Asunción Rubio

Kalman filter with a non-linear non-Gaussian observation relation

The dynamic linear model with a non-linear non-Gaussian observation relation is considered in this paper. Masreliezs theorem (see Masreliezs (1975)) of approximate non-Gaussian filtering with linear state and observation relations is extended to the case of a non-linear observation relation relation that can be approximated by a second-order Taylor expansion.ResumenEl modelo lineal dinámico con observación nolineal y no-Gausiano se estudia en este artículo. Se extiende el teorema de Masreliez (ver. Masreliez (1975)) como una aproximación de filtrado no-Gausiano con ecuación de estado lineal y ecuación de observaciones también lineal, al caso en que la ecuación de observaciones nolineal pueda aproximarse mediante la extesión de Taylor de segundo orden.

Diagnostics of Regression Model: Test of Goodness of Fit

A test statistic for goodness of fit of the M-estimates of the linear regression model is proposed and its asymptotic behaviour is described. Numerical study on real data is included.