Abstract
We propose a methodology for fitting theoretical models to data. The dependent variable (or response) and the model are transformed in the same way. Two types of transformations, power transformation and weighting, are used together to remove skewness and to induce constant variance. Our method is applied to the stock-recruitment data of four fish stocks. Also discussed are estimates of the conditional mean and the conditional quantiles of the original response.
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References
Bartlett, M.S., 1947. The use of transfanations. Bianetrics, 3, 39–52.
Beverton, R.J.H., and Holt, S.J., 1957. On the dynamics of export fish populations. Her Majesty’s Stationery Office, London, 533 p.
Bickel, P.J., and Doksum, K.A., 1981. An analysis of transformations revisited Journal of the American Statistical Association, 76 296–311.
Bac, George E.P. and Cox, David R., 1964. An analysis of transformations (with discussion). Journal of the Royal Statistical Society, Series B, 26, 211–246.
Bac, George E.P. and Hill, William J., 1974. Correcting inhanogeneity of variance with per transformation weighting. Technanetrics, 16, 385–389.
Bac, George E.P. and Jenkins, G.M., 1976. Time Series Analysis: Forecasting and Control, Revised Edition. Holden-Day: San Francisco.
Carroll, R.J., 1980. A robust method for testing transformations to achieve approximate normality. Journal of the Royal Statistical Society, Series B 42, 71–78.
Carroll, R.J. and Ruppert, D., 1982. Robust estimation in heteroscedastic linear models Annals of Statistics 10, 429–441.
Carroll, R.J. and Ruppert, D., 1984. Power transformations when fitting theoretical models to data. Journal of the American Statistical Association, 79, 321–328.
Carroll, R.J. and Ruppert, D., 1985. Transformations in regression: a robust analysis. Technanetrics, 27, 1–12.
Draper, Norman and Smith, Harry, 1981. Applied Regression Analysis, 2nd Edition. Wiley: New York.
Duan, Naihua, 1983. Smearing estimate: a nonparametric retransformation method. Journal of the American Statistical Association, 78, 605–610.
Pritchard, D.J., Downie, J., and Bacon, D.W., 1977. Further consideration of heteroscedasticity in fitting kinetic models. Technanetrics, 19, 227–236.
Ricker, W.E., 1954. Stock and recruitment. J. of Fish. Res. Board Can., 11, 559–623.
Ricker, W.E. and Smith, H.D., 1975. A revised interpretation of the history of the Speena River sockeye salmon (Oncorhynchus nerka). J. the Fish. Res. Board of Can., 32, 1369–1381.
Ruppert, D., Reish, R.L., Deriso, R.B., and Carroll, R.J., 1985. A Stochastic population model for managing the atlantic manhaden fishery and assessing managerial risks. Can. J. Fish. and Aqu. Sc.-to appear.
Walters, C.F., 1985. Bias in the estimation of functional relationships from time series data. Can. J. Fish. and Aqu. Sc., 42, 147–149.
Walters, C.F., Hilburn, R., Staley, M.J., Wong, F., 1982 Report to the Pearse Commission on Pacific Fisheries Policy, Vancouver, B.C.
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Ruppert, D., Carroll, R.J. (1985). Data Transformations in Regression Analysis with Applications to Stock—Recruitment Relationships. In: Mangel, M. (eds) Resource Management. Lecture Notes in Biomathematics, vol 61. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-46562-8_2
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DOI: https://doi.org/10.1007/978-3-642-46562-8_2
Publisher Name: Springer, Berlin, Heidelberg
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