Nonnegative estimates of variance components in a two-way random model

  • Received : 2018.01.22
  • Accepted : 2018.06.05
  • Published : 2019.07.31


This paper discusses a method for obtaining nonnegative estimates for variance components in a random effects model. A variance component should be positive by definition. Nevertheless, estimates of variance components are sometimes given as negative values, which is not desirable. The proposed method is based on two basic ideas. One is the identification of the orthogonal vector subspaces according to factors and the other is to ascertain the projection in each orthogonal vector subspace. Hence, an observation vector can be denoted by the sum of projections. The method suggested here always produces nonnegative estimates using projections. Hartley's synthesis is used for the calculation of expected values of quadratic forms. It also discusses how to set up a residual model for each projection.


Supported by : National Research Foundation of Korea (NRF)


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