Position weight matrix

Fig. 1. Converting a alignment of sites into a regular expression (RE) and a position weight matrix (PWM). The alignment of DNA sites is shown at the top. The RE (using the IUPAC ambiguity codes) is shown aligned below the sites. The corresponding counts of each letter in each alignment column—the position-specific count matrix (PSCM)—are shown in the next box. The PWM is shown below that. The last box shows the information content LOGO for the motif.

R3 is a symmetric positive definite weighting matrix. The minimization problem becomes... 

Consider GMM estimation of a regression model as shown at the beginning of Example 18.8. Let Wj be the optimal weighting matrix based on the moment equations. Let W2 be some other positive definite matrix. Compare the asymptotic covariance matrices of the two proposed estimators. Show conclusively that the asymptotic covariance matrix of the estimator based on Wj is not larger than that based on W2. 

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