# Nonparametric Power Series Estimation

### Description

Use the optimal order of power series of covariates to predict outcome. The optimal order of power series is determined by cross-validation.

### Usage

1 |

### Arguments

`formula` |
specification of the outcome model in the form like either |

`order` |
the maximal order of power series to be used. |

`m` |
the number of folds to be used in cross-validation. |

`seed` |
random starting number used to replicate cross-validation. |

### Details

This function predicts the outcome based on the optimal order of covariates power series. The optimal order of the power series is determined by cross-validation. For example, it can be used to predict the probabilty of receiving treatment inducment based on covariates.

### Value

`fitted` |
Predicted outcomes based on the estimated model. They are probabilities when the outcome is binary. |

`Lambda` |
The optimal order of power series determined by cross-validation. |

`Data.opt` |
The data including |

`CV.Res` |
The residual sum of squares of the cross-validations. |

`seed` |
The random seed. |

### Author(s)

Weihua An, Departments of Sociology and Statistics, Indiana University Bloomington, weihuaan@indiana.edu.

Xuefu Wang, Department of Statistics, Indiana University Bloomington, wangxuef@umail.iu.edu.

### References

Abadie, Alberto. 2003. "Semiparametric Instrumental Variable Estimation of Treatment Response Models." *Journal of Econometrics* 113: 231-263.

### See Also

`larf`

, `larf.fit`

### Examples

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 | ```
data(c401k)
attach(c401k)
## Not run:
# binary outcome
Z <- c401k$e401k
# covariates
X <- as.matrix(c401k[,c("inc", "male", "fsize" )])
# get nonparametric power series estimation of the regression of Z on X
zp <- npse(Z~X, order = 5, m = 10, seed = 681)
# sum of residual squares of the cross-validations
zp$CV.Res
# the opitimal order of the power series
zp$Lambda
# summary of the predictions based on the optimal power series
summary(zp$fitted)
## End(Not run)
``` |

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