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Quantitative Analysis
Parallel Processing
Numerical Analysis
C++ Multithreading
Python for Excel
Python Utilities
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I. Basic math.
II. Pricing and Hedging.
III. Explicit techniques.
IV. Data Analysis.
1. Time Series.
2. Classical statistics.
A. Basic concepts and common notation of classical statistics.
B. Chi squared distribution.
C. Student's t-distribution.
D. Classical estimation theory.
a. Sufficient statistics.
b. Sufficient statistic for normal sample.
c. Maximal likelihood estimation (MLE).
d. Asymptotic consistency of MLE. Fisher's information number.
e. Asymptotic efficiency of the MLE. Cramer-Rao low bound.
E. Pattern recognition.
3. Bayesian statistics.
V. Implementation tools.
VI. Basic Math II.
VII. Implementation tools II.
VIII. Bibliography
Notation. Index. Contents.

Sufficient statistic for normal sample.

uppose MATH is a sample from the normal distribution MATH with both parameters unknown, MATH The joint distribution for $X$ is given by MATH MATH MATH MATH Hence, the quantities MATH , MATH form the sufficient statistic.

Notation. Index. Contents.

Copyright 2007