Conditional Expectation, Conditional Independence, Introduction to Martingales

1997 ◽  
pp. 210-269 ◽  
Author(s):  
Yuan Shih Chow ◽  
Henry Teicher
Keyword(s):  
Conditional Expectation ◽  
Conditional Independence

Conditioning

2021 ◽  
pp. 190-212
Author(s):  
James Davidson
Keyword(s):  
Conditional Expectation ◽  
Conditional Independence ◽  
Theoretic Approach ◽  
Conditional Distributions

This chapter deals in depth with the concept of conditional expectation. This is defined first in the traditional “naïve” manner, and then using the measure theoretic approach. A comprehensive set of properties of the conditional expectation are proved, generalizing several results of Ch. 9, and then multiple sub‐σ‎‎‐fields and nesting are considered, concluding with a treatment of conditional distributions and conditional independence.

Corporate bond defaults are consistent with conditional independence

2010 ◽  
Vol 6 (2) ◽  
pp. 3-35 ◽  
Author(s):  
Florian Kramer ◽  
Gunter Löffler
Keyword(s):  
Conditional Independence ◽  
Corporate Bond

scholarly journals Conditional expectation in an operator algebra, I

1954 ◽  
Vol 6 (2-3) ◽  
pp. 177-181 ◽  
Author(s):  
Hisaharu Umegaki
Keyword(s):  
Operator Algebra ◽  
Conditional Expectation ◽  
Algebra I

Dichotomization, Partial Correlation, and Conditional Independence

1996 ◽  
Vol 21 (3) ◽  
pp. 264-282 ◽  
Author(s):  
András Vargha ◽  
Tamás Rudas ◽  
Harold D. Delaney ◽  
Scott E. Maxwell
Keyword(s):  
Conditional Independence ◽  
Partial Correlation ◽  
Statistical Significance ◽  
Conventional Wisdom ◽  
Predictor Variables ◽  
Lower Power ◽  
Partial Correlations ◽  
Current Article ◽  
The Difference ◽  
The Relationship

It was recently demonstrated that performing median splits on both of two predictor variables could sometimes result in spurious statistical significance instead of lower power. Not only is the conventional wisdom that dichotomization always lowers power incorrect, but the current article further demonstrates that inflation of apparent effects can also occur in certain cases where only one of two predictor variables is dichotomized. In addition, we show that previously published formulas claiming that correlations are necessarily reduced by bivariate dichotomization are incorrect. While the magnitude of the difference between the correct and incorrect formulas is not great for small or moderate correlations, it is important to correct the misunderstanding of partial correlations that led to the error in the previous derivations. This is done by considering the relationship between partial correlation and conditional independence in the context of dichotomized predictor variables.

scholarly journals Some conditional expectation identities for the multivariate normal

2010 ◽  
Vol 101 (9) ◽  
pp. 2250-2253 ◽  
Author(s):  
Christopher S. Withers ◽  
Saralees Nadarajah
Keyword(s):  
Conditional Expectation ◽  
Multivariate Normal
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