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36
votes
2answers
2k views

Probability inequalities

I am looking for some probability inequalities for sums of unbounded random variables. I would really appreciate it if anyone can provide me some thoughts. My problem is to find an exponential upper ...
30
votes
0answers
1k 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 ...
25
votes
1answer
531 views

Jaynes' $A_p$ distribution

In Jaynes' book "Probability Theory: The Logic of Science", Jaynes has a chapter (Ch 18) entitled "The $A_p$ distribution and rule of succession" in which he introduces the idea of $A_p$ distributions,...
24
votes
0answers
591 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, ...
20
votes
1answer
589 views

Wavelet-domain gaussian processes: what is the covariance?

I've been reading Maraun et al, "Nonstationary Gaussian processes in wavelet domain: Synthesis, estimation, and significant testing" (2007) which defines a class of non-stationary GPs that can be ...
20
votes
0answers
1k views

How to create a multivariate Brownian Bridge

It is known, that a standard multivariate Brownian bridge $ y(\mathbf u) $ is a centered Gaussian process with covariance function $$ \mathbb E(y(\mathbf u) y(\mathbf v)) = \prod_{j=1}^d (u_j \wedge ...
18
votes
0answers
753 views

How does a Relevance Vector Machine (RVM) work?

Relevance Vector Machines (RVMs) are really interesting models when contrasted with the highly geometrical (and popular) SVMs. In the light of a question like How does a Support Vector Machine (SVM) ...
18
votes
1answer
420 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 + ...
17
votes
1answer
2k views

AIC versus cross validation in time series: the small sample case

I am interested in model selection in a time series setting. For concreteness, suppose I want to select an ARMA model from a pool of ARMA models with different lag orders. The ultimate intent is ...
17
votes
1answer
1k 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 ...
16
votes
0answers
535 views

Fitting custom distributions by MLE

My question relates to fitting custom distributions in R but I feel it has enough of a probability element to remain on CV. I have an interesting set of data which has the following characteristics: ...
16
votes
0answers
817 views

Diagnostic plot for assessing homogeneity of variance-covariance matrices

Is there a handy plot for comparing the variance-covariance matrices of two (or perhaps more) groups? An alternative to looking at lots of marginal plots, especially in the multivariate Normal case?
16
votes
1answer
691 views

Upper bounds for the copula density?

The Fréchet–Hoeffding upper bound applies to the copula distribution function and it is given by $$C(u_1,...,u_d)\leq \min\{u_1,..,u_d\}.$$ Is there a similar (in the sense that it depends on the ...
16
votes
0answers
534 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 ...
15
votes
0answers
364 views

Distribution of $\frac{\sum_{i=1}^n X_iY_i}{\sum_{i=1}^n X_i^2}$ where $X_i,Y_i$s are i.i.d Normal variables

Suppose $X_1,\ldots,X_n,Y_1,\ldots,Y_n$ are i.i.d $\mathcal N(0,1)$ random variables. I am interested in the distribution of $$U=\frac{\sum_{i=1}^n X_iY_i}{\sum_{i=1}^n X_i^2}$$ I define $$Z=\...
15
votes
1answer
322 views

Pooling calibration plots after multiple imputation

I would like advice on pooling the calibration plots/statistics after multiple imputation. In the setting of developing statistical models in order to predict a future event (e.g. using data from ...
15
votes
0answers
702 views

Bootstrapping Generalized Least Squares

Scenario: Consider the use of bootstrapping to estimate the distribution of model parameters fitted per a linear or nonlinear generalized least squares model. In particular, assume there is a ...
15
votes
1answer
1k views

Writing out the mathematical equation for a multilevel mixed effects model

The CV Question I'm trying to give (a) detailed and concise mathematical representation(s) of a mixed effects model. I am using the lme4 package in R. What is the ...
14
votes
0answers
214 views

Does LASSO suffer from the same problems stepwise regression does?

Stepwise algorithmic variable-selection methods tend to select for models which bias more or less every estimate in regression models ($\beta$s and their SEs, p-values, F statistics, etc.), and are ...
14
votes
0answers
538 views

Is there a general expression for ancillary statistics in exponential families?

It is known that an i.i.d sample $X_1,\dots,X_n$ from a scale family with c.d.f. $F(\frac{x}{\sigma})$ has $S(X)$ as an ancillary statistic if $S(X)$ depends on the sample only through $\frac{X_1}{X_n}...
14
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0answers
634 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 ...
13
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0answers
3k views

Multivariate Beta distribution (no Dirichlet!)

