## Asymptotic expansions and curvature measures in a nonlinear regression model |

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Bates and Watts curvature and parameter curvature measures curvatures and Effron's deﬁned by BW deﬁned in Section deﬁnition Department of Economics discrepancy from normality distribution function distribution of MLE Edgeworth type asymptotic effect and intrinsic effects of nonlinearity Effron's statistical curvature especially for secretaries Expansion for MLE expansion of distribution ﬁrst order condition function of MLE Hermite polynomial Hijk are Hermite Hiroshima University April identity matrix intrinsic curvature Koichi Haekawa Likelihood ratio test log likelihood ratio maximum likelihood estimator MLE 9 MLE and LR nonlinear regression model O(T_ obtain ONTARIO LONDON CANADA order asymptotic expansion orthogonal matrix parameter effect curvature parameterization random variable relationship between BW's reparameterization RESEARCH REPORT 8907 rewrite the asymptotic si,sj,sk strictly a property T_ is strictly Taniguchi 1986 Taniguchi and Maekawa Taylor expansion Theorem third order asymptotic type asymptotic expansion University April 1989 University of Western vector Wtjk wtkwtij