Study On Several Problems Of Biased Estimation

As an extremely important kind of statistical model in the modern regression theory, linear model has a wide rage of many fields such as economic, financial, industrial, biological and pharmaceutical. Its basic theory has become one of the basic tools of statistical studies, and the parameter estimation problemcaught many scholars and experts’ eyes.The research status of parameter estimation problem tells us that the classical least-squares estimate is not a good estimate in many cases. Thus people put forward many new estimates. One of an essential category is the biased estimation, which means that the mean value isunequal to the parameter vector.The in-depth researches of this thesis mainly focus on the following aspects: the superiority of various biased estimate is compared from definition and property and the conditions of superiority are popularized; for the select of the ridge parameter k, six types of ridge parameter k are introduced in the thesis which illustrates the different results from the different methods by means of instances; additionally, Hoerl-Kennard formula is further improved and researched for sake of optimizing the choice of ridge parameter k.