A score matching estimator is defined as the minimizer of the score loss function. In the case of an exponential family with a density that satisfies boundary conditions, the score matching estimator can be explicitly written down. In this thesis, our primary focus is on applying score matching method to estimate the parameters of a Gaussian distribution N𝑑 (𝝁, 𝚺), with the goal of constructing a robust version of it. To achieve this, we start by deriving the explicit form of the score matching estimator for the unknown parameters 𝝁 and 𝚺 of the Gaussian distribution. We see that the form can be expressed as a composition of empirical mean and empirical covariance matrix. Then, replacing them to robust alternatives, we obtain the robust score matching estimator for the parameter 𝝁 and 𝚺. To observe the behavior of the estimators, we derive the concentration inequalities and conduct numerical simulations.     «

A score matching estimator is defined as the minimizer of the score loss function. In the case of an exponential family with a density that satisfies boundary conditions, the score matching estimator can be explicitly written down. In this thesis, our primary focus is on applying score matching method to estimate the parameters of a Gaussian distribution N𝑑 (𝝁, 𝚺), with the goal of constructing a robust version of it. To achieve this, we start by deriving the explicit form of the score matching...     »