Nonparametric estimation of distributions with categorical and continuous data

By Qi Li, Jeffrey S. Racine. 2003

232 citations recorded by the source corpus.

In this paper we consider the problem of estimating an unknown joint distribution which is defined over mixed discrete and continuous variables. A nonparametric kernel approach is proposed with smoothing parameters obtained from the cross-validated minimization of the estimator's integrated squared error. We derive the rate of convergence of the cross-validated smoothing parameters to their 'benchmark' optimal values, and we also establish the asymptotic normality of the resulting nonparametric kernel density estimator. Monte Carlo simulations illustrate that the proposed estimator performs substantially better than the conventional nonparametric frequency estimator in a range of settings. The simulations also demonstrate that the proposed approach does not suffer from known limitations of the likelihood cross-validation method which breaks down with commonly used kernels when the continuous variables are drawn from fat-tailed distributions. An empirical application demonstrates that the proposed method can yield superior predictions relative to commonly used parametric models.

Subfields: Artificial Intelligence, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/32e536773c3b881956da1450e6e59f2c93d110bb

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In Artificial Intelligence

In Statistics and Probability

Citations in the corpus

Testing the Significance of Categorical Predictor Variables in Nonparametric Regression Models (2006, unknown): “Econometric Reviews, 25(4):523–544, 2006 Copyright © Taylor & Francis Group, LLC ISSN: 0747-4938 print/1532-4168 online DOI: 10.1080/07474930600972590”
A nonparametric test for equality of distributions with mixed categorical and continuous data (2009, background): “Letting ( ˆ h 1 , . . . , ˆ h q ) and ( ˆ λ 1 , . . . , ˆ λ r ) denote the cross-validated values of (h 1 , . . . , h q ) and (λ 1 , . . . , λ r ), Li & Racine (2003) 1 have shown thatˆh s /h 0 s − 1 → 0 in probability, andˆλ s /λ 0 s −”
Cross-Validation and the Estimation of Conditional Probability Densities (2004, background): “Hall (1983a) and Li and Racine (2003) treated unconditional joint density estimation from mixed data.”
Modeling inter-camera space-time and appearance relationships for tracking across non-overlapping views (2008, methodology): “We have used a mixed density estimator proposed by Li and Racin [ 22 ] to obtain the space–time pdf.”
Nonparametric Econometrics: The np Package (2008, methodology): “For further details see Li and Racine (2003) who proposed the use of these generalized product kernels for unconditional density estimation and developed the underlying theory for a data-driven method of bandwidth selection for this class of estimators.”
A Dependence Metric for Possibly Nonlinear Processes (2004, background): “the summation operator and replaces ^ f(¢), ^g(¢), and ^h(¢) with the kernel probability estimators in Li & Racine (2003) .”