Regression method data imputation with or without variance equalization is also provided. Xu, where x is a vector of unknown coefficients, and Q, R, A, B, C, D, Xl, and Xu are known matrices. CLSQ Constrained least squares is a special case of the the quadratic programming problem. CLSQ is a procedure included in the QP module for computing constrained least squares regression estimates. CLSQ also computes the correct standard errors of the constrained coefficients.
Most regression models contain coefficients that can be bounded or constrained in some way.
For example, it is often known that one or more coefficients are positive or are in some range. Incorporating this information into the estimation using CLSQ always improves the t-statistics of the estimates over the unconstrained estimation. Even specifying very broad ranges for the coefficients can improve the efficiency of the estimates, and for that reason the use of CLSQ could be recommended for all least squares problems. The Effective Mix model is a constrained least squares problem for which CLSQ is suited. The QP solution yields estimates of the ideal distribution of the portfolio among the securities.