1/2/2014 (c) 2000, Ron S. Kenett, Ph.D.1 Computer Intensive Techniques (Bootstrapping) Instructor: Ron S. Kenett Course.

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Presentation transcript:

1/2/2014 (c) 2000, Ron S. Kenett, Ph.D.1 Computer Intensive Techniques (Bootstrapping) Instructor: Ron S. Kenett Course Website: Course textbook: MODERN INDUSTRIAL STATISTICS, Kenett and Zacks, Duxbury Press, 1998

1/2/2014 (c) 2000, Ron S. Kenett, Ph.D.2 Course Syllabus Understanding Variability Variability in Several Dimensions Basic Models of Probability Sampling for Estimation of Population Quantities Parametric Statistical Inference Computer Intensive Techniques Multiple Linear Regression Statistical Process Control Design of Experiments

1/2/2014 (c) 2000, Ron S. Kenett, Ph.D.3Bootstrapping A computer intensive method, introduced in 1979 by Brad Efron from Stanford University in order to pool yourself out of the mess : T Take a Random Sampling With Replacement (RSWR) and compute statistic T T Resample M times and recompute statistic T Derive Empirical Bootstrap Distribution (EBD) TT E{EBD} and STD{EBD} and EBD percentiles estimate E{T} and STD{T} and Bootstrap Confidence Interval for population parameter

1/2/2014 (c) 2000, Ron S. Kenett, Ph.D.4 Bootstrap testing of the mean Hybrid Is this significantly different from 2150 ?

1/2/2014 (c) 2000, Ron S. Kenett, Ph.D.5 Boot1smp.exe

1/2/2014 (c) 2000, Ron S. Kenett, Ph.D.6 Hybrid Hybrid Hybrid Hybrid Hybrid

1/2/2014 (c) 2000, Ron S. Kenett, Ph.D.7 X-bar Std *Derive reference distribution by computing Empirical Bootstrap Distribution

1/2/2014 (c) 2000, Ron S. Kenett, Ph.D Empirical Bootstrap Distribution of mean 0.95 conf. BI = (2109.5, ) EBD of STD Empirical Bootstrap Distribution

1/2/2014 (c) 2000, Ron S. Kenett, Ph.D.9 Bootstrapping the ANOVA Hybrid1Hybrid2Hybrid F= MSBetween/MSWithin =

1/2/2014 (c) 2000, Ron S. Kenett, Ph.D.10 F= ANOVTEST.EXE EBD of F values

1/2/2014 (c) 2000, Ron S. Kenett, Ph.D.11 Draw samples from X and Y X: Stress or Load distributions Y: Strength distribution Estimate P( X>Y) Bootstrapping Stress Strength relationships

1/2/2014 (c) 2000, Ron S. Kenett, Ph.D.12 X=.0352,.0397,.0677,.0233,.0873,.1156,.0286,.0200,.0797,.9972,.0245,.0251,.0469,.0838,.0796 Y= ,.9457, , , ,.0362, , ,.0982,.7971,.8316, ,.4373, ,.6377 P( X>Y) = 0.04 with P.95 P.95 = 0.08 EBD of P(X>Y)