A nonparametric test for similarity of marginals—With applications to the assessment of population bioequivalence

In this paper we suggest a completely nonparametric test for the assessment of similar marginals of a multivariate distribution function. This test is based on the asymptotic normality of Mallows distance between marginals. It is also shown that the n out of n bootstrap is weakly consistent, thus providing a theoretical justification to the work in Czado, C. and Munk, A. [2001. Bootstrap methods for the nonparametric assessment of population bioequivalence and similarity of distributions. J. Statist. Comput. Simulation 68, 243–280]. The test is extended to cross-over trials and is applied to the problem of population bioequivalence, where two formulations of a drug are shown to be similar up to a tolerable limit. This approach was investigated in small samples using bootstrap techniques in Czado, C., Munk, A. [2001. Bootstrap methods for the nonparametric assessment of population bioequivalence and similarity of distributions. J. Statist. Comput. Simulation 68, 243–280], showing that the bias corrected and accelerated bootstrap yields a very accurate and powerful finite sample correction. A data example is discussed.     

Guaranteed Conditional Performance of Control Charts via Bootstrap Methods

To use control charts in practice, the in‐control state usually has to be estimated. This estimation has a detrimental effect on the performance of control charts, which is often measured by the false alarm probability or the average run length. We suggest an adjustment of the monitoring schemes to overcome these problems. It guarantees, with a certain probability, a conditional performance given the estimated in‐control state. The suggested method is based on bootstrapping the data used to estimate the in‐control state. The method applies to different types of control charts, and also works with charts based on regression models. If a non‐parametric bootstrap is used, the method is robust to model errors. We show large sample properties of the adjustment. The usefulness of our approach is demonstrated through simulation studies.     

MMCTest—A Safe Algorithm for Implementing Multiple Monte Carlo Tests

Consider testing multiple hypotheses using tests that can only be evaluated by simulation, such as permutation tests or bootstrap tests. This article introduces MMCTest , a sequential algorithm that gives, with arbitrarily high probability, the same classification as a specific multiple testing procedure applied to ideal p‐values. The method can be used with a class of multiple testing procedures that include the Benjamini and Hochberg false discovery rate procedure and the Bonferroni correction controlling the familywise error rate. One of the key features of the algorithm is that it stops sampling for all the hypotheses that can already be decided as being rejected or non‐rejected. MMCTest can be interrupted at any stage and then returns three sets of hypotheses: the rejected, the non‐rejected and the undecided hypotheses. A simulation study motivated by actual biological data shows that MMCTest is usable in practice and that, despite the additional guarantee, it can be computationally more efficient than other methods.     

Developing a Social Protection Index for Asia

Social protection is increasingly seen as an important tool for poverty reduction, but to date there have been few quantitative cross‐country assessments of social protection provision. This article develops a social protection index that systematically and consistently quantifies activities at the national level. Four summary indicators representing the cost, coverage, poverty targeting and impact are scaled and weighted to produce an additive index of the overall level of social protection provision. The index is calculated for six very different Asian countries: Bangladesh, Indonesia, Mongolia, Nepal, Pakistan and Vietnam. Considerable contrasts are revealed between their levels of social protection provision.     

An Evolutionary Analysis of Buyer Insurance and Seller Reputation in Online Markets

Applying an evolutionary framework, we investigate how a reputation mechanism and a buyer insurance (as used on Internet market platforms such as eBay) interact to promote trustworthiness and trust in markets with moral hazard problems. Our analysis suggests that the costs involved in giving reliable feedback determine the gains from trade that can be obtained in equilibrium. Buyer insurance, on the other hand, can affect the trading dynamics and equilibrium selection. We find that, under reasonable conditions, buyer insurance crowds out trust, and trustworthiness. Ockenfels gratefully acknowledges the support of the Deutsche Forschungsgemeinschaft. Mengel’s research was supported by the Spanish Ministry of Education and Science (grant SEJ 2004-02172).