained after filtering a series through ARFIMA parameters. The estimator iseasy to compute and is consistent and asymptotically normally distributed for fractionallyintegrated (FI) processes with an integration order d strictly greater than -0.75. Therefore, it can be applied to both stationary and non-stationary processes. Deterministic components are also allowed in the DGP. Furthermore, as a by-product, the estimation procedure provides an immediate check on the adequacy of the specified model. This is so because the criterion function, when evaluated at the estimated values, coincides with the Box-Pierce goodness of fit statistic. Empirical applications and Monte-Carlo simulations supporting the analytical results and showing the good performance of the estimator in finite samples are also provided.