arXiv subjects
Publications and source records attributed to Gary Lorden.
A response to a letter to the editor by Schilling regarding Bartroff, Lorden, and Wang ("Optimal and fast confidence intervals for hypergeometric successes" 2022, arXiv:2109.05624)
We present an efficient method of calculating exact confidence intervals for the hypergeometric parameter representing the number of "successes," or "special items," in the population. The method inverts minimum-width acceptance intervals after shifting them to make their endpoints nondecreasing while preserving their level. The resulting set of confidence intervals achieves minimum possible average size, and even in comparison with confidence sets not required to be intervals it attains the minimum possible cardinality most of the time, and always within $1$. The method compares favorably with existing methods not only in the size of the intervals but also in the time required to compute them. The available \textsf{R} package \texttt{hyperMCI} implements the proposed method.
Suppose a process yields independent observations whose distributions belong to a family parameterized by θ\inΘ. When the process is in control, the observations are i.i.d. with a known parameter value θ_0. When the process is out of control, the parameter changes. We apply an idea of Robbins and Siegmund [Proc. Sixth Berkeley Symp. Math. Statist. Probab. 4 (1972) 37-41] to construct a class of sequential tests and detection schemes whereby the unknown post-change parameters are estimated. This approach is especially useful in situations where the parametric space is intricate and mixture-type rules are operationally or conceptually difficult to formulate. We exemplify our approach by applying it to the problem of detecting a change in the shape parameter of a Gamma distribution, in both a univariate and a multivariate setting.