# Posterior Densities for Nonlinear Regression with Equicorrelated Errors

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## Abstract

C~~~R Discussion for a erEconomic Research CBM R 8414 1989 7 I'~IINIIIIIIIIIIIIIIIIIIIIIUIIUIIININIUIiIII No. 8907 POSTERIOR DENSITIES FOR NONLINEAR REGRESSION WITH EQUICORRELATED ERRORS by J. Osiewalski February , 1989 Posterior Densities for Nonlinear Regression with Equicorrelated Errors by Jacek Osiewalski Academy of Economics ul. Rakowicka 27 31-510 Kraków Poland JEL classification: 211 Keywords: nonlinear models, Bayesian analysis, equicorrelation Abstract. For a nonlinear regression model with a constant term, it is shown that - under diffuse priors of the constant term and of the error precision - the assumption of equicorrelated errors (instead of uncorrelated ones) has no new consequences on Bayesian estimation of the (nonlinear) regression parameters (except for the constant term). February 1989 Acknowledgement: Comments by Mark Steel are gratefully acknowledged. 1 1. Introduction Main non-Bayesian results concerníng linear regression with an intercept and with equicorrelated observations were obtained long time ago. Assuming joint normality of observations, Halperin (1951) showed that certain estimators and tests of significance used in regression analysis when observations are independent are equally valid in the case of equicorrelated observations. McElroy (1969) proved that, in a linear regression model with an intercept, OLS estimators are BLU if and only if the errors have the same variances and the same nonnegative coefficient of correlation between each pair; see also Balestra (1970). Bayesian results for a linear model with equicorrelated disturbances are presented in Osiewalski (1987); it is shown that under diffuse priors of all the regression parameters and of the error variance: 1. the posterior of the correlation parameter is equal to its prior, 2. the marginal posterior of the regression parameters (except for the constant term) is the same as in the case of uncorrelated disturbances, 3. the posterior m

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