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

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. JSTOR 2283583.

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. hdl:10338.dmlcz/104230.

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. JSTOR 2284708.

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