# NPMLE for Gaussian Variance Heterogeneity

### Description

A Kiefer-Wolfowitz MLE for Gaussian models with independent variances. This
can be viewed as a general form for *χ^2* mixtures, see `Gammamix`

for a more general form for Gamma mixtures.

### Usage

1 |

### Arguments

`x` |
vector of observed variances |

`m` |
vector of sample sizes corresponding to x |

`v` |
A vector of bin boundaries, if scalar then v equally spaced bins are constructed |

`weights` |
replicate weights for x obervations, should sum to 1 |

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

### Value

An object of class `density`

with components:

`x` |
midpoints of the bin boundaries |

`y` |
estimated function values of the mixing density |

`g` |
function values of the mixture density at the observed x's. |

`logLik` |
the value of the log likelihood at the solution |

`dy` |
Bayes rule estimates of |

`status` |
the Mosek convergence status. |

### Author(s)

R. Koenker

### References

Koenker, R and I. Mizera, (2013) “Convex Optimization, Shape Constraints,
Compound Decisions, and Empirical Bayes Rules,” *JASA*, 109, 674–685.

Gu J. and R. Koenker (2014) Unobserved heterogeneity in
income dynamics: an empirical Bayes perspective, *JBES*, forthcoming.

### See Also

Gammamix for a general implementation for Gamma mixtures