# 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} }

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…

## 496 Citations

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## References

SHOWING 1-10 OF 46 REFERENCES

### A data-driven method for estimating conditional densities

- Computer Science
- 2003

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

- Mathematics, Computer Science
- 2001

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

- Mathematics
- 2004

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

- Mathematics
- 1998

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

- MathematicsTechnometrics
- 2003

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 eld.

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

- Mathematics
- 2004

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

- Economics, Mathematics
- 2000

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

- Computer Science
- 1984

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

- Mathematics
- 1987

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…