## The Annals of Applied Statistics

### Order selection in nonlinear time series models with application to the study of cell memory

Ying Hung

#### Abstract

Cell adhesion experiments are biomechanical experiments studying the binding of a cell to another cell at the level of single molecules. Such a study plays an important role in tumor metastasis in cancer study. Motivated by analyzing a repeated cell adhesion experiment, a new class of nonlinear time series models with an order selection procedure is developed in this paper. Due to the nonlinearity, there are two types of overfitting. Therefore, a double penalized approach is introduced for order selection. To implement this approach, a global optimization algorithm using mixed integer programming is discussed. The procedure is shown to be asymptotically consistent in estimating both the order and parameters of the proposed model. Simulations show that the new order selection approach outperforms standard methods. The finite-sample performance of the estimator is also examined via a simulation study. The application of the proposed methodology to a T-cell experiment provides a better understanding of the kinetics and mechanics of cell adhesion, including quantifying the memory effect on a repeated unbinding force experiment and identifying the order of the memory.

#### Article information

Source
Ann. Appl. Stat., Volume 6, Number 3 (2012), 1256-1279.

Dates
First available in Project Euclid: 31 August 2012

https://projecteuclid.org/euclid.aoas/1346418582

Digital Object Identifier
doi:10.1214/12-AOAS546

Mathematical Reviews number (MathSciNet)
MR3012529

Zentralblatt MATH identifier
06096530

#### Citation

Hung, Ying. Order selection in nonlinear time series models with application to the study of cell memory. Ann. Appl. Stat. 6 (2012), no. 3, 1256--1279. doi:10.1214/12-AOAS546. https://projecteuclid.org/euclid.aoas/1346418582

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