Final answer:
Ridge regression estimator is a statistical technique used to adjust for multicollinearity in multiple regression data by adding a bias to reduce the variance of the estimates. It is calculated using the formula β^ridge = (X^TX + kI)^(-1)X^Ty, where k is the ridge parameter.
Step-by-step explanation:
The question pertains to the ridge regression estimator, which is used in the field of statistics within mathematics. Ridge regression is a technique for analyzing multiple regression data that suffer from multicollinearity. When multicollinearity occurs, least squares estimates are unbiased, but their variances are large so they may be far from the true value. By adding a degree of bias to the regression estimates, ridge regression reduces the standard errors. The method constructs the ridge regression estimator as follows:
β^ridge = (X^TX + kI)^(-1)X^Ty
Here, X is the matrix of input features, y is the vector of outputs, β^ridge is the estimated set of coefficients, I is the identity matrix, k is a complexity parameter (also known as the ridge parameter) that controls the amount of shrinkage applied to the coefficients. This estimator is used in cases where there are more variables than observations or when a data set has multicollinearity problems, which are problems where variables are highly correlated.