Tests For the Parameters of Chirp Signal Model

In this paper, the testing of the hypothesis problem on the unknown parameters involved in one-dimensional chirp signal model is explored. To be precise, we here theoretically investigate whether the vector of unknown parameters is the same as the vector with specified parameters. For that purpose, we propose four tests based on the least squares and the least absolute deviation estimators of the unknown parameters using L_1 and L_2 distances. It is shown that the proposed tests are consistent (i.e., the power of the tests tend to one as the sample size tends to infinity). In addition, the asymptotic local power of the tests using contiguous (local) alternatives is also thoroughly studied. An extensive simulation study shows the satisfactory performance of the new tests, and the usefulness of the proposed tests is exhibited on a few benchmark real datasets that are closely associated with various chirp signal models.