IMS Lecture Notes–Monograph Series Mixtures and Monotonicity: a Review of Estimation under Monotonicity Constraints
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چکیده
Monotone and multiply monotone densities have well-known mixture representations. The underlying mixture representations give rise to a wide variety of fascinating inverse problems. We review the forward problems (estimation of the mixed density) and the inverse problems (estimation of the mixing distribution in two different guises), including Hampel’s bird resting time problem and generalizations thereof. Section 5 gives a brief review of the current status of estimation theory in a subset of these problems.
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