Asymptotic Properties
SpringerBriefs in statisticsPublished 1 January 2012
Debasis Kundu, Swagata Nandi
Citations4
Generate an AI Snapshot to get a quick, structured summary of this paper.
Study Snapshot
ObjectiveStudy objective
MethodsResearch methodology
PopulationPopulation studied
Sample sizeSample sizes
OutcomesStudy outcomes here
ResultsStudy results comes here
LimitationsResearch study limitations comes here
A concise AI-generated summary of the paper will appear here once you click Generate AI Snapshot.
Abstract
In this chapter, we discuss asymptotic properties of some of the estimators described in Chapter 3. Asymptotic results or results based on large samples deal with properties of estimators under the assumption that the sample size increases indefinitely. The statistical models, observed in signal processing literature, are mostly very complicated non-linear models. Even a single component sinusoidal component model is highly non-linear in its frequency parameter.
Keywords
Computer Science
The Annals of StatisticsAsymptotic Theory of Nonlinear Least Squares Estimation
541 Citations1981Chien-Fu Wu
IEEE Transactions on Signal ProcessingEstimating frequency by interpolation using Fourier coefficients
398 Citations1994Barry G. Quinn
A technique for obtaining an estimator that has root mean square error of order T/sup -3/2/ is presented, which involves only the Fourier components of the time series at three frequencies.
BiometrikaOn the estimation of a harmonic component in a time series with stationary independent residuals
234 Citations1971A. M. Walker
The simultaneous estimation of a time series harmonic components and covariance structure
156 Citations1952Peter Whittle
BiometrikaA fast efficient technique for the estimation of frequency
99 Citations1991Barry G. Quinn, J. Fernandes
Signal ProcessingOn modified EVLP and ML methods for estimating superimposed exponential signals
46 Citations1994Nandini Kannan, Debasis Kundu
It is observed that the standard errors for the modified methods are closer to the Cramer-Rao lower bound than before in almost all the situations and the computational cost of the modified maximum likelihood method is lower than the ordinary one.
Statistics & Probability LettersAsymptotic theory of least squares estimator of a particular nonlinear regression model
42 Citations1993Debasis Kundu
Journal of the Royal Statistical Society Series B (Statistical Methodology)A New Approach to Frequency Analysis with Amplified Harmonics
34 Citations1990B. Truong‐Van
Journal of Statistical Planning and InferenceAn efficient algorithm for estimating the parameters of superimposed exponential signals
29 Citations2002Zhidong Bai, C. Mallikarjuna Rao +2 more
An efficient computational algorithm is proposed for estimating the parameters of undamped exponential signals, when the parameters are complex valued, and the proposed estimators are consistent and the dispersion matrix of these estimators is asymptotically the same as that of the least squares estimators.
Journal of Statistical Planning and InferenceSequential estimation of the sum of sinusoidal model parameters
27 Citations2007Anurag Prasad, Debasis Kundu +1 more
Communication in Statistics- Theory and MethodsAsymptotic theory of least squares estimator of a nonlinear time series regression model
17 Citations1996Debasis Kundu, Amit Mitra
Journal of Statistical Planning and InferenceSuper efficient frequency estimation
16 Citations2011Debasis Kundu, Zhidong Bai +2 more
Statistics & Probability LettersEstimation of frequencies in presence of heavy tail errors
12 Citations2002Swagata Nandi, Srikanth K. Iyer +1 more
Journal of Statistical Computation and SimulationConsistent method for estimating sinusoidal frequencies: a non-iterative approach
11 Citations1997Amit Mitra, Debasis Kundu
Signal ProcessingEstimating the number of sinusoids in additive white noise
8 Citations1997Debasis Kundu
The strong consistency of the proposed method under the assumption of independent and identically distributed random errors is established and an upper bound of the probability of wrong detection under the same assumptions is provided.