## The Annals of Statistics

- Ann. Statist.
- Volume 33, Number 3 (2005), 1422-1454.

### Nonanticipating estimation applied to sequential analysis and changepoint detection

#### Abstract

Suppose a process yields independent observations whose distributions belong to a family parameterized by θ∈Θ. 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.

#### Article information

**Source**

Ann. Statist., Volume 33, Number 3 (2005), 1422-1454.

**Dates**

First available in Project Euclid: 1 July 2005

**Permanent link to this document**

https://projecteuclid.org/euclid.aos/1120224108

**Digital Object Identifier**

doi:10.1214/009053605000000183

**Mathematical Reviews number (MathSciNet)**

MR2195641

**Zentralblatt MATH identifier**

1077.62067

**Subjects**

Primary: 62L10: Sequential analysis 62N10 62F03: Hypothesis testing

Secondary: 62F05: Asymptotic properties of tests 60K05: Renewal theory

**Keywords**

Quality control cusum Shiryayev–Roberts surveillance statistical process control power one tests renewal theory nonlinear renewal theory Gamma distribution

#### Citation

Lorden, Gary; Pollak, Moshe. Nonanticipating estimation applied to sequential analysis and changepoint detection. Ann. Statist. 33 (2005), no. 3, 1422--1454. doi:10.1214/009053605000000183. https://projecteuclid.org/euclid.aos/1120224108