Hopfner, R., J. Jacod and L. Ladelli (1990). Local asymptotic normality and mixed normality for Markov statistical models. Probab. Theory Related Fields 86, 105{ 129. Home/Search Document Not in Database Summary Related Articles Check |
This paper is cited in the following contexts:
Empirical estimators based on MCMC data - Greenwood, Wefelmeyer (Correct)
....#nm such that Qnm = Q #nm is Hellinger di erentiable with derivative Dm, Z Q(x; dy) 0 dQnm dQ (x; y) 1=2 1 1 2 n 1=2 Dm(x; y) 1 A 2 n 1 r n (x) 3.1) where r n decreases to 0 pointwise and is integrable for large n. This version of Hellinger di erentiability is due to H opfner, Jacod and Ladelli (1990). Write P n and Pnm for the joint distribution of X 0 ; X n under Q and Qnm , respectively. As in H opfner (1993) we have a nonparametric version of local asymptotic normality for the likelihood ratio. For m 2 M , log dPnm dP n = n 1=2 n X i=1 Dm(X i 1 ; X i ) 1 2 Q(Dm) ....
Hopfner, R., J. Jacod and L. Ladelli (1990). Local asymptotic normality and mixed normality for Markov statistical models. Probab. Theory Related Fields 86, 105{ 129.
Efficient estimation in Markov chain models: an introduction - Wefelmeyer (Correct)
....Hellinger differentiable with derivative Dk, Z Q(x; dy) 0 dQ nk dQ (x; y) 1=2 Gamma 1 Gamma 1 2 n Gamma1=2 (Dk) x; y) 1 A 2 n Gamma1 r n (x) 2.5) where r n decreases to 0 pointwise and is integrable for large n. This version of Hellinger differentiability is due to Hopfner et al. 1990). Remark. Our description of the tangent space omits one important feature: The space K should contain all directions k from which we can approximate # within Theta. We have already mentioned in the previous Remark that this is not always possible. In the applications we simply try to make K as ....
Hopfner, R., Jacod, J. and Ladelli, L. (1990). Local asymptotic normality and mixed normality for Markov statistical models. Probab. Theory Related Fields 86, 105--129.
Wolfgang Wefelmeyer - Department Of Mathematics (Correct)
....Hopfner (1993) proves local asymptotic normality for Markov step processes under weaker assumptions. His argument is easily modified to cover discrete time Markov processes. To apply it, we need only check an appropriate version of Hellinger differentiability for Q nuh , condition H1 00 in Hopfner et al. 1990). Hellinger differentiability is implied by a corresponding differentiability in quadratic mean, Z r n (x; y) 2 Q(x; dy) R n (x) 3.1) with R n # 0 pointwise and R n integrable for large n. To prove (3.1) recall that m 00 (x) is continuous at = # uniformly in x. Hence there exists ....
Hopfner, R., Jacod, J. and Ladelli, L. (1990). Local asymptotic normality and mixed normality for Markov statistical models. Probab. Theory Rel. Fields 86, 105--129.
The information in the marginal law of a Markov chain - Kessler, Schick, Wefelmeyer (1998) (Correct)
....1=2 Delta N; 2.7) where N is standard normal. A parametric version of local asymptotic normality for Markov chains was first given in Roussas (1965) a nonparametric version in Penev (1991) Local asymptotic normality for Markov step processes and Hellinger differentiable Q nh in the sense of Hopfner, Jacod and Ladelli (1990), and hence for Q nh as in (2.4) is proved in Hopfner (1993a, 1993b) He starts the chain in a fixed value X 0 = x 0 , so that log d nh =d (X 0 ) vanishes. We consider a stationary chain, for which log d nh =d (X 0 ) is negligible because the invariant distribution depends continuously on ....
Hopfner, R., Jacod, J. and Ladelli, L. (1990). Local asymptotic normality and mixed normality for Markov statistical models. Probab. Theory Related Fields 86, 105--129.
