ORDINARY LEAST SQUARES ESTIMATION OF A DYNAMIC GAME MODEL

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...

Least Squares Estimation

Recursive Least Squares Estimation

We start with estimation of a constant based on several noisy measurements. Suppose we have a resistor but do not know its resistance. So we measure it several times using a cheap (and noisy) multimeter. How do we come up with a good estimate of the resistance based on these noisy measurements? More formally, suppose x = (x1, x2, . . . , xn) T is a constant but unknown vector, and y = (y1, y2, ...

Nonlinear Least-squares Estimation

The paper uses empirical process techniques to study the asymptotics of the least-squares estimator for the fitting of a nonlinear regression function. By combining and extending ideas of Wu and Van de Geer, it establishes new consistency and central limit theorems that hold under only second moment assumptions on the errors. An application to a delicate example of Wu’s illustrates the use of t...