Large Sample Properties of the Score Test Statistic in Nonlinear Regression Involving Stationary and Non-stationary Errors: An Application in Age Estimation of European Wild Rabbits from Eye Lens Weight

The purpose of this study is to determine the asymptotic distribution of score test statistics for hypothesis tests in a nonlinear regression model that includes stationary and non-stationary errors. We estimate the model parameters using the conditional maximum likelihood estimation method. Then, we derive the asymptotic distribution of score test statistics for various hypothesis tests. Through simulation studies, the empirical percentiles of the unit root test statistic are calculated and the performance of the conditional maximum likelihood estimators is derived. Additionally, the relative frequency of the unit root, autocorrelation, and regression tests are examined. The proposed method is then applied to predict the ages and age classes of the European wild rabbits (Oryctolagus cuniculus) from eye lens mass (measured by weight), to demonstrate the practical application of the theoretical findings.