C. F. Wu. Asymptotic theory of nonlinear least squares estimation. Annals of Statistics, 9:3:501--513, 1981.  Home/Search Document Not in Database Summary Related Articles Check |
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On the Threshold Effect in the Estimation of Chaotic Sequences - Hen, Merhav (Correct)
....conditions, that when SNR 1 the estimation error is asymptotically normally distributed with zero mean and variance given by the Cram er Rao bound, i.e. the maximum likelihood estimator is asymptotically unbiased and ecient. However, when SNR 0, violating a necessary condition [27] [30] for consistency of least squares (LS) estimator, the maximum likelihood estimator becomes inconsistent. Although the above mentioned approaches for estimation of chaotic sequences under noise are di erent, their qualitative performance remains the same: good performance for high enough SNR but ....
C. Wu, \Asymptotic theory of nonlinear least squares estimation," Ann. Stat., Vol. 9, pp. 501-513, 1981.
Wald Statistic For Selection Of Nested Nonlinear Models - Sabharwal, Potter (Correct)
....FIM matrix implies that the amplitude and location parameters are asymptotically uncorrelated. The authors conjecture that the above theorem holds for more general models, i.e. without requiring the FIM to be asymptotically diagonal. These rate conditions are similar to the Assumption B in [30]. 12 Note that the model classes discussed in Examples I and 2 satisfy all the conditions of Theo rem 2. The rate of growth of submatrices of FIM for Example 2 can be found in [31] where it was shown that a(N) N and (N) N 3. V. Implementation Issues and Simulation Results In this section, ....
C.-F. Wu, :'Asymptotic theory of nonlinear least squares estimation," Ann. Star., vol. 9, no. 3, pp. 501-513, 1981.
Bootstrap Approximations in a Partially Linear Regression.. - Härdle, Liang, Sommerfeld (1997) (Correct)
....T f X) Gamma1 R u 2 d b F n (u) Recall the definition of b F n (u) and the result given in Lemma 2, the asymptotic variance of p n(fi n Gamma fi n ) is oe 2 B Gamma1 : We now prove max i q ii 0. Since n Gamma1 ( f X T f X) B by Lemma 2, it follows from Lemma 3 of Wu (1981) that max i q ii 0: This completes the proof of (5) Next, we will prove (6) First we continue to give the following preliminary results. In Lemma 5, letting V i be ffl i , E and P be E and P , then we have max 1in fi fi fi n X k=1 nk (T i )ffl k fi fi fi = O P (n ....
Wu, C.F.J. (1981). Asymptotic theory of nonlinear least squares estimation. Annals of Statistics, 9, 501-513.
Consistency for the Least Squares Estimator in Non-Parametric.. - Geer, Wegkamp (1996) (2 citations) (Correct)
....Pollard (1984) Most articles about least squares estimation only contain sufficient conditions for consistency. This is of course the most interesting part from the practical point of view. Only few authors have dealt with necessary conditions for consistency of the least squares estimator (e.g. Wu (1981)) In Section 2, we will recall the sufficiency result obtained by Van de Geer (1987) and prove that the entropy conditions for consistency are indeed necessary whenever the envelope G is square integrable w.r.t. the probability measure P . However, the latter assumption is far too stringent in ....
Wu, C.F. (1981), Asymptotic theory of nonlinear least squares estimation, Ann.
On Estimation Of A Covariance Function Of Stationary Errors In A .. - Stulajter (1994) (Correct)
....distributed with some unknown variance. Under these assumptions the limit properties of an approximate least squares estimator of regression parameters and variance were derived. In this connection the classical results are given by Jennrich (1969) Box (1971) Clarke (1980) P azman (1984) Wu (1981) and others. The case of correlated errors was studied by Hannan (1971) Gallant and Goebel (1976) Gallant (1987) and Stulajter (1992) and was devoted mainly to problems of estimation of regression parameters and their limit properties. Cook and Tsai (1985) studied properties of residuals in a ....
....a) Xn X iff X 2 n X 2 b) if Xn X and Yn Y , then XnYn XY and aXn bYn aX bY c) if jXn j jY n j and Yn 0, then Xn 0 and d) if E[Xn ] 0 and Var [Xn ] 0, then Xn 0. Remarks. 1. The conditions (8) 9) and (10) are similar to those appearing in Jennrich (1969) Wu (1981) and others studying the limit properties of the least squares estimator of . It was shown in Stulajter (1991) that for consistency of estimators of a covariance function weaker conditions than for consistency of regression parameters are requiared if the regression model is linear. A ....
Wu C. F., Asymptotic theory of nonlinear least squares estimators, Ann. Stat. 9 (1981), 501--513.
Reliability Analysis Using the Least Squares Method in Nonlinear .. - Wu, Shao (1996) (1 citation) (Correct)
....to 0 in probability by (C7) C8) the Cauchy Schwarz inequality, and the fact that n 0 in probability. The second term of (7) is a (p q) Theta(p q) matrix, whose (r; s)th entry converges to 0 in probability uniformly on C = fk Gamma 0 k ffig, by (C7) C8) and Corollary A of Wu (1981). Hence, we showed that B n I p q in probability. To complete the proof, we need to show that D Gamma1=2 n ( 0 )A Gamma1 n ( 0 ) n X i=1 H i ( 0 )e i Gamma N(0; I p q ) in distribution: 8) Let be a fixed (p q) vector. It suffices to show that 0 D Gamma1=2 n ( 0 )A ....
Wu, C. F. J. (1981). Asymptotic theory of nonlinear least squares estimation. The Annals of Statistics 9, 501-513.
Estimation Using Low Rank Signal Models - Mahata (2003) (Correct)
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C. F. Wu. Asymptotic theory of nonlinear least squares estimation. Annals of Statistics, 9:3:501--513, 1981.
Linear Least Squares Estimation of Regression Models for.. - Cohen, Francos (2002) (Correct)
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C. F. Wu, Asymptotic theory of nonlinear least squares estimation, Ann. Statist. 9 (1981), 501--513.
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