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Abstract:
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In animal learning experiments, a sequence of binary responses is obtained from each animal (subject). It is observed that the responses are like independent Bernoulli outcomes with different probabilities before and after a learing point. Different animals learn at different speeds. Of interest is the distribution of the time when the animals start to learn. In this talk, we present three estimation methods based on different data settings. When the number of observations per subject (m) is large, compared with the number of subjects (n), we could use the MLE of the changepoint from each animal to give a first-order efficient estimate of the distribution. When m is relatively small, efficient estimator is still available, by local estimation methods. When both m and n are relatively small, sieve estimator based on the Bernstein polynomial performs well.
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