OVERVIEW OF LEAST-SQUARES, MAXIMUM LIKELIHOOD AND BLUP PART 2

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Presentation transcript:

OVERVIEW OF LEAST-SQUARES, MAXIMUM LIKELIHOOD AND BLUP PART 2

LIKELIHOOD-BASED INFERENCE

1. The likelihood function

3. Information (Fisher’s) contained in the likelihood

5. Asymptotic Properties of Maximum Likelihood Estimators

BEST LINEAR UNBIASED ESTIMATION AND BEST LINEAR UNBIASED PREDICTION

C. Alternative method for computing BLUE (GLS) estimator of the vector of fixed effects: known V

EXAMPLE: BLUP OF 599 WHEAT LINES

IS BLUP OVERFITTING. FITCOR<-cbind(y,MATPAIR) cor(FITCOR) Y. BLUPR IS BLUP OVERFITTING? FITCOR<-cbind(y,MATPAIR) cor(FITCOR) Y BLUPR BLUP1 BLUP2 BLUP3 BLUP4 BLUP5 1.0000000 0.7391247 0.7384688 0.7159003 0.7275751 0.7295317 0.7287069 0.7391247 1.0000000 0.9963397 0.9508149 0.9841684 0.9863276 0.9852552 0.7384688 0.9963397 1.0000000 0.9444558 0.9812627 0.9814759 0.9806144 0.7159003 0.9508149 0.9444558 1.0000000 0.9348012 0.9338615 0.9328132 0.7275751 0.9841684 0.9812627 0.9348012 1.0000000 0.9688824 0.9680241 0.7295317 0.9863276 0.9814759 0.9338615 0.9688824 1.0000000 0.9979560 0.7287069 0.9852552 0.9806144 0.9328132 0.9680241 0.9979560 1.0000000 NO EVIDENCE BUT BLUPS CLOSELY CORRELATED

####HOW ABOUT TRAINING MEAN-SQUARED ERROR ####HOW ABOUT TRAINING MEAN-SQUARED ERROR? mse<-numeric(6) for (i in 1:6){ mse[i]<-sum((y-MATPAIR[,i])**2)/n } mse [1] 0.6877218 0.6866927 0.6834385 0.6869435 0.6875240 0.6875065