M-estimators for Models with a Mix of Discrete and Continuous Parameters

Ting Fung Ma (), Juan Francisco Mandujano Reyes () and Jun Zhu ()
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Ting Fung Ma: University of South Carolina
Juan Francisco Mandujano Reyes: University of Wisconsin-Madison
Jun Zhu: University of Wisconsin-Madison

Sankhya A: The Indian Journal of Statistics, 2024, vol. 86, issue 1, No 6, 164-190

Abstract: Abstract A variety of parametric models are specified by a mix of discrete parameters, which take values from a countable set, and continuous parameters, which take values from a continuous space. However, the asymptotic properties of the parameter estimators are not well understood in the literature. In this paper, we consider the general framework of M-estimation and derive the asymptotic properties of the M-estimators of both discrete and continuous parameters. In particular, we show that the M-estimators are consistent and the continuous parameters are asymptotically normal. We also extend a large deviation principle from models with only discrete parameters to models with discrete and continuous parameters. The finite-sample properties are assessed by a simulation study, and for illustration, we perform a break-point analysis for the clinical outcomes of COVID-19 patients.

Keywords: Asymptotic distribution; Break-point analysis; COVID-19; Generalized Estimating Equation (GEE); Large deviations (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s13171-023-00317-7

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