The University of Arizona  1993-95 General Catalog

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Statistics (STAT)
Economics Building, Room 200
(520) 621-4158

Professors Yashaswini Mittal, Head, Dan Bailey (Emeritus), J.L.
Denny, Jean E. Weber

Associate Professors Scott Emerson, A. Larry Wright

Assistant Professors Chengda Yang

Study of statistics enables one to model the uncertainty in data
and draw organized scientific conclusions from it. Data from
different disciplines post different statistical problems and
hence statistics is inherently an interdisciplinary field. The
department offers both theoretical and applied courses.
Statistics is available as a major in the Master of Science and
the Doctor of Philosophy degrees.

160. Introduction to Statistics (3) I II Descriptive statistics.
Basic probability concepts and probability distributions,
elementary sampling theory and techniques of estimation,
hypothesis testing, regression and correlation. Some analysis of
variance and nonparametric tests if time permits. Not applicable
to the math major. P, MATH 117R/S.

163. Beginning Statistics in Bioscience (3) I II Basic concepts
of probability and statistics. Descriptive statistics commonly
used in biological and medical sciences such as mean, standard
deviation, odds ratio and risk. Interpretation of statistical
plots and charts. Basic idea of estimation, regression and
hypothesis testing. Emphasis on statistical concepts and
interpretations of tests. P, MATH 117R/S.

263. Statistical Methods in Biological Sciences (3) I II
Organization and summarization of data, concepts of probability,
probability distributions of discrete and continuous random
variables, point and interval estimation, elements of hypothesis
testing, regression and correlation analysis, chi-square
distribution and analysis of frequencies, introduction to
analysis of variance as well as nonparametric statistics, with
special emphasis on analysis of biological and clinical data. P,
MATH 119, 123.

275. Statistical Methods in Management (3) I II Statistical
analysis and methods with a view toward applications in business
and economics. Basic concepts of probability, random variables,
probability distributions and sampling distributions. Statistical
inference techniques such as estimation, hypothesis, testing,
regression, correlation and analysis of variance are explored
through examples and via the use of Minitab. Emphasis is put on
the interpretations of Minitab outputs rather than running the
Minitab itself. P, MATH 119, 123.

361. Statistics for Engineering and the Physical Sciences (3) I
II Probability theory, point and interval estimation, hypothesis
testing and regression analysis; applications to quality control
and reliability theory. P, 9 units of calculus.

451. Introduction to Statistical Methods (3) I II Sample spaces,
random variables, probability. Distribution: binomial, normal,
Poisson, geometric. Expectations, variance, moment generating
functions. Central limit theorem and laws of large numbers. Basic
concepts of sampling distributions. Estimation, hypothesis
testing. An introductory theoretical course emphasizing concepts,
and interpretations. Limited mathematical proofs. P, MATH 123 or
MATH 125b, and one of STAT 160, STAT 263, STAT 275, STAT 361.

464. Theory of Probability (3) I II (Identical with MATH 464) May
be convened with 564.

466a. Theory of Statistics (3) I Sampling theory, point
estimation, limiting distributions, testing hypotheses,
confidence intervals, large sample methods, elements of
multivariate analysis. P, 464. (Identical with MATH 466a) May be
convened with 566a.

468. Applied Stochastic Processes (3) II (Identical with MATH
468) May be convened with 568.

509. Statistics for Research (4) I II Statistical concepts and
methods applied to research in other scientific disciplines.
Principles of estimation and hypothesis testing for standard one
and two-sample procedures. Correlation, linear regression,.
Contingency tables and analysis of variance. Not open to majors.
P, college algebra (Identical with GENE 509 and TOX 509)

548. Introduction to Statistical Packages (3) I Basic structure
of general purpose statistical software. Data formats, storage
and transmission. Relation between hardware and software. Usage
of major statistical packages SAS, BMDP, and SPSS on both
personal and mainframe computers. Open to graduate students in
all disciplines.

551. Applied Statistics I: Regression Analysis (3) I Regression
analysis including simple linear regression, and multiple linear
regression. Regression, diagnostics, variable selection
techniques, collinearity, non-linear models and transformations,
case studies. P, 451 and 509, MATH 223.

552. Applied Statistics II: Experiment Design (3) II Principles
of designing experiments. Randomization, blocked designs,
factorial experiments, response surface designs, repeated
measures, analysis of contrasts, multiple comparisons, multiple
comparisons, and variance component analysis. P, 451/551 and 509,
MATH 223.

553. Applied Multivariate Analysis (3) II Methods for analysis of
multivariate observations. Random vectors, multivariate
expectations and covariance matrices. Multivariate normal
distribution. Hotelling's T-square distribution. Multivariate
analysis of variance and linear regression. Principal component
and discriminant analysis, classification, clustering, canonical
correlation and factor analysis. P, 451 and 509.

