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We propose probabilistic lower bounds for the number of false null hypotheses when testing multiple hypotheses of association simultaneously. The bounds are valid under general and unknown dependence structures between the test statistics. The power of the proposed estimator to detect the full proportion of false null hypotheses is discussed and compared to other estimators. The proposed estimator is shown to deliver a tight probabilistic lower bound for the number of false null hypotheses in a multiple testing situation even under strong dependence between test statistics. [ABSTRACT FROM AUTHOR]

We consider a very general class of empirical discrepancy statistics that includes the Cressie–Read discrepancy statistics and, in particular, the empirical likelihood ratio statistic. Higher-order asymptotics for expected lengths of associated confidence intervals are investigated. An explicit formula is worked out and its use for comparative purposes is discussed. It is seen that the empirical likelihood ratio statistic, which enjoys interesting second-order power properties, loses much of its edge under the present criterion. [ABSTRACT FROM AUTHOR]

Often in sequential trials some additional data become available after a stopping boundary has been reached. A method for incorporating such information from overrunning is developed, based on a maximum‐likelihood ordering of the sample space after overrunning. This yields a p‐value for the primary test and a median‐unbiased estimator and confidence intervals for the parameter under test. The context is that of observing a Brownian motion with drift, with either linear stopping boundaries in continuous time or discrete‐time group‐sequential boundaries. The methods apply to many clinical trials and are exemplified with data from a survival‐analysis‐based sequential clinical trial. [ABSTRACT FROM PUBLISHER]

The method of empirical likelihood can be viewed as one of allocating probabilities to an n-cell contingency table so as to minimise a goodness-of-fit criterion. It is shown that, when the Cressie-Read power-divergence statistic is used as the criterion, confidence regions enjoying the same convergence rates as those found for empirical likelihood can be obtained for the entire range of values of the Cressie-Read parameter λ, including − 1, maximum entropy, 0, empirical likelihood, and 1, Pearson's χ2. It is noted that, in the power-divergence family, empirical likelihood is the only member which is Bartlettcorrectable. However, simulation results suggest that, for the mean, using a, scaled F distribution yields more accurate coverage levels for moderate sample sizes. [ABSTRACT FROM AUTHOR]

Consider a sequential test applied to two streams of binary responses in a comparative clinical trial. After the completion of such a trial Woodroofe's (1992) technique for accurate confidence interval estimation for a treatment difference can be applied. In this paper the technique is extended to provide confidence intervals for the individual absolute success probabilities of the two treatments in the trial, for which no current methodology exists. Accuracy is explored by simulation of coverage probabilities and individual confidence limit probabilities. The simulations concern a triangular test and an O'Brien & Fleming test. [ABSTRACT FROM AUTHOR]

We investigate data tapering in two formulations of empirical likelihood for time series. One empirical likelihood is formed from tapered data blocks in the time domain and a second is based on the tapered periodogram in the frequency domain. Limiting distributions are provided for both empirical likelihood versions under tapering. Theoretical and simulation evidence indicates that a data taper improves the coverage accuracy of empirical likelihood confidence intervals for time series parameters, such as means and correlations. [ABSTRACT FROM AUTHOR]

We propose a new method, to construct confidence intervals for spectral mean and related ratio statistics of a stationary process, that avoids direct estimation of their asymptotic variances. By introducing a bandwidth, a self-normalization procedure is adopted and the distribution of the new statistic is asymptotically nuisance-parameter free. The bandwidth is chosen using information criteria and a moving average sieve approximation. Through a simulation study, we demonstrate good finite sample performance of our method when the sample size is moderate, while a comparison with an empirical likelihood-based method for ratio statistics is made, confirming a wider applicability of our method. [ABSTRACT FROM AUTHOR]

Test statistics from the weighted log-rank class are commonly used to compare treatment with control when there is right censoring. This paper uses saddlepoint methods to determine mid-p-values from the null permutation distributions of tests from the weighted log-rank class. Analytical saddlepoint computations replace the permutation simulations and provide mid-p-values that are virtually exact for all practical purposes. The speed of these saddlepoint computations makes it practicable to invert the weighted log-rank tests to determine nominal 95% confidence intervals for the treatment effect with right-censored data. Such analytical inversions lead to permutation confidence intervals that are easily computed and virtually identical to the exact intervals that would normally require massive amounts of simulation. [ABSTRACT FROM AUTHOR]