Functional estimation problem error, sources

The remainder of this chapter is structured as follows. In Section II the problem of deriving an estimate of an unknown function from empirical data is posed and studied in a theoretical level. Then, following Vapnik s original work (Vapnik, 1982), the problem is formulated in mathematical terms and the sources of the error related to any proposed solution to the estimation problem are identified. Considerations on how to reduce these errors show the inadequacy of the NN solutions and lead in Section III to the formulation of the basic algorithm whose new element is the pointwise presentation of the data and the dynamic evolution of the solution itself. The algorithm is subsequently refined by incorporating the novel idea of structural adaptation guided by the use of the L" error measure. The need... 

The preceding results are applied to develop a strategy that allows us to isolate the source of gross errors from a set of constraints and measurements. Different least squares estimation problems are resolved by adding one equation at a time to the set of process constraints. After each incorporation, the least square objective function value is calculated and compared with the critical value. 

Give the standard errors associated with the values of area and width that are determined from the line profile. Is the scatter in the data K and tt IT, tt IFb) as a function of (H ) or Tconsistent with those error estimates Discuss other sources of error beyond line-fit uncertainties. Comment on the agreement between (area)B/(area)A and Ah/Ag as values of Kat 25°C. If the temperature dependence of the area ratio had been measured for sample 6 rather than sample 1, would the value for the acid-catalyzed reaction be the same as A7/° for the nncatalyzed reaction What difficulty would complicate matters if one tried to determine activation energies from the temperature dependence of the line widths of acid solntions (in addition to the problem of assessing the values of 1/7Ja and 1/7 b) ... 

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