resampling methods

• bootstrapping
  • bootstrap basics (including empirical distributions, plug-in estimates, software (S-PLUS), and bootstrap history)
  • estimate of bias (and improved estimate of bias)
  • estimates of standard error, variance, and mean squared error
  • confidence intervals
    • "standard" intervals (based on asymptotic normality)
    • bootstrap-t intervals
    • percentile intervals
    • BC_a (bias-corrected and accelerated) intervals
    • ABC (approximate bootstrap confidence) intervals
  • estimate of prediction error (more than one method)
• jackknifing
  • estimate of bias
  • estimates of standard error and variance
  • confidence intervals (based on pseudo-values)
    • for variance of the main effect in a one-way random effects model
    • for variance of the random effect in a two-way mixed effects model
  • hypothesis testing (based on pseudo-values)
    • for inequality of two distribution variances

cross-validation

• estimate of prediction error (for regression and classification)
• unbiased CV method for histogram bin width selection

density estimation

• criteria for measuring goodness
  • ISE
  • IMSE and MISE
• methods
  • histograms
    • basics (including variance and bias)
    • selection of bin width
      • normal bin width reference rule
      • Freedman-Diaconis rule
      • oversmoothed bin width
      • Sturges' rule
      • unbiased cross-validation
    • two or more dimensions
  • adaptive histograms
  • average shifted histograms
  • frequency polygons
  • kernel density estimators
    • uniform kernel
    • triangle kernel
    • Epanechnikov kernel
    • Gaussion kernel

classification

• basics and the optimal Bayes classifier
• methods
  • discriminant analysis
  • k nearest neighbors
  • density estimation methods
  • CART

regression

• simple regression
  • ordinary least squares (OLS)
  • least absolute deviations (LAD)
  • M-regression (with an emphasis on asymptotic relative efficiency)
    • Huber
    • Tukey (bisquare/biweight)
    • Andrews
    • Hampel
  • least median of squares (LMS)
  • least trimmed squares (LTS)
• multiple regression
  • polynomial approximation modelling (using OLS)
  • tree-structured regression (using CART)

model/rule assessment and selection (emphasis on prediction accuracy)

• resubstitution estimate
• Mallows' statistic (C_p)
• Akaike information criteria (AIC)
• Bayesian information criteria (BIC)
• test sample estimate
• cross-validation (including a discussion of bias)
• bootstrap methods

dealing with dependent observations

• using a proper design to adjust for a blocking effect (and what happens if you don't)
• adjusting for a sequence effect w/o a full time series treatment (and what happens if you don't)
  • (although time series analysis was not emphasized, the AR1 model received a fair amount of coverage, and the MA1 model was also introduced)

dealing with heteroscedasticity

• one factor designs for continuous distributions
  • Welch's test
  • Alexander-Govern test
  • Welch-Sidák simultaneous confidence intervals (Dunnett's T3 intervals are a special case)
  • Games-Howell simultaneous confidence intervals
  • nonrobustness of the standard F test (and the Tukey studentized-range test)
  • discussion of the transformation method (and the associated danger)

dealing with monotone alternatives

• one factor designs
  • normal theory procedures
    • Abelson-Tukey test
    • modification of Abelson-Tukey test (incorporating a Satterthwaite approximation) that makes adjustments for heteroscedasticity
  • nonparametric procedures
    • Jonckheere-Terpstra test
    • one factor test similar to Page's test
• two factor designs
  • normal theory procedure: modification of Abelson-Tukey test
  • nonparametric procedure: Page's test

estimation of variance components in ANOVA models

• estimation of variance components in a one factor random effects model
  • point estimators
    • standard unbiased method of moments estimators
    • slightly improved estimators (including Hodges-Lehmann estimator)
    • maximum likelihood estimators
    • Klotz-Milton-Zacks estimators
    • Stein estimators
  • interval estimators (for main effect variance)
    • approximate method assuming normality (and incorporating a Satterthwaite approximation for the degrees of freedom)
    • jackknife method (using pseudo-values)
• interval estimation of variance component for the random effect in a two factor mixed effects model
  • approximate method assuming normality (and incorporating a Satterthwaite approximation for the degrees of freedom)
  • jackknife method (using pseudo-values)

two sample tests about variances

• standard (nonrobust) F test
• robust alternatives
  • Levene's s test
  • Shorack's APF test (a minor variation on the approach used by Box and Anderson)
  • jackknife test (using pseudo-values)

trimmed means (with an emphasis on asymptotic relative efficiency and selection of trimming proportion)

measures of performance

• bias
  • bias correction
• variance
• mean squared error (MSE) and mean absolute error (MAE)
  • bias-variance decomposition of MSE (and bias-variance trade-off)
• coverage probability and expected length for confidence intervals
• prediction error
  • for regression (average squared error)
  • for classification (misclassification rate)

Monte Carlo methods