Behaviour of the monotone single index model under repeated measurements
| Autor: | Cécile Durot, Hanna Jankowski, Fadoua Balabdaoui |
|---|---|
| Přispěvatelé: | Fédération Parisienne de Modélisation Mathématique (FP2M), Centre National de la Recherche Scientifique (CNRS), Modélisation aléatoire de Paris X (MODAL'X), Université Paris Nanterre (UPN) |
| Jazyk: | angličtina |
| Rok vydání: | 2021 |
| Předmět: |
Statistics and Probability
Generalized linear model Generalization Single-index model Inference isotonic regression single index model Goodness-of-fit 01 natural sciences 010104 statistics & probability Goodness of fit Isotonic regression Maximum likelihood Shape-constrained estimation Single index model Set identifiability Applied mathematics 0101 mathematics maximum likelihood Mathematics set identifiability 05 social sciences 050301 education Estimator [STAT.TH]Statistics [stat]/Statistics Theory [stat.TH] Monotone polygon shapeconstrained estimation Statistics Probability and Uncertainty 0503 education |
| Zdroj: | Sankhya A Sankhya A, 2021, pp.1-17. ⟨10.1007/s13171-021-00250-7⟩ Sankhya A, 85 (1) |
| ISSN: | 0976-836X 0976-8378 0972-7671 |
| DOI: | 10.1007/s13171-021-00250-7⟩ |
| Popis: | The generalized linear model is an important method in the statistical toolkit. The isotonic single index model can be thought of as a further generalization whereby the link function is assumed to be monotone non-decreasing as opposed to known and fixed. Such a shape constraint is quite natural in many statistical problems, and is fulfilled by the usual generalized linear models. In this paper we consider inference in this model in the setting where repeated measurements of predictor values and associated responses are observed. This setting is encountered in medical studies and is very different from the one considered in the classical monotone single index model studied in the literature. Here, we use nonparametric maximum likelihood estimation to infer the unknown regression vector and link function. We present a detailed study of finite and asymptotic properties of this estimator and propose goodness-of-fit tests for the model. Through an extended simulation study, we show that the model has competitive predictive performance. We illustrate our estimation approach using a Leukemia data set. Sankhya A, 85 (1) ISSN:0976-836X ISSN:0976-8378 |
| Databáze: | OpenAIRE |
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