554. Applied Time Series Analysis (3) I Methods for analysis of
time series data. Time domain techniques; ARIMA models,
estimation of process mean and autocovariance, model fitting,
forecasting methods. missing data. P, 451 and 509.

560a-560b. Probability and Random Processes (3-3) I First part of
the sequence will deal with probability. Sample spaces, basic
axioms of probability, combinatorial methods, conditional
probability and distributions, independence. Random variables,
discrete and continuous distributions. Binomial, Poisson,
geometric, normal, exponential and gamma distributions.
Transformations of random variables and Jacobians, expectation,
variance and other moments, laws of large numbers, central limit
theorem. Characteristic and generating functions. Fundamental
probability concepts without the use of measure theory. P, two
years of calculus., e.g. MATH 125a-125b and MATH 223. 560b: II
Second part of the sequence will cover elementary random
processes. Markov and stationary processes, random walk, renewal
theory, queuing networks, branching processes, Poisson processes,
martingales. Theory as well as some applications. No measure
theory requirement. P, 560a.

562. Sampling Survey Theory and Methods (3) II Introduction to
planning, execution, and analysis of surveys, methods of
sampling, estimation of population values, estimation of sampling
error and efficiency of methods. Special emphasis on finite
population applications. P, 509.

563. Nonparametric Statistics (3) I Distribution free statistical
methods for nominal and ordinal data. Measures of association.
Goodness of fit and runs tests. Analysis of one or more groups.
Correlation and regression of ranked data. P, 509.

564. Theory of Probability (3) I II (Identical with MATH 564) May
be convened with 464.

566a-566b. Theory of Statistics (3-3) 566a: I For a description
of course topics, see 466a. Graduate-level requirements include
more extensive problem sets or advanced projects. P, 464.
(Identical with MATH 566a) May be convened with 466a. 566b: II
Hypothesis testing. Type I and type II errors, Neyman-Pearson
theory, uniformly most powerful unbiased and invariant tests.
Likelihood ratio tests. Confidence intervals. Sequential
analysis, non-parametric and robust methods. Theoretical
foundation of statistical inference. P, 566a.

568. Applied Stochastic Processes (3) II (Identical with MATH
568) May be convened with 468.

572. Categorical Data Analysis (3) II Two-way contingency tables,
logistic, probit, log-log regression. Loglinear models. Model
selection techniques. Testing goodness of fit models. Numerical
methods for finding MLE. Treatment of ordinal and nominal
variables. Poisson and multinomial samplings. P, 451 and 509.

595. Colloquium
a. Statistics (1) [Rpt./3 units] I II Open to majors only

596. Seminar
a. Research Methods (1-4) [Rpt./6 units] I II

597. Workshop
a. Data Analysis (1) [Rpt./3 units] I II Open to majors only or
with permission of instructor. P, 451, 509 or equivalent.

641. Statistical Consulting (3) I II A course for statistics
graduate students providing experience in statistical consulting.
Client and statistician relationships, communication skills,
computing and graphical analysis resources, approaches to
problems with measurement error and missing data. Consulting
practice with client research problems under faculty supervision.
1R, 6L. P, advanced standing in the masters program.

660. Linear Models (3) I Multivariate normal distribution,
distribution of quadratic forms. Generalized inverses. Theory of
estimation and hypothesis tests for full rank linear models and
less than full rank models applied to regression models. Analysis
of variance models, variance component and mixed models and
unbalanced data models. Theoretical foundation course for linear
model analysis techniques. P, 566a, linear algebra, e.g. MATH

661. Probability Foundations of Mathematical Statistics (3) I
1994-95 Measure theory-based probability theory needed for
mathematical statistics. Measurable space, Lebsgue measure and
integral, distribution functions, random variables, expectation
and conditional expectation, characteristic functions, law of
large number, central limit theory, modes of convergence,
complete and sufficient statistics, martingale. P, 560a, MATH
523a, or consent of instructor.

667. Theory of Estimation (3) I Measure theory based point
estimation theory. Unbiasedness, information inequality.
Equivariance, location-scale family, exponential families.
Maximum likelihood, Bayes and minimax estimation. Admissibility
of estimators. Convergence properties. Asymptotic optimality. P,
566b, MATH 523. (Identical with MATH 667)

668. Theory of Testing of Hypotheses (3) II Measure-theory-based
hypothesis-testing theory. Simple and composite null and
alternative hypotheses. Test function. Hypothesis testing in
exponential families, testimability, i.e. uniformly most
powerful, unbiased, alpha-similar, minimax and invariant tests.
Likelihood ratio tests. Admissibility. Testing population means.
Nonparametric tests. P, 566b, MATH 523. (Identical with MATH 668)


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