Nonparametric homogeneity pursuit in functional-coefficient models

This paper explores the homogeneity of coefficient functions in nonlinear models with functional coefficients and identifies underlying semiparametric modelling structure. With initial kernel estimates, we combine classic hierarchical clustering method a generalised version information criterion to estimate number clusters, each which has common coefficient, determine membership cluster. To identify possible semi-varying framework, further introduce penalised local least squares zero coefficients, non-zero constant vary an index variable. Through nonparametric kernel-based cluster analysis approach, can substantially reduce unknown parametric components models, thereby achieving aim dimension reduction. Under some regularity conditions, establish asymptotic properties for proposed methods including consistency pursuit. Numerical studies, Monte-Carlo experiments two empirical applications, are given demonstrate finite-sample performance our methods.