• Corpus ID: 54840017

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… 

Figures and Tables from this paper

References

SHOWING 1-10 OF 21 REFERENCES
A Geometric Framework For Density Modeling
We introduce a geometric approach for estimating a probability density function (pdf) given its samples. The procedure involves obtaining an initial estimate of the pdf and then transforming it via a
A Two-Step Geometric Framework For Density Modeling
TLDR
A novel two-step approach for estimating a probability density function given its samples, with the second and important step coming from a geometric formulation, which avoids many of the computational pitfalls associated with classical conditional-density estimation methods, without losing on estimation performance.
Estimation of unimodal densities without smoothness assumptions
The Grenander estimator of a decreasing density, which is defined as the derivative of the concave envelope of the empirical c.d.f., is known to be a very good estimator of an unknown decreasing
Unimodal density estimation using Bernstein polynomials
TLDR
A flexible class of mixture of Beta densities that are constrained to be unimodal is presented and it is shown that the estimation of the mixing weights, and the number of mixing components, can be accomplished using a weighted least squares criteria subject to a set of linear inequality constraints.
UNIMODAL DENSITY ESTIMATION USING KERNEL METHODS
We suggest a method for rendering a standard kernel density estima- tor unimodal: tilting the empirical distribution. It is proposed that the amount of tilting be chosen in order to minimise, subject
Nonparametric Density Estimation under Unimodality and Monotonicity Constraints
Abstract We introduce a recursive method for estimating a probability density subject to constraints of unimodality or monotonicity. It uses an empirical estimate of the probability transform to
AN ALTERNATIVE UNIMODAL DENSITY ESTIMATOR WITH A CONSISTENT ESTIMATE OF THE MODE
The traditional maximum likelihood unimodal density estimator (Grenander (1956)) pieces together two isotonic density estimators at a known mode. It is discontinuous at the mode, and does not
Bayesian Local Extremum Splines.
TLDR
A nonparametric prior is developed over a novel class of local extremum splines and is shown to be consistent when modeling any continuously differentiable function within the class considered, and is used to develop methods for testing hypotheses on the shape of the curve.
Probability inequalities for likelihood ratios and convergence rates of sieve MLEs
Let Y 1 ,...,Y n be independent identically distributed with density p 0 and let F be a space of densities. We show that the supremum of the likelihood ratios Π i=1 n p(Y i )/p 0 (Y i ), where the
Review Papers: Recent Developments in Nonparametric Density Estimation
Abstract Advances in computation and the fast and cheap computational facilities now available to statisticians have had a significant impact upon statistical research, and especially the development
...
1
2
3
...