Novel specification tests for synchronous additive concurrent model formulation based on martingale difference divergence

This paper presents new specification tests for a general synchronous additive concurrent model formulation. As a novelty, our proposal does not require a preliminary model or error structure estimation. No tuning parameters are involved either. We develop a suitable test statistic using the marting...

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Bibliographic Details
Published in:Test (Madrid, Spain) Vol. 32; no. 3; pp. 908 - 941
Main Authors: Freijeiro-González, Laura, Febrero-Bande, Manuel, González-Manteiga, Wenceslao
Format: Journal Article
Language:English
Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.09.2023
Subjects:
Economics
Finance
Insurance
Management
Mathematics and Statistics
Original Paper
Statistical Theory and Methods
Statistics
Statistics for Business
Covariates selection
62J02
62R10
Significance tests
62G10
62H20
Martingale difference divergence (MDD)
Functional concurrent model
ISSN:1133-0686, 1863-8260
Online Access:Get full text
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Summary:This paper presents new specification tests for a general synchronous additive concurrent model formulation. As a novelty, our proposal does not require a preliminary model or error structure estimation. No tuning parameters are involved either. We develop a suitable test statistic using the martingale difference divergence coefficient. As a result, this statistic measures the departure from the conditional mean independence in the concurrent model framework, considering the information of all observed time instants. In particular, global as well as partial dependence tests are introduced. Then, we allow one to quantify the effect of a group of covariates or to apply covariates selection one by one. We obtain its asymptotic distribution under the null and propose a bootstrap algorithm to compute the p -values in practice. Through simulations, we illustrate our method, and its performance is compared to existing competitors. In addition, we use this in the analysis of three real datasets related to gait data, flu activity, and casual bike rentals.
ISSN:1133-0686
1863-8260
DOI:10.1007/s11749-023-00857-y