# MINQUE

Short description: Theory in the field of statistics

In statistics, the theory of minimum norm quadratic unbiased estimation (MINQUE)[1][2][3] was developed by C. R. Rao. Its application was originally to the problem of heteroscedasticity and the estimation of variance components in random effects models.

The theory involves three stages:

• defining a general class of potential estimators as quadratic functions of the observed data, where the estimators relate to a vector of model parameters;
• specifying certain constraints on the desired properties of the estimators, such as unbiasedness;
• choosing the optimal estimator by minimising a "norm" which measures the size of the covariance matrix of the estimators.

## References

1. Rao, C.R. (1970). "Estimation of heteroscedastic variances in linear models". Journal of the American Statistical Association 65 (329): 161–172. doi:10.1080/01621459.1970.10481070.
2. Rao, C.R. (1971). "Estimation of variance and covariance components MINQUE theory". J Multivar Anal 1: 257–275. doi:10.1016/0047-259x(71)90001-7.
3. Rao, C.R. (1972). "Estimation of variance and covariance components in linear models". Journal of the American Statistical Association 67 (337): 112–115. doi:10.1080/01621459.1972.10481212.