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Revista Colombiana de Estadística
Print version ISSN 0120-1751
Rev.Colomb.Estad. vol.43 no.2 Bogotá July/Dec. 2020 Epub Dec 05, 2020
https://doi.org/10.15446/rce.v43n2.83044
Original articles of research
Optimal Detection of Bilinear Dependence in Short Panels of Regression Data
Detección óptima de dependencia bilineal en regresión con datos de panel cortos
1Department of Mathematics, Faculty of Sciences and Techniques, Abdelmalek Essaadi University, Tangier, Morocco
2Centre Régional des Métiers de l'Education et de la Formation, Tangier, Morocco
In this paper, we propose parametric and nonparametric locally and asymptotically optimal tests for regression models with superdiagonal bilinear time series errors in short panel data (large n, small T). We establish a local asymptotic normality property- with respect to intercept µ, regression coefficient β, the scale parameter σ of the error, and the parameter b of panel superdiagonal bilinear model (which is the parameter of interest)- for a given density f 1 of the error terms. Rank-based versions of optimal parametric tests are provided. This result, which allows, by Hájek's representation theorem, the construction of locally asymptotically optimal rank-based tests for the null hypothesis b = 0 (absence of panel superdiagonal bilinear model). These tests -at specified innovation densities f 1- are optimal (most stringent), but remain valid under any actual underlying density. From contiguity, we obtain the limiting distribution of our test statistics under the null and local sequences of alternatives. The asymptotic relative efficiencies, with respect to the pseudo-Gaussian parametric tests, are derived. A Monte Carlo study confirms the good performance of the proposed tests.
Key words: Bilinear process; local asymptotic normality; local asymptotic linearity; panel data; pseudo-Gaussian tests; rank tests
En este artículo, se proponen pruebas paramétricas y no paramétricas locales y asintóticamente óptimas para modelos de regresión con errores de series temporales bilineales superdiagonales en datos de panel cortos (n grande, T pequeño). Se establece una propiedad de normalidad asintótica local con respecto a la intercepción µ, el coeficiente de regresión β, el parámetro de escala σ del error y el parámetro b del modelo bilineal superdiagonal con datos de panel (que es el parámetro de interés) para una densidad determinada f 1 de los términos de error. Se proporcionan versiones basadas en rangos de pruebas paramétricas óptimas. Este resultado permite, por el teorema de representación de Hájek, la construcción de pruebas locales basadas en rangos asintóticamente óptimas para la hipótesis nula b = 0 (ausencia del modelo bilineal superdiagonal con datos de panel). Estas pruebas, en densidades de innovación especicadas f 1 , son óptimas (más estrictas), pero siguen siendo válidas en cualquier densidad subyacente. A partir de la contigüidad, se obtiene la distribución limitante de las estadísticas de prueba, bajo la hipótesis nula y una secuencia de alternativas locales. Se deriva eficiencia relativa asintótica de las pruebas, con respecto a las pruebas paramétricas pseudo-Gaussianas. Un análisis basado en simulaciones de Monte Carlo confirma el buen desempeño de las pruebas propuestas.
Palabras clave: Datos de panel; Linealidad asintótica local; Normalidad asintótica local; Proceso bilineal; Prueba pseudo-gaussiana; Pruebas de rango
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Received: November 2019; Accepted: April 2020
This is an open-access article distributed under the terms of the Creative Commons Attribution License
