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On Parameter Estimation by Nonlinear Least Squares in Some Special Two-Parameter Exponential Type Models |
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PP: 2925-2931 |
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Author(s) |
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Darija Markovi“c,
Luka Borozan,
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Abstract |
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| 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. |
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