Dear Dr. Bakkeren: sure: proper MI as discussed by Rubin (1987) yields draws from the predictive distribution of the missing values, and the MI rules give a interval estimate of the predictive distribution. This is actually a Bayesian posterior probability interval rather than a confidence interval, but it should have good properties as a frequentist predictive interval if the model is correct. One comment is that more multiple imputes may be needed than for inferences about parameters, since the "fraction of missing information" is likely to be large. Best, Rod Little
On Thu, 21 Nov 2002 [email protected] wrote: > > Dear List members, > > I wonder if anyone could help me with the following question. Is it > possible to calculate confidence intervals for missing data itself? So not > for the underlying parameters, but for a single missing value? > I have a dataset with stock prices of some 20 equities over a period of 65 > days. For one equity the prices are missing in a consecutive period of 11 > days. I would like to 'reconstruct' the missing prices using Multiple > imputation (or the EM algorithm). I'm using the fact that the daily returns > (log of relative price changes) are distributed in a multivariate normal > way. Using the EM algorithm I can create a sequence of 11 returns, which > can be considered as the 'most likely' values, or point estimates, but I do > not get a confidence interval for these values. > Is it justifyable to use Multiple Imputation, regarding each missing value > as a parameter and simply calculate the point estimate and variance using > the well-known combining rules? Or is this approach too simple? > > > Chiel Bakkeren > > > --------------------------------------------------------------------------- > This message (including any attachments) is confidential and may be > privileged. If you have received it by mistake please notify the sender by > return e-mail and delete this message from your system. Any unauthorised > use or dissemination of this message in whole or in part is strictly > prohibited. Please note that e-mails are susceptible to change. > ABN AMRO Bank N.V. (including its group companies) shall not be liable for > the improper or incomplete transmission of the information contained in > this communication nor for any delay in its receipt or damage to your > system. ABN AMRO Bank N.V. (or its group companies) does not guarantee that > the integrity of this communication has been maintained nor that this > communication is free of viruses, interceptions or interference. > --------------------------------------------------------------------------- > > > > > > > ___________________________________________________________________________________ Roderick Little Richard D. Remington Collegiate Professor (734) 936-1003 Department of Biostatistics Fax: (734) 763-2215 U-M School of Public Health M4045 SPH II [email protected] 1420 Washington Hgts http://www.sph.umich.edu/~rlittle/ Ann Arbor, MI 48109-2029
