DPDmetoden

DPDmetoden, or the density power divergence method, is a robust estimation framework used in statistics. It belongs to the family of density power divergences introduced in the late 1990s to provide reliable parameter estimates when data contain outliers or model misspecifications. The method works by measuring the divergence between the true data distribution and a parametric model, then choosing the model parameters that minimize this divergence. A key feature is a tuning parameter that controls the balance between robustness and statistical efficiency.

In practice, the method involves a parametric model f_theta and a sample from an unknown distribution g. The density power divergence of order beta between g and f_theta is minimized with respect to theta. When beta equals zero, the procedure coincides with maximum likelihood estimation, providing full efficiency under the assumed model. For beta greater than zero, the estimator becomes more robust to atypical observations, downweighting their influence on the fitted model.

The resulting DPD estimator has a bounded influence function for any beta > 0, which helps reduce sensitivity to outliers. The choice of beta represents a trade-off: larger beta increases robustness but may reduce efficiency if the model is correct. In practice, beta is selected using robust criteria, cross-validation, or prior robustness considerations. DPD methods have been applied across a range of models, including generalized linear models, regression, and time series, where outliers or contamination are a concern.

Overall, DPDmetoden provides a principled, tunable approach to robust parameter estimation, offering a continuum between maximum likelihood and more conservative, outlier-resistant fitting.