Pseudosolution of Linear Functional Equations: Parameters Estimation of Linear Functional Relationships
This book presents the author’s new method of two-stage maximization of a likelihood function, which helps to solve a series of non-solving before the well-posed and ill-posed problems of pseudosolution computing systems of linear algebraic equations (or, in statistical terminology, parameters’ estimators of functional relationships) and linear integral equations in the presence of deterministic and random errors in the initial data. This book presents, for the first time, a solution of the...
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This book presents the author’s new method of two-stage maximization of a likelihood function, which helps to solve a series of non-solving before the well-posed and ill-posed problems of pseudosolution computing systems of linear algebraic equations (or, in statistical terminology, parameters’ estimators of functional relationships) and linear integral equations in the presence of deterministic and random errors in the initial data. This book presents, for the first time, a solution of the problem of reciprocal influence of passive errors of regressors and of active errors of predictors by computing point estimators of functional relationships.
Systems of linear algebraic equations11Analysis of passive experiments11.1Multiple linear regression analysis21.2Linear model subject to the linear constraints131.3Estimation of the normal parameter vector181.4Confluent analysis of passive experiment361.5Stable parameter estimation of the degenerated confluent model561.6Confluent-regression analysis of passive experiment671.7Stable estimation of normal parameters of the degenerated confluent-regression model84Systems of linear algebraic equations932Analysis of active and complicated experiments932.1Analysis of active experiment942.2Analysis of active-regression experiment1112.3Analysis of passive-active experiment1172.4Analysis of passive-active-regression experiment127Linear integral equations1413Analysis of passive and of active experiments1413.1Variational problems for the construction of pseudosolutions of linear integral equations1413.2About the appurtenance of Gauss-Markov processes to probability Sobolev spaces1663.3Fredholm linear integral equations with the random right-hand side errors1823.4Linear integral equation with the measured or realized core1873.5Technique of computations201
