Showing papers on "Coverage probability published in 1989"
TL;DR: It is concluded that the two-stage analysis for analysing the data from a two-treatment, two-period crossover trial is too potentially misleading to be of practical use.
Abstract: In the two-treatment, two-period crossover trial, patients are randomly allocated either to one group that receives treatment A followed by treatment B, or to another group that receives the treatments in the reverse order. Grizzle first proposed a two-stage procedure for analysing the data from such a trial. This paper examines the long-run sampling properties of this procedure, in terms of mean square error of point estimates, coverage probability of confidence intervals and actual significance level of hypothesis tests for the differences between the effects of the two treatments. The advantages of incorporating baseline observations into the analysis are also explored. Because the preliminary test for carryover is highly correlated with the analysis of data from the first period only, actual significance levels are higher than nominal levels even when there is no differential carryover. When carryover is present, the nominal level very seriously understates the actual level, and this becomes even worse when baseline observations are ignored. Increasing sample size only exacerbates the problem since this adverse behaviour then occurs at smaller values of the carryover effect. It is concluded that the two-stage analysis is too potentially misleading to be of practical use.
218 citations
TL;DR: In this article, a conditional bias correction method was proposed to correct the deficiencies in the naive EB intervals. But this method cannot account for the variability in the estimation of the hyperparameters, resulting in sub-nominal coverage probability in the EB sense defined in Morris (1983a).
Abstract: : Parametric empirical Bayes methods of point estimation for a vector of unknown parameters date to the landmark paper of James and Stein (1961). The usual approach is to use the mean of the estimated posterior distribution of each parameter, where the estimation of the prior parameters (hyperparameters) is accomplished through the marginal distribution of the data. While point estimates computed this way usually perform well, interval estimates based on the estimated posterior (called naive EB intervals) are not. They fail to account for the variability in the estimation of the hyperparameters, generally resulting in sub-nominal coverage probability in the EB sense defined in Morris (1983a). In this paper we extend the work of Carlin and Gelfand (1989), who proposed a conditional bias correction method for developing EB intervals which corrects the deficiencies in the naive intervals. We show how bias correction can be implemented in general via a Type III parametric bootstrap procedure, a sample reuse method first employed by Laird and Louis (1987).
49 citations
TL;DR: In this paper, the authors discuss the construction of bootstrap confidence bands for the distribution function F of a population for simple random sampling, but do not assume that F is continuous.
Abstract: We first discuss the construction of bootstrap confidence bands for the distribution function F of a population for simple random sampling but do not assume that F is continuous. The known alternative approach is to use the quantiles from the tabled Kolmogorov distribution. This approach is known to be conservative. It has already been shown in Bickel and Freedman (1981) that the bootstrap confidence band has the correct coverage probability asymptotically. We show by simulation that the bootstrap works well for small samples and outperforms the conservative approach, particularly for distributions that have small carriers. We also investigate the analogous problem of finding bootstrap confidence bands for the distribution function F of a population for a more complicated situation, stratified random sampling. The conservative approach in the previous situation is extended to this case when sampling is with replacement (we expect that it holds for sampling without replacement) and the supports of...
42 citations
TL;DR: Simulation results indicate that the proposed method performs quite well, and it is apparently superior to the approach of Hochberg (1981, Communications in Statistics--Theory and Methods A10, 1719-1732) for values of zeta far from 1/2.
Abstract: Halperin, Gilbert, and Lachin (1987, Biometrics 43, 71-80) obtain confidence intervals for Pr(X less than Y) based on the two-sample Wilcoxon statistic for continuous data. Their approach is applied here to ordered categorical data and right-censored continuous data, using the generalization zeta = Pr(X less than Y) + 1/2Pr(X = Y) to account for ties. Deviations from nominal coverage probability for various sample sizes and values of zeta are obtained via simulation of either three or six ordered categories based on underlying Poisson or exponential distributions. The simulation results indicate that the proposed method performs quite well, and it is apparently superior to the approach of Hochberg (1981, Communications in Statistics--Theory and Methods A10, 1719-1732) for values of zeta far from 1/2.
