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In this article, we develop a cusum test for testing for parameter changes in linear processes based on Whittle's estimator. It is shown that under regularity conditions, the test statistic converges to the sup of a Brownian bridge. The result is particularly useful in handling the change point test in stationary ARMA processes. A simulation result is provided for illustration. [ABSTRACT FROM AUTHOR]

Let X be a nonnegative random variable with cumulative distribution function F. In this article, we introduce a concept of deviation from exponentiality for F, based on the Mean Residual Life function. Our aim is to estimate this deviation under the random censorship model. For this purpose, we propose two slightly different estimators. For each one, we determine the limit distribution of an appropriately normalized version. Then, this work leads to the construction of a test of H0 : F is exponential vs. H1 : F is not exponential. It is applied to the Koziol and Green data set (Koziol, S. A., Green, S. B. (1976). A cramer-von mises statistic for randomly censored data. Biometrika 23:465–474). [ABSTRACT FROM AUTHOR]

The smooth nonparametric estimator &Qtilde;[sub n](p) of a quantile function Q(p) is defined as the solution of &Ftilde;[sub n] (&Qtilde;[sub n] (p)) = p, where &Ftilde;[sub n] is the distribution function corresponding to a kernel estimator of a density function. The asymptotic properties of the smooth quantile process, √n(&Qtilde;[sub n] (p) - Q(p)), based on randomly right censored lifetime data are studied. The bootstrap approaches to approximate the distributions of the smooth quantile processes are investigated and are used to construct simultaneous confidence bands for quantile functions. Data-based selection of the bandwidth required for computing &Ftilde;[sub n] is also investigated using bootstrap methods. A Monte Carlo simulation is carried out to assess small sample performance of the proposed confidence bands. An application to construct confidence bands for the quantile function of the time between a manuscript's submission and its first review is provided using a JASA data set. The developed results can be applied to construct simultaneous confidence bands for the difference of two quantile functions and to check whether there is a location shift or scale change for two distributions under study. [ABSTRACT FROM AUTHOR]