Dabrowski, André Robert; McDonald, David Consistent estimation in the presence of bandwidth limitation. (English) Zbl 0780.92010 J. R. Stat. Soc., Ser. B 55, No. 1, 267-289 (1993). Summary: Ion channels are molecular structures embedded in cell membranes which selectively allow ions to cross the membranes. The electrical activity of ion channels has been successfully described by a finite state space semi-Markov process. In this model, some of these states are closed and do not permit any ions to flow through the channel. The remaining states are open and permit ions to cross with a fixed conductance, producing a fixed measurable current across the cell membrane. If the patch of cell membrane under study contains several channels, only the aggregate amount of current crossing the membrane is observable.Several estimation and testing procedures have been developed which estimate the model parameters based on the transitions of this output current process. A significant difficulty in the analysis of such a record is bandwidth limitation, or time interval omission. Events of short duration, such as a channel opening shortly followed by a channel closing, are missed by the recording machinery.We compute a first-order correction term to the count of current level transitions when the current record is bandwidth limited. For small bandwidths, this leads to improved estimates for the mean open time, the mean closed time and the probability that a channel is open at an arbitrary time. We introduce a more general correction process valid for larger bandwidths as well. We apply our techniques to simulated ion channel data and to patch clamp data from pond snails. Cited in 2 Documents MSC: 92C30 Physiology (general) 92C40 Biochemistry, molecular biology 62P10 Applications of statistics to biology and medical sciences; meta analysis 62M05 Markov processes: estimation; hidden Markov models 60K20 Applications of Markov renewal processes (reliability, queueing networks, etc.) Keywords:missed events; multiple openings; simulated alternating renewal process; cell membranes; electrical activity of ion channels; finite state space semi-Markov process; output current process; bandwidth limitation; time interval omission; channel opening; channel closing; first-order correction term; count of current level transitions; mean open time; mean closed time; ion channel PDFBibTeX XMLCite \textit{A. R. Dabrowski} and \textit{D. McDonald}, J. R. Stat. Soc., Ser. B 55, No. 1, 267--289 (1993; Zbl 0780.92010)