In this paper, we propose parametric and nonparametric locally andasymptotically 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 f1 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 f1– 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.

Many estimation methods have been proposed for the parameters of the regression models with serially correlated errors. In this work, we develop an asymptotic theory for estimation in the short panel data models with bilinear error. We propose a comparative study by simulation between several estimators (adaptive, ordinary and weighted least squares) for the coefficients of panel data models when the errors are bilinear serially correlated. As a consequence of the uniform local asymptotic normality property, we obtain adaptive estimates of the parameters. Finally, we illustrate the performance of the proposed estimators via Monte Carlo simulation study. We show that the adaptive estimates are more efficient than the weighted and ordinary least squares estimates.