Some results in non-parametric calibration
Misquitta, Penelope Patricia
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In statistical terminology, calibration is the problem of recovering the value of the control variable when the value of the response is given. Mathematically, it is the problem of determining the values ofthe independent variables that respond to a given function value: in other words, the problem involves finding a level set. In practice, the problem may in principle occur whenever a regression model is appropriate. Below we will describe some specific instances from medicine, ecology, and chemometry. To cover these examples, we will have to allow both the control and the response to be multivariate. Since the dimension of the response is often at least as large as that of the control, calibration may in many cases lead to a uniquely determined response. This is in particular true in chemometry where the dimension of the response is usually significantly larger than that of the control.