### Abstract

Much empirical research in the social sciences is concerned with estimating conditional mean functions. The most frequently used estimation methods assume that the conditional mean function is known up to a set of constant parameters that can be estimated from data. Such methods are called 'parametric.' Their use greatly simplifies estimation and inference but is rarely justified by theoretical or other a priori considerations. Estimation and inference based on convenient but incorrect assumptions about the form of the conditional mean function can be highly misleading. Semiparametric methods reduce the strength of the assumptions required for estimation and inference, thereby reducing the opportunities for obtaining misleading results. In addition, semiparametric methods mitigate certain disadvantages of fully nonparametric methods that make no assumptions about the shape of the conditional mean function. This article describes three important semiparametric models for conditional mean functions. They are single index, partially linear, and additive models. These models are compared with parametric and fully nonparametric models. An example based on real data illustrates the pitfalls of parametric models and the advantages of semiparametric models.

Original language | English (US) |
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Title of host publication | International Encyclopedia of the Social & Behavioral Sciences: Second Edition |

Publisher | Elsevier Inc. |

Pages | 598-603 |

Number of pages | 6 |

ISBN (Electronic) | 9780080970875 |

ISBN (Print) | 9780080970868 |

DOIs | |

State | Published - Mar 26 2015 |

### Keywords

- Conditional mean function
- Kernel estimator
- Nonparametric additive model
- Partially linear model
- Single index model

### ASJC Scopus subject areas

- Social Sciences(all)

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## Cite this

*International Encyclopedia of the Social & Behavioral Sciences: Second Edition*(pp. 598-603). Elsevier Inc.. https://doi.org/10.1016/B978-0-08-097086-8.42169-0