Hildreth–Lu estimation, named for Clifford Hildreth and John Y. Lu, is a method for adjusting a

linear model In statistics, the term linear model is used in different ways according to the context. The most common occurrence is in connection with regression models and the term is often taken as synonymous with linear regression model. However, the term ...

in response to the presence of

serial correlation Autocorrelation, sometimes known as serial correlation in the discrete time case, is the correlation of a signal with a delayed copy of itself as a function of delay. Informally, it is the similarity between observations of a random variable as ...

in the

error term In mathematics and statistics, an error term is an additive type of error. Common examples include: * errors and residuals in statistics, e.g. in linear regression * the error term in numerical integration In analysis, numerical integration ...

. It is an iterative procedure related to the

Cochrane–Orcutt estimation Cochrane–Orcutt estimation is a procedure in econometrics, which adjusts a linear model for serial correlation in the error term. Developed in the 1940s, it is named after statisticians Donald Cochrane and Guy Orcutt. Theory Consider the mode ...

. The idea is to repeatedly apply

ordinary least squares In statistics, ordinary least squares (OLS) is a type of linear least squares method for choosing the unknown parameters in a linear regression model (with fixed level-one effects of a linear function of a set of explanatory variables) by the prin ...

to :

y_t - \rho y_ = \alpha(1-\rho)+(X_t - \rho X_)\beta + e_t \,

for different values of

\rho

between −1 and 1. From all these auxiliary regressions, one selects the pair ''(α, β)'' that yields the smallest

residual sum of squares In statistics, the residual sum of squares (RSS), also known as the sum of squared estimate of errors (SSE), is the sum of the squares of residuals (deviations predicted from actual empirical values of data). It is a measure of the discrepan ...

See also

References

Further reading