| In certain animal learning experiments, animals undergo a sequence of trials, each of which results in either a success or a failure. Typically, each animal's success rate is modeled as undergoing an abrupt change at some point along the sequence. The unobserved change-point is viewed as the point at which the animal has learned. The change-point differs among animals and estimation of the distribution of the change-points from the sequences of successes and failures is of interest.;In this dissertation, three methods are proposed for estimating the change-point distribution, each appropriate for different scenarios. We show that when the number of observations per subject (m) is large relative to the number of subjects (n), the empirical distribution function of subject-specific maximum likelihood estimates of the change-points is first-order efficient and further smoothing based on a kernel function can increase second-order efficiency. When m is relatively small, the isotonized local regression estimate also attains first-order efficiency when the nuisance parameters, the probabilities of success before and after learning are known. When the nuisance parameters are unknown, we show that an alternative estimator based on the Bernstein Polynomials outperforms estimators with better asymptotic properties in finite sample simulations.;In addition to the discrete-time model for animal learning experiments, we also examine the continuous-time setting in which the observations are taken at random time points. Parallel estimators based on the maximum likelihood estimates of the change-points, local regression and the Bernstein polynomials are developed and their asymptotic properties are examined. |