31 citations
TL;DR: In this article, the authors show that confidence sets recentered at Stein-type estimators have larger coverage probability then the usual confidence ellipsoids, however, the minimum coverage probability of these improved sets is identical to that of the usual sets, so that only 1 − α can be actually reported.
25 citations
TL;DR: A new class of confidence sets for the mean of a p-variate normal distribution (p≥3) is introduced in this paper, which are neither spheres nor ellipsoids.
Abstract: A new class of confidence sets for the mean of a p-variate normal distribution (p≥3) is introduced They are neither spheres nor ellipsoids We show that we can construct our confidence sets so that their coverage probabilities are equal to the specified confidence coefficient Some of them are shown to dominate the usual confidence set, a sphere centered at the observations Numerical results are also given which show how small their volumes are
14 citations
TL;DR: In this article, the theory of a parametric empirical Bayes (PEB) normal distribution tolerance bound is derived, and the PEB K factors are smaller than those of the classical approach, so fewer samples are required to achieve equal precision.
Abstract: The theory of a parametric empirical Bayes (PEB) normal distribution tolerance bound is derived. Classical tolerance intervals are based on the assumption of a fixed unknown standard deviation, σ, and mean, μ. Such intervals assume no prior knowledge about the possible value of σ. The empirical Bayes approach assumes that there is prior knowledge of the value of σ, which can be characterized in terms of a translated beta density (with shape parameters α, β and range parameters A. B). The resulting PEB K factors are smaller than those of the classical approach, so fewer samples are required to achieve equal precision. An example illustrates potential cost savings. Extensive tables are not provided, since the PEB K factors depend on (α, β, A, B), as well as the sample size, confidence, and coverage probability. Since the exact computation is intensive, I suggest an approximation based on the noncentral t distribution. The degrees of freedom and noncentrality parameters are obtained by matching the first two...
10 citations
01 Jan 1989
7 citations
TL;DR: A bound on the order of convergence of the remainder term in the coverage probability of a fixed quantile of the survival distribution is obtained as the prescribed tolerance on the width of the interval shrinks to zero as mentioned in this paper.
Abstract: A bound on the order of convergence of the remainder term in the coverage probability of a fixed quantile of the survival distribution is obtained as the prescribed tolerance on the width of the interval shrinks to zero.
4 citations
TL;DR: In this paper, a class of invariant sequential procedures for constructing one sided and two sided confidence sets for a parameter γ in Rk, with the property that they have a coverage probability at least 1 −a and probability of covering a certain set of false values at most β, is considered.
Abstract: We consider a class of invariant sequential procedures for constructing one sided and two sided confidence sets for a parameter γ in Rk, with the property that they have a coverage probability at least 1 ‒a and probability of covering a certain set of false values at most β. The asymptotic properties of the stopping time are studied and the limiting values of the error probabilities are found as the parameter approaches the boundary points. Applications are made to the problem of simultaneous confidence sets for the mean and variance of a normal random vari¬able and for its multivariate analogue.
3 citations
01 Jan 1989
TL;DR: In this article, an approximate linear model, or nonparametric regression, relates instrument readings y to standards x and a method is derived for constructing interval estimates of displacements x 1 − x 2 between standards based on corresponding instrument readingsy 1,y 2, and the results of a calibration experiment.
Abstract: Suppose that an approximate linear model, or nonparametric regression, relates instrument readings y to standards x. A method is derived for constructing interval estimates of displacements x 1 − x 2 between standards based on corresponding instrument readings y 1,y 2, and the results of a calibration experiment.
TL;DR: In this paper, the authors consider the batching approach to interval estimation of the mean of a stochastic process based upon simulation output, using batch means processes generated from underlying AR(1) processes and M/M/1 queueing systems.
TL;DR: In this article, the authors derived second order asymptotic expansions for the coverage probability of a fixed-width sequential confidence interval for an unknown parameter x in the inverse linear regression model.
Abstract: Non-linear renewal theory is used to derive second order asymptotic expansions for the coverage probability of a fixed-width sequential confidence interval for an unknown parameter xin the inverse linear regression model. These expansions are obtained for a two-stage sequential procedure, proposed by Perng and Tong (1974) for the construction of a confidence interval for x.