D.N. Politis: Current Classes

287C Homework: 287C HW

287A take-home final (due under the door of APM5747 by 1pm on Wed March 19):

Ch. 4: do exercises 9, 10, 13, 17, 19;

Ch. 5: do exercises 3, 20; and the following exercise:

Let X_t=Y_t+W_t where the Y series is independent of the W series. Assume Y_t satisfies an AR(1) model (with respect to some white noise), and W_t satisfies a different AR(1) model (with respect to some other white noise). Show that X_t is not AR(1) but it is ARMA(p,q) and identify p and q. [Hint: show that the spectral density of X_t is of the form of an ARMA(p,q) spectral density.]

END OF FINAL

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Winter 2008: MATH 281B "Mathematical Statistics"

Instructor: Dimitris Politis, dpolitis@ucsd.edu ; Office hours: MW 1:30-3pm at APM 5747

TA: Michael Scullard, mscullar@math.ucsd.edu ; Office hour: F 1-2pm at APM 6333

GRADES:

HW = 35%, Midterm (in-class) = 25%, Final (take home) =40%

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Winter 2007: MATH 282A "Applied Statistics"

Time/Room: MF 4:00--4:50 pm at APM 5829; W 4:00--4:50 pm at Seqoya Hall, Room 148 (in Econ. Dept.)
Office hours: MF 5:00-5:45, W 3:00-3:45, or by appointment (email: dpolitis@ucsd.edu)

The theory and practice of linear regression and linear models will be discussed. Least squares will be defined by means of projections in n-dimensional Euclidean space. Choosing the regression model (its dimension, etc.) will also be addressed. Prerequisite: a basic statistics course and linear algebra-or instructor consent.

282A Textbooks:

Seber and Lee, Linear regression analysis, Wiley, 2003, 2nd ed. (required)
Draper and Smith, Applied regression analysis, 3rd ed., Wiley (recommended)

GRADES:

HW = 20%, Midterm (in-class) = 30%, Final (take home) =50%

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Spring 2007: MATH 282B "Applied Statistics"

Time: 4pm-5pm
Room: APM 5829
Office hours: TBA or by appointment (email: dpolitis@ucsd.edu)

Departures from underlying assumptions in regression. Model selection. Nonlinear regression. Introduction to nonparametric regression. Prerequisite: 282A

282B Textbooks (recommended):

Elements of Statistical Learning, by Hastie-Tibshirani-Friedman,Springer(2002),
Nonlinear regression analysis and it's application, by Bates and Watts,Wiley(1988)
Nonlinear regression, by Seber and Wild,Wiley(2003)
Nonparametric smoothing and lack-of-fit tests, by J. Hart, Springer(1997)

282B COMPUTATIONAL HOMEWORK PROBLEM :

Consider the model: Y=f(X)+error where f is a polynomial of finite (but unknown) degree.

The data (with n=21) are below:

Y=(-5.07 -3.63 -1.92 -0.72 -0.79 -2.00 0.69 0.63 -0.92 1.05 -1.33 0.04 -0.14 -2.10 -0.43 -0.71 1.10 0.75 3 .36 4.17 4.57)

and X=(-2.0 -1.8 -1.6 -1.4 -1.2 -1.0 -0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0)

a) Use the four methods (residual diagnostic plots searching for patterns, forward and backward F-tests, and Mallows Cp) to pick the optimal order of the polynomial to be fitted. Do all four give the same answer? Explain?

b) With the optimal order obtained from Mallows Cp fit the model and get parameter estimates (including the error variance). If in your final model you see some parameter estimates that are close to zero, perform a test to see if they are significantly different from zero or not (in which case they should not be included in the model.

c) In your final model, do diagnostic plots to confirm your assumptions (what are they?) on the errors.

d) FOR EXTRA CREDIT (OR IN LIEU OF FINAL PROJECT): Repeat part (a) with ridge regression and/or the lasso, and compare with results of part (a).

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Spring 2007: MATH 289A "Topics on the Bootstrap"

Time: 3pm-4pm
Room: APM 7421
Office hours: TBA or by appointment (email: dpolitis@ucsd.edu)

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Winter 2006: MATH 287A "Time Series Analysis"
Time/Room: MWF 4-5pm at APM 6218

Office hours: TBA by appointment (email: dpolitis@ucsd.edu)

Weak and strict stationarity of time series, i.e. stochastic processes in discrete time. Breakdowns of stationarity and remedies (differencing, trend estimation, etc.). Optimal (from the point of view of Mean Squared Error) one-step-ahead prediction and interpolation; connection with Hilbert space methods, e.g. orthogonal projection. Autoregressive (AR), Moving Average (MA), and Autoregressive-Moving Average (ARMA) models for stationary time series; causality, invertibility, and spectral density. Maximum Entropy models for time series, and Kolmogorov's formula for prediction error. Estimation of the ARMA parameters given data; determination of the ARMA model order using criteria such as the AIC and BIC. Nonparametric estimation of the mean, the autocovariance function, and the spectral density in the absence of model assumptions. Confidence intervals for the estimated quantities via asymptotic normality and/or bootstrap methods. Prerequisite: a basic statistics and probability course or instructor consent.

287A Textbooks:

Time Series: Theory and methods, 2nd ed. Brockwell and Davis, Springer (1991) (required)

GRADES:

HW = 40%, Midterm (in-class) = 20%, Final (take home) =40%

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