Welcome to CSI 970

Alternatives to Least Squares

We will use the book Alternatives to Least Squares, by Birkes and Dodge. Over the course of the semester each participant will give one or more lectures. The lectures will incorporate live sessions with S-Plus, Matlab, or other software.

You can download the PostScript versions of the lectures as they are available.

The schedule is:

• September 7
  Cliff Sutton: Overview of alternatives to least squares.

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• September 14
  Jim Gentle: Some properties of L1 estimators. (PostScript)
  

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• September 21 -- October 12
  Gentle and others: Experiments with L1 estimators.
  Some programs to experiment with:
  • l1sens.s View changes to an L1 fit.
  • rdexp.s Generate double exponentials (Laplace variates).
  • l1test.s Implement the approximate t-test for zero slope following an L1 fit.
  • powerl1.s Monte Carlo simulation of the power of the the approximate t-test for zero slope following an L1 fit.
  • powerl2.s Monte Carlo simulation of the power of the L2 test (the standard t-test following a least squares fit).
  • powerql1.s Monte Carlo simulation of the power of the Chow-type test following an L1 fit (compare with the t-like test for p=1).
  All of the programs for Monte Carlo experimentation allow for specification of a standard error distribution (i.e. one with no parameters, and presumably one with zero mean), and an ``error scale''. The model simulated is then:
  y <- 1 + x %*% trueb + errscale*errdist(n)

  Question: Which of the two L1 tests is better for use in simple linear regression?

  Question: If the errors have a double exponential distribution, how does the power of the t-test based on the (invalid) least squares fit (i.e., the ``normal test'') compare with the t-like test using the L1 fit? In particular, for sample size 40, evenly spaced x's, at the point where the power of the normal test is 0.50, is the power of the t-like test at least 0.60?

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• October 19
  Charles Perry: M estimation

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• October 26
  Summary; discussion of S-Plus programs for experimentation.

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• November 2
  Sameena Salvucci: the test with the M-estimator.
  Programs for experimenting with tests following M-estimation:
  • powerqm.s Monte Carlo simulation of the power of the Chow-type test following M estimation.
  • modrreg.s Modified version of rreg that allows specification of the scale estimate.

  Question: Is the size of this test unacceptably large when the errors have a Laplace distribution?

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• November 9
  Sameena Salvucci: more on M-estimation

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• November 16
  Kwang-Su Yang: nonparametric fitting
  Programs for experimenting with tests following M-estimation:
  • nonreg.s Program for simple linear regression using a nonparametric method.
  • powerqn.s Monte Carlo simulation of the power of the test using the nonparametric method and the forearm data.
  • The forearm data.

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• November 30
  Kwang-Su Yang: more on nonparametric regression

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• December 7
  Review and summary. Plans for writing a paper.

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