On Weighted Least Squares Estimation of Elementary Chirp Model

Abstract

In this article, we consider the estimation of the parameters of a multiple-component elementary chirp model based on weighted least squares estimators (WLSEs). Recently, Mittal et al. (2023) have proposed least squares estimators (LSEs) to estimate the parameters of the elementary chirp model. However, it has been observed that LSEs are quite sensitive to outliers. The least absolute deviation estimators and Huber's M-estimators are robust estimators for estimation in the presence of outliers. However, computing these robust estimators is numerically challenging, and deriving their statistical properties is not straightforward under the same error assumption as LSEs. We prove the strong consistency and asymptotic normality of WLSEs under the same error assumptions as those of LSEs. We have also considered sequential WLSEs to estimate the parameters, which are less computationally involved and have the same asymptotic properties as WLSEs. Based on extensive numerical studies, it has been observed that the behavior of the proposed estimators is better than that of LSEs in the presence of outliers. We also discuss the choice of weight function, as the performance of the proposed estimators depends on the weight function. For illustration, we have presented a simulation study, where outliers are present anywhere in the data, not only in a specific portion. We have also analyzed a synthetic dataset and a real dataset. The performance is quite satisfactory.