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Estimation theory – Branch of statistics to estimate models based on measured data; Identifiability – Statistical property which a model must satisfy to allow precise inference; Parameter identification problem – Parameter estimation technique in statistics, particularly econometrics
In statistics, the variance inflation factor (VIF) is the ratio of the variance of a parameter estimate when fitting a full model that includes other parameters to the variance of the parameter estimate if the model is fit with only the parameter on its own. [1]
Estimation theory is a branch of statistics that deals with estimating the values of parameters based on measured empirical data that has a random component. The parameters describe an underlying physical setting in such a way that their value affects the distribution of the measured data.
A given regression method will ultimately provide an estimate of , usually denoted ^ to distinguish the estimate from the true (unknown) parameter value that generated the data. Using this estimate, the researcher can then use the fitted value ^ = (, ^) for prediction or to assess the accuracy of the model in explaining the data.
Conversely, if we know the value of the latent variables , we can find an estimate of the parameters fairly easily, typically by simply grouping the observed data points according to the value of the associated latent variable and averaging the values, or some function of the values, of the points in each group.
and this can be minimized with respect to the stability constant value, K, and a parameter such the chemical shift of the species HG (nmr data) or its molar absorbency (uv/vis data). The minimization can be performed in a spreadsheet application such as EXCEL by using the in-built SOLVER utility. This procedure is applicable to 1:1 adducts.