article · SIAM Journal on Matrix Analysis and Applications · 1990

Monotone Correlation and Monotone Disjunct Pieces

Devendra Chhetry, Jan de Leeuw, Allan R. Sampson

Cited by 2Abstract and details only

Abstract

Suppose X, Y are random variables taking Values on the $m \times n$ lattice $\{ x_1 < \cdots < x_m \} \times \{ y_1 < \cdots < y_n \}$ with $Q = \{ \operatorname{Prob}(X = x_i ,Y = y_j )\} $. Let $\rho _{\rm CMC} (Q)$ and $\rho _{\rm DMC} (Q)$ be the concordant and discordant monotone correlations defined, respectively, by the maximum and minimum of correlation $f(X)$, g(Y) over all f, g increasing with nonzero variances. A number of results concerning $\rho _{\rm CMC} (Q)$ and $\rho _{\rm DMC} (Q)$ and their evaluations are obtained. One result shows that $\rho _{\rm CMC} (Q) = 1$, if and only if Q consists of at least two increasing disjunct pieces, i.e., $Q = \operatorname{Diag} (Q_1 ,Q_2 )$. Necessary and sufficient conditions are also given for $\rho _{\rm CMC} (Q) = \rho _{\rm DMC} (Q)$.

Cite this paper

APA 7

Chhetry, D., de Leeuw, J., & Sampson, A. R. (1990). Monotone Correlation and Monotone Disjunct Pieces. SIAM Journal on Matrix Analysis and Applications, 11(3), 361–368. https://doi.org/10.1137/0611024

MLA 9

Chhetry, Devendra, et al. “Monotone Correlation and Monotone Disjunct Pieces.” SIAM Journal on Matrix Analysis and Applications, vol. 11, no. 3, 1990, pp. 361–68, https://doi.org/10.1137/0611024.

Chicago

Chhetry, Devendra, Jan de Leeuw, and Allan R. Sampson. 1990. “Monotone Correlation and Monotone Disjunct Pieces.” SIAM Journal on Matrix Analysis and Applications 11 (3): 361–68. https://doi.org/10.1137/0611024.

Harvard

Chhetry, D., de Leeuw, J. and Sampson, A.R. (1990) ‘Monotone Correlation and Monotone Disjunct Pieces’, SIAM Journal on Matrix Analysis and Applications, 11(3), pp. 361–368. Available at: https://doi.org/10.1137/0611024.

BibTeX

@article{chhetry1990monotone,
  title = {{Monotone Correlation and Monotone Disjunct Pieces}},
  author = {Chhetry, Devendra and de Leeuw, Jan and Sampson, Allan R.},
  journal = {SIAM Journal on Matrix Analysis and Applications},
  volume = {11},
  number = {3},
  pages = {361--368},
  year = {1990},
  doi = {10.1137/0611024}
}

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