22
votes
0answers
837 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: ...
12
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 ...
11
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 ...
11
votes
0answers
144 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 $r$ ...
11
votes
0answers
377 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 ...
10
votes
0answers
110 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 ...
10
votes
0answers
116 views

Are data handling errors already 'priced in' to statistical analysis?

Ok, fair warning--this is a philosophical question that involves no numbers. I've been thinking a lot about how errors creep into data sets over time and how that should be treated by analysts--or if ...
10
votes
0answers
269 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 ...
9
votes
0answers
269 views

Model selection with Firth logistic regression

In a small data set ($n\sim100$ ) that I am working with, several variables give me perfect prediction/separation. I thus use Firth logistic regression to deal with the issue. If I select the best ...
9
votes
0answers
525 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. ...
9
votes
0answers
501 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 $$\widehat{\beta}_{QR} = \min_{b} \sum^{n}_{i=1} \rho_\tau (y_i - X'_i b_\tau)$$ ...
9
votes
0answers
566 views

Clustered standard errors vs. multilevel modeling?

I've skimmed through several books (Raudenbush & Bryk, Snijders & Bosker, Gelman & Hill, etc.) and several articles (Gelman, Jusko, Primo & Jacobsmeier, etc.), and I still haven't ...
9
votes
0answers
861 views

Intraclass Correlation Coefficients (ICC) with Multiple Variables

Suppose I have measured some variable in siblings, which are nested within families. The data structure looks like this: family sibling value ------ ------- ----- 1 1 y_11 1 2 ...
8
votes
0answers
46 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 ...
8
votes
0answers
76 views

How to calculate prediction intervals for LOESS?

I have some data that I fitted using a LOESS model in R, giving me this: The data has one predictor and one response, and it is heteroscedastic. I also added confidence intervals. The problem is ...
8
votes
0answers
273 views

Advanced regression modeling examples

I'm looking for an advanced linear regression case study illustrating the steps required to model complex, multiple non-linear relationships using GLM or OLS. It is surprisingly difficult to find ...
8
votes
0answers
438 views

MLEs from glmer {lme4} in R

Numerically deriving the MLEs of GLMM is difficult and, in practice, I know, we should not use the brute force optimization (e.g., using optim in a simple way). But ...
8
votes
0answers
83 views

Thesaurus for statistics and machine learning terms

Does there exist any reference thesaurus for statistics and machine learning terms? I know that Wikipedia articles often contain synonyms, but I would like to have a mere thesaurus that I could go ...
8
votes
0answers
155 views

Penalized spline confidence intervals based on cluster-sandwich VCV

This is my first post here, but I've benefited a lot from this forum's results popping up in google search results. I've been teaching myself semi-parametric regression using penalized splines. ...
8
votes
0answers
1k views

How to analyze longitudinal count data: accounting for temporal autocorrelation in GLMM?

Hello statistical gurus and R programming wizards, I am interested in modeling animal captures as a function of environmental conditions and day of the year. As part of another study, I have counts ...
8
votes
0answers
2k views

Using statistical significance test to validate cluster analysis results

I am surveying the use of statistical significance testing (SST) to validate the results of cluster analysis. I have found several papers around this topic, such as "Statistical Significance of ...
8
votes
0answers
491 views

What data and statistics skills are currently in high demand and where are they in high demand?

I have a job doing data analysis in finance. My current job is such that I don't have much exposure to things happening in the rest of my industry or other industries. I have a fair amount of ...
8
votes
0answers
316 views

Physical/pictoral interpretation of higher-order moments

I'm preparing a presentation about parallel statistics. I plan to illustrate the formulas for distributed computation of the mean and variance with examples involving center of gravity and moment of ...
7
votes
0answers
107 views

What's the minimum of $\mu (1-\mu)/ \sigma^2$ over all continuous unimodal distributions on a bounded interval $[0,1]$?

All distributions on a bounded interval $[0,1]$ satisfy: $$\sigma^2 \le \mu (1-\mu)$$ where $\mu$ is the mean and $\sigma^2$ the variance. Now suppose that the distribution is unimodal, in the ...
7
votes
0answers
73 views

Why does inversion of a covariance matrix yield partial correlations between random variables?

I heard that partial correlations between random variables can be found by inverting the covariance matrix and taking appropriate cells from such resulting precision matrix (this fact is mentioned in ...
7
votes
0answers
162 views
+50

Help in finding the estimator from Poisson point process

Considering a set of $n$ points that are $d$ dimensional and are independently and uniformly distributed on a surface. The points are homogeneous poisson point process. Considering nearest neighbor ...
7
votes
0answers
125 views

How to derive the CRLB for Gaussian case AR model

An univariate autoregressive process AR(p) process is expressed as $$y(n) = \sum_{j=1}^p a_jy(n-j) + u(n) $$ is excited by Gaussian sequence, $u$. Is there a resource / reference for a lucid ...
7
votes
0answers
225 views

Blind source separation of convex mixture?

Suppose I have $n$ independent sources, $X_1, X_2, ..., X_n$ and I observe $m$ convex mixtures: \begin{align} Y_1 &= a_{11}X_1 + a_{12}X_2 + \cdots + a_{1n}X_n\\ ...&\\ Y_m &= a_{m1}X_1 + ...
7
votes
0answers
144 views

Why does the scikit-learn bootstrap function resample the test set?

When using bootstrapping for model evaluation, I always thought the out-of-bag samples were directly used as a test set. However, this appears not to be the case for the scikit-learn bootstrap ...
7
votes
0answers
2k views

What does the anova() command do with a lmer model object?

