The coding theorem and ordinary least-squares models in economics

C Ordinary Least Squares and Poisson Regression Models

With an assumption of normality for the regression error term, OLS also corresponds to Maximum Likelihood (ML) estimation. The note contains the statistical model and all expressions that are needed to carry out estimation and essential model diagnostics. Both concise matrix notation as well as more extensive full summation notation are employed, to provide a direct link to “loop” structures in...

Differentially Private Ordinary Least Squares

More specifically, we use Theorem B.1 from (Sheffet, 2015) that states that given a matrix A whose all of its singular values at greater than T ( , δ) where T ( , δ) = 2B (√ 2r ln(4/δ) + 2 ln(4/δ) ) , publishing RA is ( , δ)differentially private for a r-row matrix R whose entries sampled are i.i.d normal Gaussians. Since we have that all of the singular values of A′ are greater than w (as spec...

Differentially Private Ordinary Least Squares

Linear regression is one of the most prevalent techniques in machine learning; however, it is also common to use linear regression for its explanatory capabilities rather than label prediction. Ordinary Least Squares (OLS) is often used in statistics to establish a correlation between an attribute (e.g. gender) and a label (e.g. income) in the presence of other (potentially correlated) features...

Regional hydrologic analysis: Ordinary and generalized least squares revisited

Generalized least squares (GLS) regional regression procedures have been developed for estimating river flow quantiles. A widely used GLS procedure employs a simplified model error structure and average covariances when constructing an approximate residual error covariance matrix. This paper compares that GLS estimator (b̂GLS MC ), an idealized GLS estimator (b̂GLS E ) based on the simplifying as...

A Comparison of Ordinary Least Squares and Logistic Regression