Functional Data Analysis and Its Applications

This lecture introduce Functional Data Analysis (FDA) with real-world examples. Techniques in FDA such as Functional Principal Component Analysis are discussed. Applications of FDA in R are demonstrated with the accompanied code scripts. Finally, comparisons between classical longitudinal data models and FDA are drawn and extensions to other issues in FDA are addressed.

Theory of Statistics I - Distributions (STP 501)

Teaching Assistant

Introduces rigorous probability theory, including distributions and expectations of random variables, transformations of random variables and order statistics, generating functions and basic limit concepts. Supplements the understanding of applied statistics with a firm grasp of the probabilistic underpinnings of theoretical statistics.

Theory of Statistics II - Inference (STP 502)

Teaching Assistant

Pesents techniques and basic results of mathematical statistics at a rigorous level. Develops the structure of statistical inference procedures, including the principles of data reduction, theory of estimation, confidence sets, hypothesis testing, and prediction for common parametric models.

Large Sample Theory (STP 527)

Teaching Assistant

Types of convergence, central limit theorems, theory of maximum likelihood estimation, efficiency, robustness, influence functions, theory of bootstrap methods.

Applied Analysis (APM 503)

Teaching Assistant

Convergence sequences and series of functions; metric space topology, compactness, completeness and the Ascoli-Arzela Theorem; Contraction Mapping Principle, Implicit Function Theorem; intro to Lebesgue integration leading to $L^p$-spaces; properties of Hilbert spaces, Fourier transform. Students should have knowledge of linear algebra, multivariable calculus, and analysis at the undergraduate level.

Probability (STP 421)

Grader

Laws of probability, combinatorial analysis, random variables, probability distributions, expectations, moment-generating functions, transformations of random variables, and central limit theorem.

Intermediate Real Analysis (MAT 472)

Grader

Introduces analysis in metric spaces with emphasis on the real line.

• Ping-Han.Huang@asu.edu
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