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Mathematics
Set Theory, Logic, Probability, Statistics
What are the commonly used estimators in regression models?
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[QUOTE="FactChecker, post: 6869562, member: 500115"] You should specify what the situation is when "we" linearize the model. I don't think there is any good answer that fits all situations. I know of two common situations: 1) When the random errors are a percentage of the ##Y## values. The model is ##Y = e^{\epsilon} *f(X)##. Taking logarithms puts it into the linear form ##\ln(Y) = \ln(f(X)) + \epsilon##, where ##\epsilon## is N(0, ##\sigma##). In this case, least squares can still be used. 2) When the parameters of ##Y = a_0 + a_1 X + \epsilon## are not expected to have constant parameters, ##a_i##, The relationship is locally linearized and there is a linear model with "scheduled" coefficients, ##a_i(z)##, which are functions of some external parameters, ##z##. For fixed values of ##z##, the situation is standard. I am only familiar with the two situations I mentioned above. There may be many other situations that others can comment on. [/QUOTE]
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Mathematics
Set Theory, Logic, Probability, Statistics
What are the commonly used estimators in regression models?
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