Stat 101: Estimation

• Admistrivia
  • Homework due last day of class

Introduction to Estimation and Confidence intervals

• Suppose your assistant come screaming into your office and says: "We have gone out of bounds on the control chart!"

  • Yikes! How bad is it?
  • Is going off any control chart equally bad?
  • It would be a big change if it went off the daily control chart.
  • It would be a very small change if it went off the annual control chart.
  • Both require corrective actions, but they differ.
  • Speed is of the importance for the daily problem--whereas accuracy is of importance for the annual chart.
  • Confidence intervals try to capture this concept.
  • Two pieces: best guess and accuracy
  • Today we will study the idea of good guessing
  • Tomarrow we study accuracy

• Guessing = estimation

• Estimate the width of a wire
  • Situation: Manufacturing memory. One important "wire width" should be about 50 nm.
  • Data: We use an atomic force microscope to measure widths several times aday.
  • Goal: Guess average width for all chips manufactured today.
  • estimator 1 = ave of 10 measurements made today (X₁ + ... + X₁₀)/10
  • Estimator 2 = ave of 1000 measurements made over the past 100 days
  • Estimator 2 could be biased

• Estimators are random variables!

• Estimators have distributions, means, variances

Estimation

• Unbiased: E(estimator) = truth
  • What if there are many unbiased estimators to choose from? (mean, median, max+min/2 all are unbiased)
  • Picking the one with the smallest standard deviation is called picking the "most efficient" estimator

• Consistent
  • Is the estimator close when n is large?
  • Example: using the median to estimate mu in an exponential. Median --> half life which doesn't equal the mean.

Last modified: Mon Nov 29 09:13:46 EST 1999