Showing papers by "Rameshwar D. Gupta published in 2000"
TL;DR: In this paper, the asymptotic behavior of the least squares estimators of the parameters are obtained in presence of stationary noise for the undamped exponential model, which is well known that this model does not satisfy the sufficient conditions of Jennrich (1969), Wu (1981), or Kundu (1991) for the least square estimators to be consistent.
Abstract: SYNOPTIC ABSTRACTSuperimposed exponential signals play an important role in Statistical Signal Processing and Time series analysis. In this note, the asymptotic behavior of the least squares estimators of the parameters are obtained in presence of stationary noise for the undamped exponential model. It is well known that this model does not satisfy the sufficient conditions of Jennrich (1969), Wu (1981) or Kundu (1991) for the least squares estimators to be consistent even when the errors are independent and identically distributed random variables with mean zero and finite variance. This paper extends some of the earlier works of Hannan (1971, 1973), Walker (1971), Bai, Chen, Krishnaiah, Wu and Zhao (1991), Rao and Zhao (1993), Kundu (1995) and Kundu and Mitra (1996, 2000) in different ways. Some numerical experiments are performed to observe the small sample behavior of the least squares estimators.
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TL;DR: In this article, the first k significant digits in the radix expansion in base b of Y = X 1/α were derived, and it was shown that as k→∞, Y k converges in distribution to the uniform distribution on the set {0,1,…,b−1}.