engleski

On Parameter Estimation by Nonlinear Least Squares in Some Special Two-Parameter Exponential Type Models

Two-parameter growth models of exponential type f(t ; a, b) = g(t)exp(a+bh(t)), where a and b are unknown parameters and g and h are some known functions, are frequently employed in many different areas such as biology, finance, statistic, medicine, ect. The unknown parameters must be estimated from the data (wi , ti, yi), i = 1, ..., n, where ti denote the values of the independent variable, yi are respective estimates of regression function f and wi > 0 are some data weights. A very popular and widely used method for parameter estimation is the method of least squares. In practice, to avoid using nonlinear regression, this kind of problems are commonly transformed to linear, which is not statistically justified. In this paper we show that for strictly positive g and strictly monotone h original nonlinear problem has a solution. Generalization in the lp norm (1 ≤ p < ∞) and some illustrative examples are also given.

two-parameter models ; least squares ; parameter estimation ; existence problem ; data fitting

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