Estimating the order of sinusoidal models using the adaptively penalized likelihood approach: Large sample consistency properties

•In this paper, we use the PAL based order estimation method for estimating the number of components of a superimposed nonlinear sinusoidal model.•We have proved that the estimator of the model order using the PAL rule is large sample consistent.•Simulation examples are presented to illustrate the performance of the PAL method for small sample sizes and to compare it with three standard methods, namely, the usual AIC, the usual BIC and the asymptotic MAP rule.•The PAL rule can also be extended for estimating the number of components for similar nested superimposed nonlinear 1-d and 2-d signal models.

Recently, the paper [2] introduced a method for model order estimation based on penalizing adaptively the likelihood (PAL). In this paper, we use the PAL based order estimation method for a nonlinear sinusoidal model and study its asymptotic statistical properties. We prove that the estimator of the model order using the PAL rule is consistent. Simulation examples are presented to illustrate the performance of the PAL method for small sample sizes and to compare it with that of three information criterion-based methods.