Asymptotically exact confidence intervals of cusum and cusumsq tests: a numerical derivation using simulation technique

ASYMPTOTICALLY EXACT CONFIDENCE INTERVALS OF CUSUM AND CUSUMSQ TESTS: A Numerical Derivation Using Simulation Technique

In testing a structural change, the approximated confidence intervals are conventionally used for CUSUM and CUSUMSQ tests. This paper numerically derives the asymptotically exact confidence intervals of CUSUM and CUSUMSQ tests. It can be easily extended to nonnormal and/or nonlinear models.

Exact Confidence Intervals

Confidence Intervals and Hypothesis Tests

Overview: Recall that a point estimator for a parameter of interest is a statistic which is a function of the random variables from which our sampling method chooses values. The properties of such an estimator, such as having a small bias or a small mean square error, are usually dependent only upon certain features of the sampling distribution of the statistic, such as its mean or variance. Ho...

Exact short Poisson confidence intervals

The authors propose a new method for constructing a confidence interval for the expectation θ of a Poisson random variable. The interval they obtain cannot be shortened without the infimum over θ of the coverage probability falling below 1 − α. In addition, the endpoints of the interval are strictly increasing functions of the observed variable. An easy-to-program algorithm is provided for comp...

Accurate Tests and Intervals Based on Linear Cusum Statistics

Suppose that we are monitoring incoming observations for a change in mean via a cusum test statistic. The usual nonparametric methods give first and second order approximations for the oneand two-sided cases. We show how to improve the order of these approximations for linear statistics.