Asymptotic properties of the least squares estimators of a two dimensional model

Abstract

In this paper we investigate the theoretical properties of the least squares estimators of the multidimensional exponential signals under the assumptions of additive errors.The strong consistency and asymptotic normality of the least squares estimators of the different parameters are obtained. We discuss two particular cases in details. It is observed that several one or two dimensional results follow from our results. Finally we discuss some open problems.

Noise space decomposition method for two-dimensional sinusoidal model

“…, δ 2p . Then the linear parameters of the corresponding one dimensional model (8) are obtained and finally we obtain the prediction error of this model (8).…”

MTSI Algorithm for Frequencies Estimation of 2-D Superimposed Exponential Model in Multiplicative and Additive Noise which is Stationary

“…Much work focus on the parameters estimation of homogeneous random field consisting of harmonic field and purely indeterministic field i.e. harmonic or superimposed exponential model in additive noise [9,10,11,12,13] while little attention has been paid to estimate the parameters of homogeneous random field consisting of evanescent field and purely indeterministic field. [5] used a two-stage procedure to jointly estimate the parameters of the harmonic, evanescent components of a real-valued homogeneous random field.…”

“…It is necessary to find a more accurate and computationally efficient algorithm for the estimation of the frequencies of the evanescent component. It is known that both maximum likelihood estimator (MLE) [14] and LSE [9,10,15] have excellent statistical performance when there exists only harmonic and purely indeterministic component in the random field, and MLE is equivalent to LSE when there is only additive Gaussian noise. The orders of convergence rate of the LSE for…”

“…means bo-unded in probability), which are expected to be the best [10]. But their high computation burden limits their applications in practice.…”

On discrete-domain multidimensional sinusoidal models

“…Several authors consider model (3) or its variants under different assumptions on X(m, n). See, for example, Barbieri and Barone [12], Cabrera and Bose [13], Chun and Bose [14], Hua [15], Kundu and Gupta [16], Lang and McClellan [17], Kundu and Mitra [18], Nandi and Kundu [19], Kundu and Nandi [20,21], Rao et al [22] and Mitra and Stoica [23]. Estimation of different parameters, asymptotic properties of different estimators and Cramer-Rao lower bound are obtained when X(m, n)'s are independent and identically distributed (i.i.d.)…”