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Optimal detection of bilinear dependence in short panels of regression data. (English) Zbl 1454.62210

Summary: 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 \(\mu\), regression coefficient \(\beta\), the scale parameter \(\sigma\) 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.

MSC:

62J02 General nonlinear regression
62H20 Measures of association (correlation, canonical correlation, etc.)
62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
62G08 Nonparametric regression and quantile regression
62D20 Causal inference from observational studies
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