Integrating the evidence from evidence factors in observational studies

Summary A sensitivity analysis for an observational study assesses how much bias, due to nonrandom assignment of treatment, would be necessary to change the conclusions of an analysis that assumes treatment assignment was effectively random. The evidence for a treatment effect can be strengthened if two different analyses, which could be affected by different types of biases, are both somewhat insensitive to bias. The finding from the observational study is then said to be replicated. Evidence factors allow for two independent analyses to be constructed from the same dataset. When combining the evidence factors, the Type I error rate must be controlled to obtain valid inference. A powerful method is developed for controlling the familywise error rate for sensitivity analyses with evidence factors. It is shown that the Bahadur efficiency of sensitivity analysis for the combined evidence is greater than for either evidence factor alone. The proposed methods are illustrated through a study of the effect of radiation exposure on the risk of cancer. An R package, evidenceFactors, is available from CRAN to implement the methods of the paper.

Some characterization based exponentiality tests and their Bahadur efficiencies

We propose new exponentiality tests based on a recent characterization. We construct integral and Kolmogorov-type statistics, derive their asymptotics and calculate the Bahadur efficiency against some common alternatives. We also obtain a class of locally optimal alternatives for each test. In case of small samples tests are compared with some common exponentiality tests.

Asymptotic efficiency of exponentiality tests based on order statistics characterization

We propose new scale-invariant tests for exponentiality based on the characterization in terms of order statistics. Limiting distributions and large deviations of new statistics are described and their local Bahadur efficiency for common alternatives is calculated.