# Estimate of the variance component in Fay Herriot Model using Residual Maximum Likelihood, REML.

### Description

This function returns a list with one element in it which is the estimate of the variance component in the Fay Herriot Model using residual maximum likelihood method. The estimates are obtained as a solution of equations known as REML equations. The solution is obtained numerically using Fisher-scoring algorithm. For more details please see the package vignette and the references. Note that our function does not accept any missing values.

### Usage

1 | ```
resimaxilikelihood(response, designmatrix, sampling.var,maxiter)
``` |

### Arguments

`response` |
a numeric vector. It represents the response or the observed value in the Fay Herriot Model |

`designmatrix` |
a numeric matrix. The first column is a column of ones(also called the intercept). The other columns consist of observations of each of the covariates or the explanatory variable in Fay Herriot Model. |

`sampling.var` |
a numeric vector consisting of the known sampling variances of each of the small area levels. |

`maxiter` |
maximum number of iterations of fisher scoring |

### Details

For more details see the package vignette

### Value

`estimate` |
estimate of the variance component |

### Author(s)

Abhishek Nandy

### References

On measuring the variability of small area estimators under a basic area level model. Datta, Rao, Smith. Biometrika(2005),92, 1,pp. 183-196 Large Sample Techniques for Statistics, Springer Texts in Statistics. Jiming Jiang. Chapters - 4,12 and 13. Small Area Estimation, JNK Rao,Wiley 2003 Variance Components, Wiley Series in Probability and Statistics,2006 Searle, Casella, Mc-Culloh

### See Also

`prasadraoest`

`maximlikelihood`

`fayherriot`

### Examples

1 2 3 4 |

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