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\title{Statistics}
\author{Last Updated: 1978}
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Certification in Statistics as part of the requirement for the PhD in
Mathematics includes the following:

\begin{enumerate}
\item Familiarity with undergraduate level probability and statistics.
  Representative undergraduate texts include Hogg and Craig, Lindgren,
  Mood Graybill and Bose, Fisz, Cox and Hinckley, and Neter and
  Wasserman.
\item Understanding of the theoretical basis of the core of
  statistics, as represented in Wilks in the following sections:
  \begin{enumerate}
  \item Characteristic and generating functions.  Sections 5.1, 5.3,
    and 5.4.
  \item Multivariate normal.  Section 7.3 and 7.4.
  \item Sampling theory.  Sections 8.4 and 8.7.
  \item Asymptotic theory.  Sections 9.3 and 9.4.
  \item Linear estimation.  Sections 10.1, 10.2, 10.3, and 10.4.
  \item Estimation.  Sections 12.1, 12.2, 12.3, 12.4, and 12.5.
  \item Testing.  Sections 13.1, 13.2, 13.3, 13.4, 13.7, and 13.8.
  \end{enumerate}
\item Some knowledge of two of the following additional areas of
  statistics. The principal reference is again Wilks. Other texts are
  also listed. The order in which texts are listed is not meant to
  suggest preference; the student should decide that after examining
  the texts and possibly discussing her or his plan with an advisor.
\item Decision Theory. Wilks (Chapter 16), Ferguson, Wald 1950.
\item Nonparametric and distribution free statistics. Wilks (Chapters
  11 and 14), Rohatgi (Chapter 8), Wasan, Hollander, and Wolfe.
\item Multivariate statistics. Wilks (Chapter 18), Anderson, Rao.
  
\item Sequential analysis. Wilks (Chapter 15), Rohatgi (Chapter 14),
  Wald 1947.
\item Linear statistical models---regression, analysis of variance,
  design of experiments. Wilks (Chapter 10), Graybill, Rao.
\end{enumerate}

\subsection*{Bibliography}

\begin{enumerate}
\item Anderson, T. W., \textit{An Introduction to Multivariate Statistical
  Analysis},  Wiley, 1958.
\item Cochran, W. G., \textit{Sampling Techniques}, Third Edition,
  Wiley, 1977.
\item Cox, D. R., and Hinckley, D. V., \textit{Theoretical
    Statistics}, Chapman and Hall, 1974.
\item Ferguson, T. E., \textit{Mathematical Statistics: A Decision
    Theoretic Approach}, Academic Press, 1967.
\item Fisz, M., \textit{Probability Theory and Mathematical
    Statistics}, Wiley, 1963.
\item Fraser, D. A. S., \textit{Nonparametric Methods in Statistics},
  Wiley,
\item Graybill, F. A., \textit{Theory and Application of the Linear
    Model}, North Scituate, MA, Duxbury Press, 1976.
\item Hogg, R. V., and Craig, A. T., \textit{Introduction to
    Mathematical Statistics}, Third Edition, Macmillan, 1970.
\item Hollander, M. and Wolfe, D. A., \textit{Nonparametric
    Statistical Methods}, Wiley, 1973.
\item Lindgren, B. W., \textit{Statistical Theory},  Third Edition,
  Macmillan, 1976.
\item Lehman, E. L., \textit{Testing Statistical Hypotheses},  Wiley,
  1959.
\item Mood, A. M., Graybill, F. A., and Boes, D. C.,
  \textit{Introduction to the Theory of Statistics}, Third Edition,
  McGraw-Hill, 1974.
\item Nemenyi, \textit{et.al.}, \textit{Statistics from Scratch},
  Holden-Day, 1977.
\item Neter, J., and Wasserman, W., \textit{Applied Linear Statistical
    Methods}, Irwin, 1974.
\item Rao, C. R., \textit{Linear Statistical Inference and Its
    Applications}, Wiley, 1965.
\item Rohatgi, V. K., \textit{An Introduction to Probability Theory
    and Mathematical Statistics}, Wiley, 1976.
\item Scheffe, H., \textit{The Analysis of Variance}, Wiley, 1959.
\item Wald, A. (1947), \textit{Sequential Analysis},  Wiley, 1947.
\item Wald, A. (1950), \textit{Statistical Decision Functions}, Wiley,
  1950.
\item Wasan, M. T., \textit{Parametric Estimation}, McGraw-Hill, 1970.
\item Wilks, S. S., \textit{Mathematical Statistics},  Wiley, 1962.
\end{enumerate}

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