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In the first stage of a two-stage, drop-the-losers design, a candidate for the best treatment is selected. At the second stage, additional observations are collected to decide whether the candidate is actually better than the control. The design also allows the investigator to stop the trial for ethical reasons at the end of the first stage if there is already strong evidence of futility or superiority. Two types of tests have recently been developed, one based on the combined means and the other based on the combined p-values, but corresponding interval estimators are unavailable except in special cases. The problem is that, in most cases, the interval estimators depend on the mean configuration of all treatments in the first stage, which is unknown. In this paper, we prove a basic stochastic ordering lemma that enables us to bridge the gap between hypothesis testing and interval estimation. The proposed confidence intervals achieve the nominal confidence level in certain special cases. Simulations show that decisions based on our intervals are usually more powerful than those based on existing methods. [ABSTRACT FROM PUBLISHER]

An integrated likelihood depends only on the parameter of interest and the data, so it can be used as a standard likelihood function for likelihood-based inference. In this paper, the higher-order asymptotic properties of the signed integrated likelihood ratio statistic for a scalar parameter of interest are considered. These results are used to construct a modified integrated likelihood ratio statistic and to suggest a class of prior densities to use in forming the integrated likelihood. The properties of the integrated likelihood ratio statistic are compared to those of the standard likelihood ratio statistic. Several examples show that the integrated likelihood ratio statistic can be a useful alternative to the standard likelihood ratio statistic. [ABSTRACT FROM PUBLISHER]

We propose pseudo-score confidence intervals for parameters in models for discrete data. The confidence interval is obtained by inverting a test that uses a Pearson chi-squared statistic to compare fitted values for the working model with fitted values of the model when a parameter of interest takes various fixed values. For multinomial models, the pseudo-score method simplifies to the score method when the model is saturated and otherwise it is asymptotically equivalent to score and likelihood ratio test-based inferences. For cases in which ordinary score methods are impractical, such as when the likelihood function is not an explicit function of model parameters, the pseudo-score method is feasible. We illustrate the method for four such examples. Generalizations of the method are also presented for future research, including inference for complex sampling designs using a quasilikelihood Pearson statistic that compares fitted values for two models relative to the variance of the observations under the simpler model. [ABSTRACT FROM PUBLISHER]

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]

We use the empirical likelihood method to derive a test and thus a confidence interval based on the rank estimators of the regression coefficient in the accelerated failure time model. Standard chi-squared distributions are used to calculate the p-value and to construct the confidence interval. Simulations and examples show that the chi-squared approximation to the distribution of the log empirical likelihood ratio performs well, and has some advantages over the existing methods. [ABSTRACT FROM AUTHOR]

We study methods for constructing confidence intervals and confidence bands for estimators of receiver operating characteristics. Particular emphasis is placed on the way in which smoothing should be implemented, when estimating either the characteristic itself or its variance. We show that substantial undersmoothing is necessary if coverage properties are not to be impaired. A theoretical analysis of the problem suggests an empirical, plug‐in rule for bandwidth choice, optimising the coverage accuracy of interval estimators. The performance of this approach is explored. Our preferred technique is based on asymptotic approximation, rather than a more sophisticated approach using the bootstrap, since the latter requires a multiplicity of smoothing parameters all of which must be chosen in nonstandard ways. It is shown that the asymptotic method can give very good performance. [ABSTRACT FROM AUTHOR]

A multivariate Gaussian graphical Markov model for an undirected graph G, also called a covariance selection model or concentration graph model, is defined in terms of the Markov properties, i.e. conditional independences associated with G, which in turn are equivalent to specified zeros among the set of pairwise partial correlation coefficients. By means of Fisher's z‐transformation and Šidák's correlation inequality, conservative simultaneous confidence intervals for the entire set of partial correlations can be obtained, leading to a simple method for model selection that controls the overall error rate for incorrect edge inclusion. The simultaneous p‐values corresponding to the partial correlations are partitioned into three disjoint sets, a significant set S, an indeterminate set I and a nonsignificant set N. Our model selection method selects two graphs, a graph ĜSI whose edges correspond to the set S∪I, and a more conservative graph ĜS whose edges correspond to S only. Similar considerations apply to covariance graph models, which are defined in terms of marginal independence rather than conditional independence. The method is applied to some well‐known examples and to simulated data. [ABSTRACT FROM AUTHOR]

We consider construction of two-sided nonparametric confidence intervals in a smooth function model setting. A nonparametric likelihood approach based on Stein's least favourable family is proposed as an alternative to empirical likelihood. The approach enjoys the same asymptotic properties as empirical likelihood, but is analytically and computationally less cumbersome. The simplicity of the method allows us to propose and analyse asymptotic and bootstrapping techniques as a means of reducing coverage error to levels comparable with those obtained by more computationally-intensive techniques such as the iterated bootstrap. A simulation study confirms that coverage error may be substantially reduced by simple analytic adjustment of the nonparametric likelihood interval and that bootstrapping the distribution of the nonparametric likelihood ratio results in very desirable coverage accuracy. [ABSTRACT FROM PUBLISHER]

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]

The block bootstrap confidence interval for dependent data can outperform the conventional normal approximation only with nontrivial studentization which, in the case of complicated statistics, calls for specialist treatment and often results in unstable endpoints. We propose two double block bootstrap approaches for improving the accuracy of the block bootstrap confidence interval under very general conditions. The first approach calibrates the nominal coverage level and the second calculates studentizing factors directly from a block bootstrap series without the need for nontrivial analytical treatment. We prove that the two approaches reduce the coverage error of the block bootstrap interval by an order of magnitude with simple tuning of block lengths at the two block bootstrapping levels. Empirical properties of the procedures are investigated by simulations and application to an econometric time series. [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]