This work is concerned with the estimation problem of linear model when thesample size is extremely large and the data dimension can vary with the samplesize. In this setting, the least square estimator based on the full data is not feasiblewith limited computational resources. Many existing methods for this problem arebased on the sketching technique which uses the sketched data to perform leastsquare estimation. We derive fine-grained lower bounds of the conditional meansquared error for sketching methods.

This work is concerned with the estimation problem of linear model when thesample size is extremely large and the data dimension can vary with the samplesize. In this setting, the least square estimator based on the full data is not feasiblewith limited computational resources. Many existing methods for this problem arebased on the sketching technique which uses the sketched data to perform leastsquare estimation. We derive fine-grained lower bounds of the conditional meansquared error for sketching methods. Our result implies that when thedimension is large, there is hardly a sampling method can have a faster convergencerate than the uniform sampling method.