23
votes
0answers
1k 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: ...
14
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 ...
13
votes
0answers
163 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 ...
13
votes
0answers
358 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 ...
11
votes
0answers
887 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. ...
11
votes
0answers
323 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 ...
9
votes
0answers
518 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 ...
9
votes
0answers
331 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
752 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
2k 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 ...
9
votes
0answers
937 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 ...
9
votes
0answers
233 views

Fisher information in a hierarchical model

Given the following hierarchical model, $$ X \sim {\mathcal N}(\mu,1), $$ and, $$ \mu \sim {\rm Laplace}(0, c) $$ where $\mathcal{N}(\cdot,\cdot)$ is a normal distribution. Is there a way to get an ...
8
votes
0answers
198 views

Help in how the paper derives the CRLB for Gaussian ARMA 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, $u$. Paper : On the Computation of the Cramer-Rao Bound ...
8
votes
0answers
255 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 ...
8
votes
0answers
151 views

State-of-the-art in deduplication

What are the state-of-the-art methods in record deduplication? Deduplication is also sometimes called: record linkage, entity resolution, identity resolution, merge/purge. I know for example about ...
8
votes
0answers
3k 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 ...
8
votes
0answers
353 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 ...
8
votes
0answers
290 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 ...
8
votes
0answers
376 views

Link Anomaly Detection in Temporal Network

I came across this paper that uses link anomaly detection to predict trending topics, and I found it incredibly intriguing: The paper is "Discovering Emerging Topics in Social Streams via Link Anomaly ...
8
votes
0answers
3k 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 ...
8
votes
0answers
169 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
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
529 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
350 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
108 views

In statistical learning theory, isn't there a problem of overfitting on a test set?

Let's consider the problem about classifying the MNIST dataset. According to Yann LeCun's MNIST Webpage, 'Ciresan et al.' got 0.23% error rate on MNIST test set using Convolutional Neural Network. ...
7
votes
0answers
68 views

Tail of the inverse cdf

I am almost sure I have already seen the following result in statistics but I can't remember where. If $X$ is a positive random variable and $E(X)<\infty$ then $\epsilon F^{-1}(1-\epsilon) \to 0$ ...
7
votes
0answers
142 views

When is t-SNE misleading?

Quoting from one of the authors: t-Distributed Stochastic Neighbor Embedding (t-SNE) is a (prize-winning) technique for dimensionality reduction that is particularly well suited for the ...
7
votes
0answers
238 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
1k views

How to interpret a QQ-plot of p-values

I am doing GWAS SNP association studies on diseases by using a software called plink (http://pngu.mgh.harvard.edu/~purcell/plink/download.shtml). With association results I get p-values for all the ...
7
votes
0answers
1k views

Trouble finding good model fit for count data with mixed effects - ZINB or something else?

I have a very small data set on solitary bee abundance that I am having trouble analysing. It’s count data, and almost all the counts are in one treatment with most of the zeroes in the other ...
7
votes
0answers
504 views

Comparing regression coefficients of same model across different data sets

I'm evaluating two (2) refrigerants (gases) that were used in the same refrigeration system. I have saturated suction temperature ($S$), condensing temperature ($D$), and amperage ($Y$) data for the ...
7
votes
0answers
198 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
258 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
184 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
507 views

Predicting count data with random forest

Can a Random Forest be trained to appropriately predict count data? How would this proceed? I have quite a extensive range of values so classification doesn't really make sense. If I would use ...
7
votes
0answers
3k views

Choosing complexity parameter in CART

In the rpart() routine to create CART models, you specify the complexity parameter to which you want to prune your tree. I have seen two different recommendations for choosing the complexity ...
7
votes
0answers
134 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
396 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
253 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
1k 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
708 views

Simulating time-series given power and cross spectral densities

I am having trouble generating a set of stationary colored time-series, given the covariance matrix (their PSDs and CSDs). I know that, given two time-series $y_{I}(t)$ and $y_{J}(t)$, I can ...
7
votes
0answers
264 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
90 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
833 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
251 views

Standard error of sample standard deviation of proportions

I recently started reading Gelman and Hill's, "Data Analysis Using Regression and Multilevel/Hierarchical Models" and the question is based on that: The sample contains 6 observations on proportions: ...
7
votes
0answers
805 views

How do I algorithmically determine values of T1 & T2 for canopy clustering?

I am trying to use canopy clustering to provide initial clusters for KMeans in mahout. Is there a way to determine / approximate the values of the distance thresholds T1 & T2 algorithmically? ...
7
votes
0answers
1k 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
434 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
571 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 ...
6
votes
0answers
82 views

Fitting the differences between two curves

The problem I'm trying to solve is to algorithmically figure out whether two curves converge or diverge in a graph (visually the problem is almost trivial). For examples: The left one is ...

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