Fitting y equals beta x when variance depends on x

John Van Dyke
1964 Journal of Research of the National Bureau of Standards Section B Mathematics and Mathematical Physics  
This paper prese nts some results concerni ng the selection of a me thod for estimating the slope of a straight line through the origin. For fitting the line y= {3x whe n th e variance of y is proportional to xP, it is well known that the bes t estimate of {3 de pe nds on p. In practi ce, howe ver, only integer values of p 1Y0uld be convenient to work with. One of the estim ators appropriate for p = 0,1,2 would probably be used if the value of p we re in fac t fractional, or if it we re only
more » ... if it we re only a(lproximately known . This paper provides so me guides for c hoosing the bes t among these es timators in a partic ular situation. Formulas for the bes t es timators of {3 and th eir varian ces are give n. Estimators of {3 appropriate for integer valu es of p are co mpared in the case wh en p is not integral, but is kn ow n, a nd in the case whe n p is only approximately known . Es tima tio n of th e varian ces of es tim ators of {3 is co nside red. Finall y, so me res ult s are give n on th e effec t of th e s pac ing of th e x valu es on the co mp ari so n of the es tim a tors.
doi:10.6028/jres.068b.012 fatcat:ybkjjpmt6va77gewm2tcrpmtam