TY - JOUR
T1 - Cluster analysis with regression of non-Gaussian functional data on covariates
AU - Jiang, Jiakun
AU - Lin, Huazhen
AU - Peng, Heng
AU - Fan, Gang Zhi
AU - Li, Yi
N1 - Funding Information:
This research was supported by the National Natural Science Foundation of China (Nos. 11931014 and 11829101) and the Fundamental Research Funds for the Central Universities (No. JBK1806002) of China. We sincerely thank Professor Yuhong Yang for his very helpful comments and suggestions. We are grateful to the editor, the review editor, and two anonymous reviewers for their constructive comments and suggestions that led to an improved article.
Publisher Copyright:
© 2021 Statistical Society of Canada
PY - 2022/3
Y1 - 2022/3
N2 - Cluster analysis with functional data often imposes normality assumptions on outcomes and is typically carried out without covariates or supervision. However, nonnormal functional data are frequently encountered in practice, and unsupervised learning, without directly tying covariates to clusters, often makes the resulting clusters less interpretable. To address these issues, we propose a new semiparametric transformation functional regression model, which enables us to cluster nonnormal functional data in the presence of covariates. Our model incorporates several unique features. First, it omits the normality assumptions on the functional response, which adds more flexibility to the modelling. Second, our model allows clusters to have distinct relationships between functional responses and covariates, and thus makes the clusters formed more interpretable. Third, unlike various competing methods, we allow the number of clusters to be unspecified and data-driven. We develop a new method, which combines penalized likelihood and estimating equations, to estimate the number of clusters, regression parameters, and transformation functions simultaneously; we also establish the large-sample properties such as consistency and asymptotic normality. Simulations confirm the utility of our proposed approach. We use our proposed method to analyze Chinese housing market data and garner some interesting findings.
AB - Cluster analysis with functional data often imposes normality assumptions on outcomes and is typically carried out without covariates or supervision. However, nonnormal functional data are frequently encountered in practice, and unsupervised learning, without directly tying covariates to clusters, often makes the resulting clusters less interpretable. To address these issues, we propose a new semiparametric transformation functional regression model, which enables us to cluster nonnormal functional data in the presence of covariates. Our model incorporates several unique features. First, it omits the normality assumptions on the functional response, which adds more flexibility to the modelling. Second, our model allows clusters to have distinct relationships between functional responses and covariates, and thus makes the clusters formed more interpretable. Third, unlike various competing methods, we allow the number of clusters to be unspecified and data-driven. We develop a new method, which combines penalized likelihood and estimating equations, to estimate the number of clusters, regression parameters, and transformation functions simultaneously; we also establish the large-sample properties such as consistency and asymptotic normality. Simulations confirm the utility of our proposed approach. We use our proposed method to analyze Chinese housing market data and garner some interesting findings.
KW - Cluster analysis
KW - functional data
KW - longitudinal data
KW - semiparametric transformation functional regression
KW - supervised learning
UR - http://www.scopus.com/inward/record.url?scp=85121360356&partnerID=8YFLogxK
U2 - 10.1002/cjs.11680
DO - 10.1002/cjs.11680
M3 - Journal article
AN - SCOPUS:85121360356
SN - 0319-5724
VL - 50
SP - 221
EP - 240
JO - Canadian Journal of Statistics
JF - Canadian Journal of Statistics
IS - 1
ER -