Publication

Monotonicity Constraints in the Estimation of Distributions with Smoothing Splines

2000
Reports

Abstract

A non-parametric method of distribution estimation for univariate data is presented. The idea is to adapt the smoothing spline procedure used in regression to the estimation of distributions via a scatterplot smoothing of theempirical distribution function. An explicit formula for the estimator is obtained by minimizing a penalized weighted sum of squares. The issue of monotonicity of the resulting function is discussed in detail and the estimator's large sample properties are studied.

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2000
Reports

Abstract

Official source

Related concepts (32)

Estimation theory

Estimation theory is a branch of statistics that deals with estimating the values of parameters based on measured empirical data that has a random component. The parameters describe an underlying physical setting in such a way that their value affects the distribution of the measured data. An estimator attempts to approximate the unknown parameters using the measurements.

Density estimation

In statistics, probability density estimation or simply density estimation is the construction of an estimate, based on observed data, of an unobservable underlying probability density function. The unobservable density function is thought of as the density according to which a large population is distributed; the data are usually thought of as a random sample from that population. A variety of approaches to density estimation are used, including Parzen windows and a range of data clustering techniques, including vector quantization.

Maximum likelihood estimation

In statistics, maximum likelihood estimation (MLE) is a method of estimating the parameters of an assumed probability distribution, given some observed data. This is achieved by maximizing a likelihood function so that, under the assumed statistical model, the observed data is most probable. The point in the parameter space that maximizes the likelihood function is called the maximum likelihood estimate. The logic of maximum likelihood is both intuitive and flexible, and as such the method has become a dominant means of statistical inference.

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Monotonicity Constraints in the Estimation of Distributions with Smoothing Splines

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