Likelihood ratio tests for positivity in polynomial regressions

Naohiro Kato and Satoshi Kuriki

Journal of Multivariate Analysis, 2013, vol. 115, issue C, 334-346

Abstract: A polynomial that is nonnegative over a given interval is called a positive polynomial. The set of such positive polynomials forms a closed convex cone K. In this paper, we consider the likelihood ratio test for the hypothesis of positivity that the estimand polynomial regression curve is a positive polynomial. By considering hierarchical hypotheses including the hypothesis of positivity, we define nested likelihood ratio tests, and derive their null distributions as mixtures of chi-square distributions by using the volume-of-tubes method. The mixing probabilities are obtained by utilizing the parameterizations for the cone K and its dual provided in the framework of Tchebycheff systems for polynomials of degree at most 4. For polynomials of degree greater than 4, the upper and lower bounds for the null distributions are provided. Moreover, we propose associated simultaneous confidence bounds for polynomial regression curves. Regarding computation, we demonstrate that symmetric cone programming is useful to obtain the test statistics. As an illustrative example, we conduct data analysis on growth curves of two groups. We examine the hypothesis that the growth rate (the derivative of growth curve) of one group is always higher than the other.

Keywords: Chi-bar square distribution; Cone of positive polynomials; Moment cone; Symmetric cone programming; Tchebycheff system; Volume-of-tubes method (search for similar items in EconPapers)
Date: 2013
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0047259X12002473
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:jmvana:v:115:y:2013:i:c:p:334-346

Ordering information: This journal article can be ordered from
http://www.elsevier.com/wps/find/supportfaq.cws_home/regional
https://shop.elsevie ... _01_ooc_1&version=01

DOI: 10.1016/j.jmva.2012.10.016

Access Statistics for this article

Journal of Multivariate Analysis is currently edited by de Leeuw, J.

More articles in Journal of Multivariate Analysis from Elsevier
Bibliographic data for series maintained by Catherine Liu ().