Reversible Markov chains and optimality of symmetrized.. - Greenwood, Wefelmeyer (1998) (Correct)
....a sequence Q nh which is Hellinger differentiable with derivative h, Z Q(x; dy) dQ nh =dQ) x; y) 1=2 Gamma 1 Gamma n Gamma1=2 1 2 h(x; y) 2 n Gamma1 r n (x) 2.1) with r n decreasing to 0 pointwise and integrable for large n. This version of differentiability is due to Hopfner, Jacod and Ladelli (1990). Remark. In the full model we can take Q nh (x; dy) Q(x; dy) 1 n Gamma1=2 h n (x; y) 2.2) with h n = h n Gamma Qh n and h n = h1 (jhjn 1=8 ) 2.3) Write P n and P nh for the joint distribution of X 0 ; X n under Q and Q nh , respectively. As in Hopfner (1993) we have a ....
Hopfner, R., Jacod, J. and Ladelli, L. (1990). Local asymptotic normality and mixed normality for Markov statistical models. Probab. Theory Related Fields 86, 105--129.
Quasi-Likelihood Models and Optimal Inference - Wefelmeyer (2 citations) (Correct)
....Greenwood and Wefelmeyer (1992) and Bickel (1993) Under our conditions a proof may be obtained directly, or by modifying the argument of Hopfner (1993) who treats Markov step processes. We need only check an appropriate version of Hellinger differentiability for Q nuh , condition H1 00 in Hopfner et al. 1990). Here it reads Z i 1 n Gamma1=2 h(x; y) j 1=2 Gamma 1 Gamma n Gamma1=2 1 2 h(x; y) 2 Q(x; dy) n Gamma1 r n (x) with r n decreasing to zero pointwise and integrable for large n. This is true because h is bounded and hence Omega Q square integrable. The only of the ....
Hopfner, R., Jacod, J. and Ladelli, L. (1990). Local asymptotic normality and mixed normality for Markov statistical models. Probab. Theory Related Fields 86 105-- 129.
Empirical estimators for semi-Markov processes - Greenwood, Wefelmeyer (1996) (Correct)
....is implicit in Malinovskii (1992) The lemma remains true if differentiability (2.4) is replaced by an appropriate variant of Hellinger differentiability. For Markov step processes, with transition distribution Q(x; dy; ds) Q 1 (x; dy) x) exp ( Gammas(x) ds; compare condition H1 00 in Hopfner et al. 1990). Versions of Lemma 4 for Markov step processes are contained in Hopfner (1993a, 1993b) He writes the approximation to the likelihood ratio in a different way. Local asymptotic normality for Markov step processes is also implicit in Malinovskii (1989) The strong differentiability condition (2.4) ....
Hopfner, R., Jacod, J. and Ladelli, L. (1990). Local asymptotic normality and mixed normality for Markov statistical models. Probab. Theory Related Fields 86, 105--129.
Information bounds for Gibbs samplers - Greenwood, McKeague, Wefelmeyer (1995) (Correct)
....differentiable: Z Q (d) x; dy) 0 dQ (d)nh dQ (d) x; y) 1=2 Gamma 1 Gamma 1 2 n Gamma1=2 (K (d) h) x; y) 1 A 2 n Gamma1 r n (x) for h 2 H, where r n decreases to 0 pointwise and is integrable for large n. This version of Hellinger differentiability is adapted from Hopfner, Jacod and Ladelli (1990). From Hopfner (1993) we obtain a nonparametric version of local asymptotic normality: If the Gibbs sampler for with deterministic sweep is positive Harris recurrent, then we have for h 2 H, log dP (d)nh =dP (d) n Gamma1=2 p X q=1 (K (d) h) X (q Gamma1)k ; X qk ) Gamma 1 2 khk 2 ....
Hopfner, R., Jacod, J. and Ladelli, L. (1990). Local asymptotic normality and mixed normality for Markov statistical models. Probab. Theory Related Fields 86, 105--129.
Autoregression Approximation of a Nonparametric Diffusion Model - Milstein, Nussbaum (1996) (Correct)
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Hopfner, R. , Jacod, J., Ladelli, L. (1990). Local asymptotic normality and mixed normality for Markov statistical models. Probab. Th. Rel. Fields 86 105-129
On parameter estimation for ergodic Markov chains with.. - Veretennikov (1998) (Correct)
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R.Hoepfner, J.Jacod, L.Ladelli (1990) Local asymptotic normality and mixed normality for Markov statistical models, PTRF, 86, 105-129.
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