Topics in Modern Statistics

Topics:

• Nonparametric Regression
  1. Univariate Nonparametric Regression
     • kernel estimation
     • local polynomial regression
     • smoothing splines
     • generalized Fourier series
       • polynomial regression
       • trigonometric regression (Fourier series)
       • wavelets
  2. Multivariate Nonparametric Regression
     • semiparametric models
     • additive models, backfitting algorithm
     • projection pursuit
     • Alternating Conditional Expectations (ACE)
     • Additive and Variance Stabilizing Transformation (AVAS)
     • Multiple Adaptive Regression Splines (MARS)
     • neural networks
• Classification
  • discriminant analysis
  • logistic regression, multinomial logistic regression
  • neural networks
  • support vector classifiers, support vector machines (SVM)
  • k-nearest neighbour
  • classification trees (CART)
  • bagging, boosting, random forests
• Clustering
  • probablistic methods: mixture modeling, nonparametric density estimation
  • cluster analysis
    • combinatorial algorithms
    • partioning methods: K-means, K-medoids
    • hierarchical clustering: agglomerative and divisive methods

Literature

• Nonparametric Regression :
  Efromovich, S. Nonparametric Curve Estimation.
  Eubank, R.L. Spline Smoothing and Nonparametric Regression.
  Fan, J. and Gijbels, I. Local Polynomial Modelling and Its Applications.
  Friedman, F., Hastie, T. and Tibshirani, R. The Elements of Statistical Learning.
  Hardle, W., Muller, M., Sperlich, S. and Werwatz, A. Nonparametric and Semiparametric Models.
  Hastie, T.J. and Tibshirani, R.J. Generalized Additive Models.
  Izenman, A.J. Modern Multivariate Statistical Techniques.
  Simonoff, J.S. Smoothing Methods in Statistics.
  Takezawa, K. Introduction to Nonparametric Regression.
  Wasserman, L. All of Nonparametric Statistics.
  others

  Classification & Clustering :

  Bishop, C.M. Pattern Recognition and Machine Learning.

  Friedman, F., Hastie, T. and Tibshirani, R. The Elements of Statistical Learning.

  Gordon, A.D. Classification.

  Izenman, A.J. Modern Multivariate Statistical Techniques.

  Mirkin, B. Mathematical Classification and Clustering.

  others

Homework Exercises:

Exam: