## Acknowledgements • TABLE OF CONTENTS (1973)

### BibTeX

@MISC{Oifallon73acknowledgements•,

author = {Judith R. Oifallon and I Chapter},

title = {Acknowledgements • TABLE OF CONTENTS},

year = {1973}

}

### OpenURL

### Abstract

### Citations

1425 |
An Introduction in Multivariate Statistical Analysis
- Anderson
- 1958
(Show Context)
Citation Context ...f the random variable Y in the i th population,~ i=1,2. This decision rule is optimal in that it minimizes the total probability of misclassification among all decision rules based on Y (cf. Anderson =-=[1]-=-, p. 131, Theorem 6.3.1). DEFINITION: PROCEDURE: The optimaZ linear disariminant funation (OLDF) is the linear function y* = d*'X which has the property that the optimal decision rUle-based on y* has ... |

101 |
The Statistical Utilization of Multiple Measurements
- Fisher
- 1938
(Show Context)
Citation Context ...partition in the case of truncation is parallel to the boundary for the optimal partition when there is no truncation. There is another well-known linear discriminant function, one proposed by Fisher =-=[7]-=- for use in cases when the optimal discriminant function is nonlinear. This "best linear" discriminant function (BLDF) is defined to be the linear function Z = D..'K (10) which has the property that t... |

24 |
Classification into two multivariate normal distributions with different covariance matrices
- Anderson, Bahadur
- 1962
(Show Context)
Citation Context ...ns of the ~-plane assigned to each population according to the optimal decision rule) should be done. Comparisons could then be made with the optimal.twocell partitions developed by Anderson &Bahadur =-=[2]-=-, Clunies-Ross &Riffenburgh [6], etc. For Chapter IV a much larger numerical stUdy must be done in order to discover the nature of the interaction between the truncation effect and the effect of the r... |

15 |
Some inequalities on Mill’s ratio and related functions
- Sampford
- 1953
(Show Context)
Citation Context ... nonzero real number and o = Varl (~) + Var2 (~) t 1..= E I (3£) - E2(~)' provided 0 is a positive-definite matrix and l..~Q. proof: From definitions (11),(13), and (14), we have (n':xJ2 n'!2n10 Rao =-=[12]-=- states, in result (If..l.l), p.48, that such a function of ..!l attains its supremum when.!l = ~fl.x. ,. It is clear that the value of R2 is unchanged when .!l = ce-l.x. for any real c~O. o Now, when... |

12 |
1812 . Theorie Analytique des Probabilities
- LAPLACE
(Show Context)
Citation Context ...oposed by Birnbaum [4] s R(x) > 2/(x + Ix 2+4) s we get an upper bound of unity for wet) when t<O; i.e. wet) < 1 for every t<o. Using the following upper bound for R(x)s which was proposed by Laplace =-=[10]-=- s R(x) $ x-I - x-S + 3x-S s we get the following lower bound for wet) when t<O: t 6 +7t 4 -6t 2 +9 wet) ~ 1 - (t4_tz+3)2 s which tends to 1 as t + _00. Therefores wet) + 1 as t + _00. i.) To show tha... |

9 |
An inequality for Mill’s ratio
- Birnbaum
- 1942
(Show Context)
Citation Context ...egative; the complement of the strip including the parallel lines, x2 =y* - dXl and x2 =yO - dxl , where y* and yO are zeros of U(y). Any additional zeros in an interval about the origin must satisfy =-=[4]-=- or [5]: [4. J If there is an odd number of these zeros, one of them must be a defines a line within a partition cell in such a walf that all points in the cell that are not on the line remain in the ... |

6 |
Inequalities for the Mills’ Ratio
- Boyd
- 1959
(Show Context)
Citation Context ... f(t) ~ get) iff f(t)[l - 0(1)] < get) as t ~ ~. proof: When k=O, (14) holds. 5*>k=0 for all 0>1, by Lemma 5; and so, by Lemma 4, Since (5*/0) could be relatively small, for R(t), t>O, stated by Boyd =-=[5]-=-: let us consider bounds ~;::;:~1T~_-:- < R(t) < ---:.1T:....- _ It z +21T + (1T-l)t (1T-2)[/t 2 + 21T/(1T-2)2 + 2t/(1T-2)] In somewhat simplified notation (14) can be written X R(X) = w, (16) with { ... |

5 |
Plane truncation in normal populations
- Tallis
- 1965
(Show Context)
Citation Context ...appearance within each chapter. Minor results are generally designated by letters or lower-case Roman6 numerals inside parentheses. A proper name followed by a number in square brackets, e.g. Tallis =-=[13]-=-, refers to a specific book or paper listed in the Bibliography.CHAPTER II LINEAR DISCRIMINATION BETWEEN TWO BIVARIATE NORMAL POPULATIONS WITH EQUAL COVARIANCE MATRICES BASED ON A TRUNCATED SAMPLING ... |

2 |
Geometric interpretation of admissible linear decision boundaries for two multivariate normal distributions
- Bechtel, Gavin, et al.
- 1971
(Show Context)
Citation Context ...iscrimination between two multivariate normal populations having unequal covariance matrices: Kullback [9], Clunies-Ross and Riffenburgh [6], Anderson and Bahadur [2], and Bechtel, Gavin, and Bachand =-=[3]-=-. However, in each of these papers the stated purpose is to find a linear bounda~ which partitions the X-space into exactly two cells and which is in some sense "optimal"; that is, to find a linear fu... |

1 |
Geometry and linear discrimination, Biometrika
- Clunies-Ross, Riffenburgh
- 1960
(Show Context)
Citation Context ...ach population according to the optimal decision rule) should be done. Comparisons could then be made with the optimal.twocell partitions developed by Anderson &Bahadur [2], Clunies-Ross &Riffenburgh =-=[6]-=-, etc. For Chapter IV a much larger numerical stUdy must be done in order to discover the nature of the interaction between the truncation effect and the effect of the relative positions of the two po... |