Sequential Fixed-width Confidence Interval Research Articles

Sequential fixed-width confidence intervals for quantiles in the presence of censoring

This paper studies the asymptotic properties of sequential fixed-width confidence intervals for quantiles of the survival distribution function in the random censorship model. The interval is formed by a pair of quantiles of the product-limit estimator. The set up requires new results on the almost sure behaviour of such empirical quantiles.

Generalized order statistics, Bahadur representations, and sequential nonparametric fixed-width confidence intervals

Let X 1,…, X n be an i.i.d. sample from df F, let H F be the df of h( X 1,…, X m ), based on a given ‘kernel’ h( x 1,…, x m ), and consider confidence interval estimation of a parameter of the form H -1 F ( p). This paper introduces confidence intervals formed by a pair of ‘generalized order statistics’, develops Bahadur-type representation theory for these order statistics, and constructs corresponding sequential fixed-width confidence interval procedures. Previous work of Bahadur (1966) and Geertsema (1970) is sharpened and extended.

Sequential confidence intervals based on generalized m-statistics

A broad class of statistics including U-statistics and generalized quantiles (U- quantiles) can be viewed as solutions to an equation of the form . For these generalized M- estimators we develop weak and strong representations. As an application of the weak representation we show a central limit theorem for Mn. From the a.s. representation for mn the asymptotic properties of sequential fixed width confidence intervals based on these estimators are derived. The results in this paper unify and extend earlier work of Geertsema (1970), Jureckova (1979), Boos (1980) and Choudhury and Serfling (1985).

Fixed Length Interval Estimation of the Location Parameter of a Pareto Distribution

A sequential fixed-width confidence interval for the location parameter of a Pareto distribution with unknown shape parameter is developed. The procedure Is shown to be asymptotically consistent and asymptotically efficient in the sense of Chow and Robbins (1965).

Sequential Nonparametric Fixed-Width Confidence Intervals for $U$-Statistics

A sequential fixed-width confidence interval for the mean of a $U$-statistic, having coverage probability approximately equal to preassigned $\alpha$, is presented. The main result, Theorem 2, shows that the sequential procedure is asymptotically efficient in the sense of Chow and Robbins (1965) and assumes only finiteness of the second moment of the kernel, the weakest possible condition. The paper follows naturally from Sproule (1974) and Sproule (1969), the primary reference.

Sequential fixed-width confidence intervals for a nonparametric density function

In this paper sequential fixed-width confidence intervals for a nonparametric density function are derived. These are formed from certain values of a kernel density estimator. The efficiency of such procedures is measured in terms of the expected stopping time.

On the Uniformity of Sequential Procedures

An extension of a central limit theorem for a mean of a random number of observations is given. A natural application occurs in the area of fixed-width confidence intervals. We provide an example which shows that the standard procedure does not preserve the intended coverage probability uniformly over nontrivial sets of distribution functions. The major weak convergence result is used to provide conditions for and a simple proof of such uniformity. The results are also shown to hold for M-estimates of location. 1. Introduction. This paper has evolved from a study of the uniformity of central limit theorem approximations for sequential fixed-width confidence intervals and related ranking and selection procedures. The main weak convergence result concerns a process W#(s, t) = n-I Etn8] {Gt(Xi) -EGt(Xl)X