Hopefully this is a question that someone here can answer for me on the nature of decomposing sums of squares from a mixed-effects model fit with lmer (from the ...
7
votes
0answers
182 views

Bound for Arithmetic Harmonic mean inequality for matrices?

NOTE: This question has originally been posted in MSE, but it did not generate any interest. It was first posted there, because the question itself is a pure matrix-algebra question. Nevertheless, ...
7
votes
0answers
129 views

Using percentiles as predictors - good idea?

I am thinking about a problem which is to predict log(spend) of a customer using linear regression. I am considering what features to use as input and wondering if it would be OK to use the ...
7
votes
0answers
230 views

p-value adjustment for Local Moran's I statistic (LISA)

I'm working with some exploratory spatial analysis in R using spdep package. I came across an option to adjust p-values of local indicators of spatial association (LISA) calculated using ...
7
votes
0answers
298 views

Unique (?) idea for forecasting sales

I'm working on developing a model to predict total sales of a product. I have about a year and a half of bookings data, so I could do a standard time series analysis. However, I also have a lot of ...
7
votes
0answers
169 views

Generalised least squares: from regression coefficients to correlation coefficients?

For least squares with one predictor: $y = \beta x + \epsilon$ If $x$ and $y$ are standardised prior to fitting (i.e. $\sim N(0,1)$), then: $\beta$ is the same as the Pearson correlation ...
7
votes
0answers
152 views

Analyze a football match: similar players with DBSCAN and similar trajectories with TRACLUS

I'm trying to analyze a dataset that originates from sensors located near players' shoes in a match (http://www.orgs.ttu.edu/debs2013/index.php?goto=cfchallengedetails). I decided to look at ...
7
votes
0answers
272 views

Luce choice axiom, question about conditional probability

I'm reading Luce (1959). Then I found this statement: When a person chooses among alternatives, very often their responses appear to be governed by probabilities that are conditioned on the ...
7
votes
0answers
2k views

Unable to fit negative binomial regression in R (attempting to replicate published results)

Attempting to replicate the results from the recently published article, Aghion, Philippe, John Van Reenen, and Luigi Zingales. 2013. "Innovation and Institutional Ownership." American Economic ...
7
votes
0answers
125 views

Identification of parameters problem

I always struggle to get the true essence of identification in econometrics. I know that we state that a parameter (say $\hat{\theta}$) can be identified if by simply looking at its (joint) ...
7
votes
0answers
358 views

Can these data be aggregated into a proportion for a binomial glm?

We asked 60 people to list as many restaurant franchises in Atlanta as they could. The overall list included over 70 restaurants, but we eliminated those that were mentioned by fewer than 10% of the ...
7
votes
0answers
230 views

Can I use optimally scaled variables for a factor analysis to account for rotation? If I can then how?

I have discussed this issue several times in this site, but I am asking it again for a final justification from the experts of our community. I wanted to extract four factors (I should call dimensions ...
7
votes
0answers
968 views

Multiple imputation questions for multiple regression in SPSS

I am currently running a multiple regression model using imputed data and have a few questions. Background: Using SPSS 18. My data appears to be MAR. Listwise deletion of cases leaves me with only ...
7
votes
0answers
129 views

Bayesian, MDL or ML interpretation of cross-validation?

Is there any known Bayesian, ML or MDL interpretation of cross-validation? Can I interpret cross validation as performing the right update on a specifically crafted prior?
7
votes
0answers
265 views

How can we bound the probability that a random variable is maximal?

Suppose we have $N$ independent random variables $X_1$, $\ldots$, $X_n$ with finite means $\mu_1 \leq \ldots \leq \mu_N$ and variances $\sigma_1^2$, $\ldots$, $\sigma_N^2$. I am looking for ...
7
votes
0answers
259 views

Distribution of inverse Wishart to a power?

In a related question, I had asked about the norm induced by an inverse Wishart matrix. I am interested in generalizing that result somewhat. Let $A\sim\mathcal{W}_p\left(I,n\right)$, a Wishart matrix ...
7
votes
0answers
80 views

Estimation and functional space

In the first chapter of the book Algebraic Geometry and Statistical Learning Theory which talks about the convergence of estimations in different functional space, it mentions that the Bayesian ...
7
votes
0answers
690 views

Link between variance and pairwise distances within a variable

Please, prove that if we have two variables (equal sample size) $X$ and $Y$ and the variance in $X$ is greater than in $Y$, then the sum of squared differences (i.e., squared euclidean distances) ...
7
votes
0answers
990 views

How to use G Power 3 to calculate statistical power in mixed design ANOVA with unequal group sample sizes

In G power 3, ANOVA repeated measures within-between interaction: Only the total sample size is reported assuming equal sample size for the two groups. My questions are: How would it work if the ...
7
votes
0answers
398 views

Marginal distribution of the diagonal of an inverse Wishart distributed matrix

Suppose $X\sim InvWishart(\nu, \Sigma_0)$. I'm interested in the marginal distribution of the diagonal elements $diag(X) = (x_{11}, \dots, x_{pp})$. There are a few simple results on the distribution ...
7
votes
0answers
543 views

How can I assess GEE/logistic model fit when covariates have some missing data?

I have fit two generalized estimating equation (GEE) models to my data: 1) Model 1: Outcome is longitudinal Yes/No variable (A) (year 1,2,3,4,5) with longitudinal continuous predictor (B) for years ...

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