Quasi-identifiability of multipath change-point models with general link functions

Document Type : Original Article

Author

Masoud Majidizadeh

Department of Statistics, Faculty of Mathematical Sciences, Shahid Beheshti University, Tehran, Iran

10.22067/smps.2026.96138.1055

Abstract

The non-singularity of the Fisher information matrix is a fundamental requirement for standard asymptotic inference. The framework developed by Asgharian (2014) shows that, for identifiable and smooth models, the set of singular parameter values is negligible. This result was previously established for multipath change-point (MCP) models in which the change hazard is specified through a proportional odds ratio structure. In this work, we substantially broaden that setting by proving the quasi-identifiability of MCP models under a general class of strictly monotone link functions, encompassing the probit, logit, and complementary log-log models as special cases. Our main result demonstrates that, for this broad family of models, the injectivity of the link function is sufficient to guarantee quasi- identifiability under standard regularity conditions. Consequently, the general singularity theory applies directly, implying that the Fisher information matrix is nonsingular for almost all parameter values. This, in turn, justifies standard likelihood-based inference for a considerably wider and more flexible class of models

Keywords

Fisher information matrix

Link function

Multipath change-point models, Quasi-identifiability, Singularities

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