سوال ۱۸ کنکور ارشد علوم کامپیوتر ۱۳۹۹

Read the following passage and answer the question by choosing the best choice.

PASSAGE 1

Perhaps the richest and most exciting area of application of the projection theorem is the area of statistical estimation. It appeals in virtually all branches of science, engineering, and social science for the analysis of experimental data, for control of systems subject to random disturbances, or for decision making based on incomplete information.

All estimation problems discussed in this chapter are formulated as equivalent minimum norm problems in Hilbert space and are resolved by an appropriate application of the projection theorem. This approach has several practical advantages but limits our estimation criteria to various forms of least squares. At the outset, however, it should be pointed out that there are a number of different least squares estimation procedures which as a group offer broad flexibility in problem formulation. The differences lie primarily in the choice of optimality criterion and in the individual assumptions required. In this chapter three basic forms of least squares estimation are distinguished and examined.

Least squares is, of course, only one of several established approaches to estimation theory, the main alternatives being maximum likelihood and Bayesian techniques. These other techniques usually require a complete statistical description of the problem variables in terms of joint probability distribution functions, whereas least squares requires only means, variances, and covariances. Although a thorough study of estimation theory would certainly include other approaches as well as least squares, we limit our discussion to those techniques that are derived as applications of the projection theorem. In complicated problems the equations resulting from the other approaches are often nonlinear, difficult to solve, and impractical to implement. It is only when all variables have Gaussian statistics that these techniques produce linear equations, in which case the estimate is identical with that obtained by least squares. In many practical situations then, the analyst is forced by the complexity of the problem to either assume Gaussian statistics or to employ a least-squares approach. Since the resulting estimates are identical, which is used is primarily a matter of taste.

Question: The projection theorem ------------.