From: A survey of Monte Carlo methods for parameter estimation
Let us compute the set of IS weights (potentially different from those of Eq. (71)), |
\({\rho }_{n,t}^{(m)} = \frac {\pi (\boldsymbol {\theta }_{n,t}^{(m)})}{\Omega _{n,t}(\boldsymbol {\theta }_{n,t}^{(m)})},\) |
where Ω_{n,t} are chosen in such a way that they do not jeopardize the consistency of the IS estimators, and they can be equal to \(w_{n,t}^{(m)}\) in Eq. (71) or not |
(see Table 3). Two different procedures are used in literature: |
P1 Apply some resampling strategy to \(\{\boldsymbol {\mu }_{n,t-1}\}_{n=1}^{N}\), with probabilities according to the weights \(\rho _{n,t}^{(m)}\), to obtain \(\{\boldsymbol {\mu }_{n,t}\}_{n=1}^{N}\) [95, 274, 286]. Nonlinear transformations of \(\rho _{n,t}^{(m)}\) can also be applied [279]. |
P2 Build estimators of some moments of π employing \(\rho _{n,t}^{(m)}\), and use this information to obtain \(\{\boldsymbol {\mu }_{n,t}\}_{n=1}^{N}\) [96, 98, 287]. |