# NPMLE for Longitudinal Gaussian Means and Variances Model

### Description

A Kiefer-Wolfowitz NPMLE procedure for estimation of a Gaussian model with independent mean and variance components with weighted longitudinal data. This version exploits a Student t decomposition of the likelihood.

### Usage

1 | ```
WTLVmix(y, id, w, u = 300, v = 300, ...)
``` |

### Arguments

`y` |
A vector of observations |

`id` |
A strata indicator vector indicating grouping of y |

`w` |
A vector of weights corresponding to y |

`u` |
A vector of bin boundaries for the mean effects |

`v` |
A vector of bin boundaries for the variance effects |

`...` |
optional parameters to be passed to KWDual to control optimization |

### Value

A list consisting of the following components:

`u` |
midpoints of the mean bin boundaries |

`fu` |
the function values of the mixing density of the means |

`v` |
midpoints of the variance bin boundaries |

`fv` |
the function values of the mixing density of the variances. |

`logLik` |
log likelihood value for mean problem |

`du` |
Bayes rule estimate of the mixing density means. |

`dv` |
Bayes rule estimate of the mixing density variances. |

`status` |
Mosek convergence status |

### Author(s)

J. Gu and R. Koenker

### References

Gu, J. and R. Koenker (2015) Empirical Bayesball Remixed, preprint

### See Also

WGLVmix for a more general bivariate mixing distribution version