Abstract

LMAKRI, Aziz; AKHARIF, Abdelhadi  and  MELLOUK, Amal. Optimal Detection of Bilinear Dependence in Short Panels of Regression Data. Rev.Colomb.Estad. [online]. 2020, vol.43, n.2, pp.143-171.  Epub Dec 05, 2020. ISSN 0120-1751.  https://doi.org/10.15446/rce.v43n2.83044.

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.

Keywords : Bilinear process; local asymptotic normality; local asymptotic linearity; panel data; pseudo-Gaussian tests; rank tests.

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