Cross-Validation and the Estimation of Conditional Probability Densities

@article{Hall2004CrossValidationAT,
  title={Cross-Validation and the Estimation of Conditional Probability Densities},
  author={Peter Hall and Jeffrey S. Racine and Qi Li},
  journal={Journal of the American Statistical Association},
  year={2004},
  volume={99},
  pages={1015 - 1026}
}
  • P. Hall, J. Racine, Qi Li
  • Published 1 December 2004
  • Computer Science
  • Journal of the American Statistical Association
Many practical problems, especially some connected with forecasting, require nonparametric estimation of conditional densities from mixed data. For example, given an explanatory data vector X for a prospective customer, with components that could include the customer's salary, occupation, age, sex, marital status, and address, a company might wish to estimate the density of the expenditure, Y, that could be made by that person, basing the inference on observations of (X, Y) for previous clients… 

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References

SHOWING 1-10 OF 46 REFERENCES

A data-driven method for estimating conditional densities

This article extends the idea of cross-validation (CV) for choosing the smoothing parameter of the “double-kernel” local linear regression for estimating a conditional density and optimizes the estimated conditional density function by minimizing the integrated square error (ISE).

NONPARAMETRIC ESTIMATION OF A GENERALIZED ADDITIVE MODEL WITH AN UNKNOWN LINK FUNCTION

An estimator for a new model that nests single-index, additive, and multiplicative models is described and the new model achieves dimension reduction without the need for choosing between single- index, multiplicative, and multiplier specifications.

A crossvalidation method for estimating conditional densities

We extend the idea of crossvalidation to choose the smoothing parameters of the 'double-kernel' local linear regression for estimating a conditional density. Our selection rule optimises the

Smoothing sparse contingency tables

Smoothing has become synonymous with a variety of nonparametric methods used in the estimation of functions. To smooth is to sand away the rough edges from a set of data. More precisely, the aim of

The Statistical Analysis of Failure Time Data

This book complements the other references well, and merits a place on the bookshelf of anyone concerned with the analysis of lifetime data from any Ž eld.

Efficient Estimation of Average Treatment Effects With Mixed Categorical and Continuous Data ∗

In this paper we consider the nonparametric estimation of average treatment effects when there exist mixed categorical and continuous covariates. One distinguishing feature of the approach presented

Efficient Estimation of Average Treatment Effects Using the Estimated Propensity Score

It is shown that weighting with the inverse of a nonparametric estimate of the propensity Score, rather than the true propensity score, leads to efficient estimates of the various average treatment effects, whether the pre-treatment variables have discrete or continuous distributions.

An alternative method of cross-validation for the smoothing of density estimates

An alternative method of cross-validation, based on integrated squared error, recently also proposed by Rudemo (1982), is derived, and Hall (1983) has established the consistency and asymptotic optimality of the new method.

On Smoothing Sparse Multinomial Data

Summary Asymptotic theory is developed for the problem of smoothing sparse multinomial data, with emphasis on the criterion of mean summed square error of estimators of the probability mass