Showing papers on "Coverage probability published in 1986"

On the Bootstrap and Confidence Intervals

Abstract: We derive an explicit formula for the first term in an unconditional Edgeworth-type expansion of coverage probability for the nonparametric bootstrap technique applied to a very broad class of "Studentized" statistics. The class includes sample mean, $k$-sample mean, sample correlation coefficient, maximum likelihood estimators expressible as functions of vector means, etc. We suggest that the bootstrap is really an empiric one-term Edgeworth inversion, with the bootstrap simulations implicitly estimating the first term in an Edgeworth expansion. This view of the bootstrap is reinforced by our discussion of the iterated bootstrap, which inverts an Edgeworth expansion to arbitrary order by simulating simulations.

Improved Confidence Sets for the Coefficients of a Linear Model with Spherically Symmetric Errors

Abstract: Under the assumption of normal errors, confidence spheres for $p(p \geq 3)$ coefficients of a linear model centered at the positive part James-Stein estimators were recently proved, by Hwang and Casella, to dominate the usual confidence set with the same radius. In this paper, the same domination results are established under various spherically symmetric distributions. These distributions include uniform distributions, double exponential distributions, and multivariate $t$ distributions.

Two stage fixed width confidence intervals for the common location parameter of several exponential distributins

Abstract: Two stage sampling schemes are introduced for use in estimating the common location parameter (guarantee time) of two or more exponential distributions with a confidence interval of prespecified width whose coverage probability is at least a given nominal value. Exact expressions for all moments of order r ≥ 1 of the associated two stage sample sizes and for the actual coverage probabilities are derived. The performance of the procedures in a variety of two population, moderate fixed sample size cases is examined via numerical studies involving both exact calculations and Monte Carlo simulations. No new tables are needed to implement any of the proposed methods. A modified two stage procedure is recommended for practical use

Sequential confidence intervals with beta protection in one-parameter families

Abstract: A sequential confidence interval (CI) for a real parameter ? of the form [L,00) is proposed, based on a consistent and asymptotically normal sequence ?,, T?, ? ? -of real valued statistics. This CI is required to satisfy the coverage probability P{L >l-a for every ?, and to provide beta protection at f(?): ? {L r + c"r(T) and a terminal decision L = p(T?), in which the functions t and ? ? 2 depend on f and the asymptotic variance s . Asymptotic values are derived for ? {L > ?} and ? {L < f(?)} as ? varies over values for which t(?) -? ??.

Statistical properties of a procedure for analyzing pulse voltametric data

Abstract: O'Dea et al. (1983, J. Phys. Chem.97, 3911-3918) proposed an empirical procedure for obtaining estimates and confidence intervals for kinetic parameters in a model for pulse voltammetric data. Their goal was to find a procedure that would run in real time, not necessarily one that would have well-defined statistical properties. In this paper we investigate some of the statistical properties of their procedure. We show that their estimation method is equivalent to maximum likelihood estimation, and their confidence intervals, while related to likelihood ratio confidence regions, have a coverage probability that is not fixed and that is potentially quite large. We suggest modifications of their procedure that lead to more traditional confidence intervals. We examine the effect on their procedure of the presence of nuisance paramters. Finally we discuss the possibility of serially correlated errors.