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Below is my attempt at a comparison between the two above-mentioned methods of estimation. Does anything in the table lack in validity and/or accuracy? Should any properties, advantages/disadvantages be eked out? Any suggestions/comments would be most appreciated!

MLE:

(1) Very accurate for a large N as the pdf of a^ would be unbiased

(2) No loss of information; all data are represented

(3) Quite complicated to solve mathematically

(4) Applicable for varied models, even non-linear

(5) Errors of estimation could be readily found: the 1sigma

error bars are those at which the logarithm falls by 0.5 from

its maximum

(6) Pdf must be known in advance

(7) In case pdf is false, goodness of fit may not be determined

LSE:

(1) Very accurate for a relatively small N as estimators would be biased

(2) -

(3) Finding the suitable linear model is quite simple mathematically

(4) Very convenient to use for linear models; very intricate for

non-linear ones

(5) -

(6) Variance and mean must be known in advance

(7) Method is very sensitive to unusual data values but

goodness of fit may be determined, through chi-squared

test e.g.

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# Comparing Least Squares and Maximum Likelihood?

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