Abstract
Solving semiparametric models can be computationally challenging because the dimension of parameter space may grow large with increasing sample size. Classical Newton’s method becomes quite slow and unstable with an intensive calculation of the large Hessian matrix and its inverse. Iterative methods separately updating parameters for the finite dimensional component and the infinite dimensional component have been developed to speed up single iterations, but they often take more steps until convergence or even sometimes sacrifice estimation precision due to sub-optimal update direction. We propose a computationally efficient implicit profiling algorithm that achieves simultaneously the fast iteration step in iterative methods and the optimal update direction in Newton’s method by profiling out the infinite dimensional component as the function of the finite-dimensional component. We devise a first-order approximation when the profiling function has no explicit analytical form. We show that our implicit profiling method always solves any local quadratic programming problem in two steps. In two numerical experiments under semiparametric transformation models and GARCH-M models, as well as a real application using NTP data, we demonstrated the computational efficiency and statistical precision of our implicit profiling method.
Original language | English (US) |
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Pages (from-to) | 3203-3234 |
Number of pages | 32 |
Journal | Statistical Papers |
Volume | 65 |
Issue number | 5 |
DOIs | |
State | Published - Jul 2024 |
Bibliographical note
Publisher Copyright:© The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature 2023.
Keywords
- Bundled parameters
- Profiling estimation
- Semiparametric models