Two sample tests for Semi-Markov processes with parametric sojourn time distributions: an application in sensory analysis

Cindy Frascolla, Guillaume Lecuelle, Pascal Schlich and Hervé Cardot ()
Additional contact information
Cindy Frascolla: Institut de Mathématiques de Bourgogne, UMR CNRS 5584, Université de Bourgogne
Guillaume Lecuelle: UMR AgroSup Dijon-CNRS-INRAE-Université de Bourgogne
Pascal Schlich: UMR AgroSup Dijon-CNRS-INRAE-Université de Bourgogne
Hervé Cardot: Institut de Mathématiques de Bourgogne, UMR CNRS 5584, Université de Bourgogne

Computational Statistics, 2022, vol. 37, issue 5, No 18, 2553-2580

Abstract: Abstract Developing statistical approaches that are able to compare the probability law of qualitative trajectories can be of real interest in many fields of science such as economics and sociology, quality control or epidemiology. This work is motivated by an application in sensory analysis in which subjects indicate the succession of perceived sensations over time using a list of attributes. In Lecuelle (Food Qual Prefer 67:59–66, 2018), Semi-Markov Processes (SMPs) are introduced to model such data, allowing to take into account the dynamics via the transitions from one attribute to another as well as the duration law of each attribute. One of the major challenges of sensory analysis is to determine if two tasted products are perceived differently. For that purpose, the present paper introduces a statistical testing procedure based on the likelihood ratio between two semi-Markov processes, assuming a parametric form for the sojourn time distributions. Three approaches are evaluated to compute the p-value: a first one based on the asymptotic law of the likelihood ratio, a second one based on the parametric bootstrap and a third one based on permutations. These approaches are compared on Monte-Carlo simulated data both in terms of empirical levels under the null hypothesis and statistical powers under alternatives. We also develop partial tests to compare two processes on either their initial probabilities and transition matrices or their sojourn time distributions. Simulations show that permutation approaches perform better in nearly all situations and especially for small and moderate sample sizes. Finally, the proposed tests are illustrated on real datasets which consist in perceived sensations over time during the tasting of different chocolates and cheeses.

Keywords: Gamma distribution; Likelihood ratio test; Parametric bootstrap; Permutation test; Qualitative continuous time process; Temporal dominance of sensations (TDS); Weibull distribution (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s00180-022-01210-x Abstract (text/html)
Access to the full text of the articles in this series is restricted.

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:spr:compst:v:37:y:2022:i:5:d:10.1007_s00180-022-01210-x

Ordering information: This journal article can be ordered from
http://www.springer.com/statistics/journal/180/PS2

DOI: 10.1007/s00180-022-01210-x

Access Statistics for this article

Computational Statistics is currently edited by Wataru Sakamoto, Ricardo Cao and Jürgen Symanzik

More articles in Computational Statistics from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().