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You have a completely crossed three-way design, Gender x Question x Couple, with one observation in each cell. Do an analysis of variance. G and Q are fixed, C is random. The error term for the G main effect is the GC interaction. The error term for the GQ interaction is the GQC interaction. (Don't forget the correct for non-sphericity.) If the GQ ...

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Yes it is possible to use the Kaplan method to estimate left-censored data. The Wiki article is actually pretty decent Check it out

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A high dimensional multivariate data set would simply be a data set with lots of variables. These days, most data sets qualify. Exactly how many variables makes it "high" is not, as far as I know, generally agreed to.

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I have came across a paper where they stated that: "The product of independent log-normal quantities also follows a log-normal distribution", pp-345. It also have very rich understanding of the Lognormal Distribution. You can download the Article from here: http://stat.ethz.ch/~stahel/lognormal/bioscience.pdf As for the Second question, If I come across any ...

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Marginalising out $x_c$ means that you can forget about the last row and column of the covariance and $\mu_c$ in the mean vector. http://en.wikipedia.org/wiki/Multivariate_normal_distribution#Conditional_distributions $$p(x_a|x_b)=\mathcal{N}\left(\mu_{a|b},\Sigma_{a|b}\right)$$ Where $\mu_{a|b},\Sigma_{a|b}$ is given in the above link.

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OK, scratching my own itch. We want the $1-\alpha$ level curve of $y \sim N_2(\mu,\Sigma)$ The $1-\alpha$ level curve of the $\mathcal N_2(0,I)$ distribution function is a circle of radius $\sigma = \sqrt{ \chi^2_{2,1-\alpha} }$ centred at the origin. This holds because if we consider some $x$ drawn from that distribution then \$\mathbb P(x^T x \le ...

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