Rukhin et al. (2010) proposed the non-overlapping template matching test as one of methods for statistical testing of randomness in cryptographic applications. This test is the very interesting, but statistical properties of this test and any methods on setting the template have not been shown. Our new contribution in this paper is to propose a modified version of this test including the setting of the template and to show how this modified test works effectively by some simulation studies.
SummaryThe maximum full likelihood estimator in the proportional hazard model is explored in relation to the maximum partial likelihood estimator. In the scalar parameter, case both the estimators have a common sign, and the absolute value of the former is strictly greater than that of the latter except for trivial cases. We point out also that the maximum full likelihood estimator after a simple modification of the likelihood equation provides a good approximation to the maximum partial likelihood estimator. Similar results are valid for the likelihood ratio tests.
A k-sample modified Baumgartner statistic is proposed. For k = 3, the limiting distribution of a k-sample Baumgartner statistic is derived with a procedure similar to Anderson-Darling (1952). For the case of k ≥ 4, a saddlepoint approximation is used to approximate the limiting distribution of the k-sample Baumgartner statistic. The critical values are given for k = 3 to 10, 25, 50 and 100.
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