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Optimal Detection of Bilinear Dependence in Short Panels of Regression Data

  • Autores: Aziz Lmakri, Abdelhadi Akharif, Amal Mellouk
  • Localización: Revista Colombiana de Estadística, ISSN-e 2389-8976, ISSN 0120-1751, Vol. 43, Nº. 2, 2020, págs. 143-171
  • Idioma: inglés
  • DOI: 10.15446/rce.v43n2.83044
  • Títulos paralelos:
    • Detección óptima de dependencia bilineal en regresión con datos de panel cortos
  • Enlaces
  • Resumen
    • español

      Resumen 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.

    • English

      Abstract 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.

  • Referencias bibliográficas
    • Akharif, A.,Hallin, M.. (2003). 'Efficient detection of random coefficients in autoregressive models'. Annals of Statistics. 31. 675-704
    • Allal, J.,El Melhaoui, S.. (2006). 'Tests de rangs adaptatifs pour les modèles de régression linéaire avec erreurs arma'. Annales...
    • Azzalini, A.,Capitanio, A.. (2003). 'Distributions generated by perturbation of symmetry with emphasis on a multivariate skew t-distribution'....
    • Baltagi, B.,Li, Q.. (1995). 'Testing AR(1) against MA(1) disturbances in an error component model'. Journal of Econometrics. 68. 133
    • Benghabrit, Y.,Hallin, M.. (1992). 'Optimal rank-based tests against first-order superdiagonal bilinear dependence'. Journal ofStatistical...
    • Benghabrit, Y.,Hallin, M.. (1996). 'Rank-based tests for autoregressive against bilinear serial dependence'. Journal of Nonparametric...
    • Bennala, N.,Hallin, M.,Paindaveine, D.. (2012). 'Pseudo-gaussian and rank-based optimal tests for random individual effects in large n...
    • Cassart, D.,Hallin, M.,Paindaveine, D.. (2011). 'A class of optimal tests for symmetry based on local Edgeworth approximations'. Bernoulli....
    • Chernoff, H.,Savage, I. R.. (1958). 'Asymptotic normality and efficiency of certain nonparametric tests'. Annals of Mathematical Statistics....
    • Dutta, H.. (1999). 'Large sample tests for a regression model with autoregressive conditional heteroscedastic errors'. Communications...
    • Elmezouar, Z. C.,Kadi, A. M.,Gabr, M. M.. (2012). 'Linear regression with bilinear time series errors'. Panamerican Mathematical Journal....
    • Fihri, M.,Akharif, A.,Mellouk, A.,Hallin, M.. (2020). 'Efficient pseudo-gaussian and rank-based detection of random regression coefficients'....
    • Grahn, T.. (1995). 'A conditional least squares approach to bilinear time series'. Journal of Time Series Analysis. 16. 509
    • Granger, C. W. J.,Andersen, A. P.. (1978). An Introduction to Bilinear Time Series Models. Vandenhoeck and Ruprecht. Göttingen.
    • Guegan, D.. (1981). 'Etude d'un modèle non linéaire, le modèle superdiagonal d'ordre 1'. CRAS Série. 95
    • Guegan, D.,Pham, D. T.. (1992). 'Power of the score test against bilinear time series models'. Statistica Sinica. 2. 157
    • Hájek, J.,Sidák, Z.. (1967). Theory of Rank Tests. Academic Press. New York.
    • Hallin, M.,Mehta, C.. (2015). 'R-estimation for asymmetric independent component analysis'. Journal of the American Statistical Association....
    • Hallin, M.,Mélard, G.. (1988). 'Rank-based tests for randomness against first-order serial dependence'. Journal of the American Statistical...
    • Hallin, M.,Taniguchi, M.,Serroukh, A.,Choy, K.. (1999). 'Local asymptotic normality for regression models with long-memory disturbance'....
    • Hallin, M.,Werker, B. J. M.. (2003). 'Semi-parametric efficiency, distribution-freeness and invariance'. Bernoulli. 9. 137
    • Hristova, D.. (2005). 'Maximum likelihood estimation of a unit root bilinear model with an application to prices'. Studies in Nonlinear...
    • Hwang, S. Y.,Basawa, I. V.. (1993). 'Parameter estimation in a regression model with random coefficient autoregressive errors'. Journal...
    • Kim, I.. (2014). 'A study on the test of homogeneity for nonlinear time series panel data using bilinear models'. Journal of Digital...
    • Kreiss, J.-P.. (1987). 'On adaptive estimation in stationary ARMA processes'. The Annals of Statistics. 15. 112
    • Le Cam, L. M.. (1986). Asymptotic Methods in Statistical Decision Theory. Springer-Verlag. New York.
    • Le Cam, L. M.,Yang, G. L.. (2000). Asymptotics in Statistics: Some Basic Concepts. 2. Springer-Verlag. New York.
    • Lee, S. H.,Kim, S. W.,Lee, S. D.. (2013). 'Test of homogeneity for panel bilinear time series model'. The Korean Journal of Applied...
    • Lillo, R. L.,Torrecillas, C.. (2018). 'Estimating dynamic panel data. A practical approach to perform long panels'. Revista Colombiana...
    • Maravall, A.. (1983). 'An application of nonlinear time series forecasting'. Journal of Business & Economic Statistics. 1. 66-74
    • Noether, G. E.. (1949). 'On a theorem by wald and wolfowitz'. The Annals of Mathematical Statistics. 20. 455
    • Pesaran, H.. (2015). Time Series and Panel Data Econometrics. Oxford University Press. Oxford, UK.
    • Pham, T. D.,Tran, L. T.. (1981). 'On the first-order bilinear time series model'. Journal of Applied Probability. 18. 617
    • Quinn, B. G.. (1982). 'Stationarity and invertibility of simple bilinear models'. Stochastic Processes and their Applications. 12....
    • Rao, T. S.,Gabr, M.. (1984). An introduction to bispectral analysis and bilinear time series models. Springer Science & Business Media.
    • Saikkonen, P.,Luukkonen, R.. (1991). 'Power properties of a time series linearity test against some simple bilinear alternatives'....
    • Swensen, A. R.. (1985). 'The asymptotic distribution of the likelihood ratio for autoregressive time series with a regression trend'....
    • Tan, L.,Wang, L.. (2015). 'The lasso method for bilinear time series models'. Communications in Statistics - Simulation and Computation....
    • Wald, A.. (1943). 'Tests of statistical hypotheses concerning several parameters when the number of observations is large'. Transactions...
    • Weiss, A. A.. (1986). 'ARCH and bilinear time series models: Comparison and combination'. Journal of Business and Economic Statistics....
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