Estimation of functional parameters without assuming that the functions belong to a prespecified finite-dimensional class appears in many applications and statistical problems from probability density estimation to regression and time series analysis. This course covers some classical techniques in this area such as kernel estimation, splines, wavelets and other orthonormal basis expansions as well as some more modern methods such as neural networks. Model selection and parameter tuning techniques including cross-validation and penalization are also addressed. Prerequisite: Math 3200 and Math 493 (concurrently taken is fine), a good course in linear algebra (Math 309 or 429), and some fundamentals of computer programming (CSE 131).
Course Attributes: FA NSM; AS NSM