# Shape-Constrained Univariate Density Estimation

@article{Dasgupta2018ShapeConstrainedUD, title={Shape-Constrained Univariate Density Estimation}, author={Sutanoy Dasgupta and Debdeep Pati and Ian H. Jermyn and Anuj Srivastava}, journal={arXiv: Methodology}, year={2018} }

While the problem of estimating a probability density function (pdf) from its observations is classical, the estimation under additional shape constraints is both important and challenging. We introduce an efficient, geometric approach for estimating pdfs given the number of its modes. This approach explores the space of constrained pdf's using an action of the diffeomorphism group that preserves their shapes. It starts with an initial template, with the desired number of modes and arbitrarily…

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