Statistical Computing with R 讲义（练习及答案）

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Maryland大学Eric V. Slud的课件

[size=+2]OUTLINE of Course TOPICS statistics705_umd_slud.zip (4.83 MB)

2011-11-8 01:25:06 上传

   1. Introduction to R:

Starting and quitting R, on-line help, R operators and functions, creating
R objects, data types (vectors, matrices, factors, functions, lists), managing
data (combining  objects, subsetting, creation of frames), R graphics.

   2. Monte Carlo and Simulation in R:

Basic random number generation, applications of LLN and CLT  in simulations,
numerical integration, importance sampling, empirical distributions, Markov Chain
Monte Carlo. Managing loops in R.

   3. Numerical Optimization in Statistics:

Objective functions in statistics, and managing functions in  R. Linear and nonlinear
least squares, special considerations in maximizing likelihoods, penalized likelihood,
steepest descent, quasi-Newton-Raphson methods, constrained maximization, EM
algorithm. Diagnostics for misspecified models.

   4. Linear and Generalized Linear Models:

Regression summaries, model fitting, prediction, model updating, analysis of residuals,
model criticism, ANOVA, generalized linear  models, specifying link and variance
functions, stepwise model selection, deviance analysis.

Comparisons of implementations in R and SAS. Fitting mixed-effect (generalized)
linear models in R.

   5. Bootstrapping Methodology:

Parametric bootstrap, empirical CDF, bootstrap standard errors and confidence intervals,
estimation of bias, jackknife, application to regression.

   6. Smoothing & Nonparametric Regression:

Spline smoothing, kernel smoothing, selecting tuning parameters by cross-validation.
Graphical aspects of smoothing.

   7. MCMC and the Gibbs Sampler.

Definitions and basic ideas of MCMC ad Gibbs-Sampler simulation methodology,
including a brief introduction to `Bayesian Computing' using BUGS through R.

   8. Mixed and Multilevel Models fitted and interpreted via
       Likelihood methods and Bayes (MCMC) methods in R.

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