Unanswered Questions

22
votes
0answers
922 views

SVD of correlated matrix should be additive but doesn't appear to be

I'm just trying to replicate a claim made in the following paper, Finding Correlated Biclusters from Gene Expression Data, which is: Proposition 4. If $X_{IJ}=R_{I}C^{T}_{J}$. then we have: ...
20
votes
1answer
481 views

When is binomial distribution function above/below its limiting Poisson distribution function?

Let $B(n,p,r)$ denote the binomial distribution function (DF) with parameters $n \in \mathbb N$ and $p \in (0,1)$ evaluated at $r \in \{0,1,\ldots,n\}$: \begin{equation} B(n,p,r) = \sum_{i=0}^r ...
16
votes
0answers
646 views

What is the difference between conditional and unconditional quantile regression?

The conditional quantile regression estimator by Koenker and Basset (1978) for the $\tau^{th}$ quantile is defined as $$ \widehat{\beta}_{QR} = \min_{b} \sum^{n}_{i=1} \rho_\tau (y_i - X'_i b_\tau) $$ ...
15
votes
1answer
185 views

Shrunken $r$ vs unbiased $r$: estimators of $\rho$

There has been some confusion in my head about two types of estimators of the population value of Pearson correlation coefficient. A. Fisher (1915) showed that for bivariate normal population ...
15
votes
1answer
640 views

How the Pearson's Chi Squared Test works

Following a recent down vote I have been trying to check my understanding of the Pearson Chi Squared test. I usually use the chi squared statistic (or reduced chi squared statistic) for fitting or ...
13
votes
0answers
1k views

Random forests for multivariate regression

I have a multi-output regression problem with $d_x$ input features and $d_y$ outputs. The outputs have a complex, non-linear correlation structure. I'd like to use random forests to do the ...
12
votes
0answers
167 views

Prediction interval based on cross-validation (CV)

In the text books and youtube lectures I learned a lot about iterative models such as boosting, but I never saw anything about deriving a prediction interval. Cross validation is used for the ...
12
votes
0answers
300 views

Training a basic Markov Random Field for classifying pixels in an image

I am attempting to learn how to use Markov Random Fields to segment regions in an image. I do not understand some of the parameters in the MRF or why the expectation maximisation I perform fails to ...
12
votes
0answers
1k views

Inverting the Fourier Transform for a Fisher distribution

The characteristic function of Fisher $\mathcal{F}(1,\alpha)$ distribution is: $$C(t)=\frac{\Gamma \left(\frac{\alpha +1}{2}\right) U\left(\frac{1}{2},1-\frac{\alpha }{2},-i t \alpha \right)}{\Gamma ...
12
votes
0answers
183 views

Testing certain contrasts: Is this provably a hard problem, or not?

I posted this to mathoverflow and no one's answering: Scheffé's method for identifying statistically significant contrasts is widely known. A contrast among the means $\mu_i$, $i=1,\ldots,r$ of $r$ ...
12
votes
0answers
414 views

What are the options in proportional hazard regression model when Schoenfeld residuals are not good?

I am doing a Cox proportional hazards regression in R using coxph, which includes many variables. The Martingale residuals look great, and the Schoenfeld residuals ...
12
votes
1answer
312 views

Phylogenetic dependent variables: ANOVA?

I understand deriving a covariance matrix from phylogenetic data to make $cov(X,Y) = 0$ for two variables you're making a regression on. But what happens if you have one continuous variable, that ...
11
votes
0answers
100 views

Does Stein's Paradox still hold when using the $l_1$ norm instead of the $l_2$ norm?

Stein's Paradox shows that when three or more parameters are estimated simultaneously, there exist combined estimators more accurate on average (that is, having lower expected mean squared error) than ...
10
votes
0answers
720 views

Can the Burnham-Anderson book on multimodel inference be recommended?

As motivated by the recent change of the default model selection statistic in the R's forecast package from AIC to AICc, I am curious whether the latter is indeed applicable wherever the former is. ...
10
votes
1answer
318 views

$ARIMA(p,d,q)+X_t$, Simulation over Forecasting period

I have time series data and I used an $ARIMA(p,d,q)+X_t$ as the model to fit the data. The $X_t$ is an indicator random variable that is either 0 (when I don’t see a rare event) or 1 (when I see the ...

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