The Recursive Algorithm Of Least Squares Estimation For Linear Model

The content of the linear model is very rich, and the least square algorithm is the best part among them, and recursive least squares algorithm has been widely applied in data processing. In using normal least square algorithm to estimating the unknown parameters in models, forecasting precision is determined by the accuracy of the statistical data and the dynamic characteristics of the new data and so on.In this paper, the results of the recursive algorithm for least squares estimation of the previous studies, the linear model and generalized linear model coefficients, the recursive parameter estimation of linear models and generalized linear models were further study and proposed new recursive algorithm.According to the original data to set up the linear model, we get the relationship between the least square algorithm of coefficient of the new samples and the least square algorithm of coefficient of old samples. This relationship is called sample data for taking in the fresh. If we removed an outdated data, we get the relationship between the least square algorithm of coefficient of the new samples and the least square algorithm of coefficient of old samples. This relationship is called sample data for getting rid of the stale. More over, the relationship among new samples, eliminating samples and the original samples is called sample data for getting rid of the stale. Let us suppose that collection of data by the order of time a number of number, and be connect with the number of batches (batch number:n=1,2,…). This paper describes a new linear model of the data which join the new. the data which rid of the old,the data which new data instead of old one for least squares estimation of the data coefficient is called a n-recursive algorithm.In general conditions, we always hypothesis that the error of the linear regressive model is the same variance and irrelevant. But a lot of practical problems, their error variance may not be equal, and related to each other. Based on the recursive algorithm of the generalized linear model, obtained a new kind of generalized linear models of the sample which join the new, the sample which rid of the old,the sample which new data instead of old one for least squares estimation of the data coefficient is called a n-recursive algorithm.