• The approximation for the distribution function of a test statistic is extremely important in statistics. A distribution-free test for stochastic ordering in the competing risks model has been proposed by Bagai et al. (1989). Herein, we performed a standard saddlepoint approximation in the tails for the Bagai statistic under finite sample sizes. We then compared the saddlepoint approximation ...

Fisher randomization tests for Neyman’s null hypothesis of no average treatment effects are considered in a finite population setting associated with completely randomized experiments with more than two treatments. The consequences of using the F statistic to conduct such a test are examined both theoretically and computationally, and it is argued that under treatment effect heterogeneity, use ...

Based on an omnibus likelihood ratio test statistic for the equality of several variance-covariance matrices following the complex Wishart distribution and a factorization of this test statistic with associated p-values, change analysis in a time series of multilook, polarimetric SAR data in the covariance matrix representation is carried out. The omnibus test statistic and its factorization de...

Treatment means in factorial experiments are lattice ordered when there is an increase in mean response as the level of any factor is increased while holding the other factors fixed. Such means occur naturally in many experiments. A nonparametric test for lattice-ordered means involving a Kendall-type statistic will be summarized for k-factor factorial experiments. Specifically, the form of the...

Based on an omnibus likelihood ratio test statistic for the equality of several variance-covariance matrices following the complex Wishart distribution with an associated p-value and a factorization of this test statistic, change analysis in a short sequence of multilook, polarimetric SAR data in the covariance matrix representation is carried out. The omnibus test statistic and its factorizati...

Capturing dependence among a large number of high dimensional random vectors is a very important and challenging problem. By arranging n random vectors of length p in the form of a matrix, we develop a linear spectral statistic of the constructed matrix to test whether the n random vectors are independent or not. Specifically, the proposed statistic can also be applied to n random vectors, each...

A. Distribution of the test statistic In the sequential test, we first compute the test statistic from a mini-batch of size m. If a decision cannot be made with this statistic, we keep increasing the mini-batch size by m datapoints until we reach a decision. This procedure is guaranteed to terminate as explained in Section 4. The parameter ✏ controls the probability of making an error in a sing...

Classical statistical theory offers validity under restricted assumptions. However, in practice, it is a common approach to perform statistical analysis based on data-driven model selection [1], which guarantees none of results of classical statistical theory. Those results include hypothesis testings and confidence intervals which are useful tools of measuring fitness of models. Considering th...