Teresa Alpuim

The kalman filter in the estimation of area precipitation

The aim of this paper is to provide appropriate statistical methods to obtain accurate area rainfall estimates based on both weather radar and raingauge observations. As known from previous work, a good way to combine the two types of measurements is via a state space representation and the use of the Kalman filter. In this paper a three step procedure is proposed. Also, several state space representations are discussed and a new method of estimation of the parameters is proposed. Finally, a practical study is made, where the results of different models are compared. Copyright

On the efficiency of regression analysis with AR(p) errors

In this paper we will consider a linear regression model with the sequence of error terms following an autoregressive stationary process. The statistical properties of the maximum likelihood and least squares estimators of the regression parameters will be summarized. Then, it will be proved that, for some typical cases of the design matrix, both methods produce asymptotically equivalent estimators. These estimators are also asymptotically efficient. Such cases include the most commonly used models to describe trend and seasonality like polynomial trends, dummy variables and trigonometric polynomials. Further, a very convenient asymptotic formula for the covariance matrix will be derived. It will be illustrated through a brief simulation study that, for the simple linear trend model, the result applies even for sample sizes as small as 20.