What is a multidimensional generalization of the Beta distribution, in compliance with the following specification? I am not looking for the Dirichlet distribution. I am looking for a generalization ...
13
votes
1answer
1k views

Standardized dependent variable within a group in panel data models?

Does standardizing of a dependent variable within the identifying group make sense? The following working paper (Deforestation slowdown in the Legal Amazon; Prices or Policies?, pdf) uses a ...
12
votes
1answer
884 views

How to compare of two Spearman correlations matrices?

I have two non-parametric rank correlations matrices emp and sim (for example, based on Spearman's $\rho$ rank correlation ...
12
votes
0answers
748 views

Bayesian Q-learning

Suppose that, for every state $s$, there is a set of actions $\mathcal{A}(s)$ that can be chosen in that state. Let $Q(s, a)$ denote the expected utility of choosing action $a \in \mathcal{A}(s)$ in ...
12
votes
1answer
1k views

Ratios in Regression, aka Questions on Kronmal

Recently, randomly browsing questions triggered a memory of on off-hand comment from one of my professors a few years back warning about the usage of ratios in regression models. So I started reading ...
12
votes
0answers
403 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 ...
11
votes
1answer
735 views

In Random Forest, why is a random subset of features chosen at the node level rather than at the tree level?

My Question: Why does random forest consider random subsets of features for splitting at the node level within each tree rather than at the tree level? Background: This is something of a history ...
11
votes
0answers
2k views

Getting started with bayesian structural models using MCMC

I'm trying to learn bayesian structural time series analysis. For a variety of reasons I need to use Python (mostly pymc3) not R so please do not suggest the ...
11
votes
0answers
4k views

Specify correlation structure for different groups in mixed-effects model (lme4/nlme)

I am trying to account for spatial autocorrelation in a linear mixed-effects model in R with measurements repeated in time. BodyMass has been collected once per <...
11
votes
0answers
882 views

Implementation of CoVaR (a systemic risk measure) in R

I'm trying to estimate CoVaR using bivariate DCC GARCH in R. The concept of CoVaR is the dependence adjusted of VaR, which was first introduced by Adrian and Brunnermeier (2011). However, this ...
11
votes
0answers
2k views

When does a UMP test fail to exist?

I have a sample $X=(X_1, ...,X_n)\sim N(\mu,\sigma^2)$ with $\sigma^2$ known. The hypotheses are $H_0: \mu=\mu_0, H_1:\mu \neq \mu_0$. I know that in such a case an UMP test does not exist and so ...
11
votes
0answers
669 views

What is the intuition behind the expected transaction value for a customer in the gamma-gamma model?

Background and Motivation: I was reading the paper RFM and CLV: Using Iso-Value Curves for Customer Base Analysis by Peter S. Fader, Bruce G. S. Hardie and Ka Lok Lee, in an attempt to gain some ...
11
votes
0answers
1k views

Rademacher complexity of logistic regression

Consider logistic regression. We have the logistic loss function, $\phi: R\rightarrow [0,1], \phi(u)=\log(1+\exp(-u))$, which is Lipschitz, and we have the linear function class $F=\{f_w:R^d \...
11
votes
1answer
520 views

Expectation Maximization Clarification

I found very helpful tutorial regarding EM algorithm. The example and the picture from the tutorial is simply brilliant. Related question about calculating probabilities how does expectation ...
11
votes
0answers
1k views

The role of scale parameter in GEE

I am learning the generalized estimating equations (GEE) and the geepack R package. There are some questions that I am a little confused. In a GEE-constructed ...
11
votes
0answers
323 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. ...
11
votes
0answers
1k views

Tail inequality on sum of product of normal variables

For independent random variables $ x_1,..,x_n$ and $y_1,...,y_n$ following normal distribution $N(0,1)$, I need a simple estimate formula for $P(| \sum_1^n x_iy_i | \leq nt ) \leq e^{(?)}$ for $t>...
11
votes
0answers
4k views

How to compute confidence interval in ANOVA with repeated measures?

I made a model using repeated measures univariate ANOVA in R. ...
11
votes
0answers
962 views

Testing for a significant difference between ML estimates: Likelihood ratio or Wald test?

I am trying to test whether or not there is a significant difference between maximum likelihood estimates of two genetic parameters (selection and dominance) across two environments with genotype data ...
11
votes
0answers
321 views

Are non-square latin hypercubes viable?

At https://github.com/OpenMDAO/OpenMDAO-Framework/issues/599 it is stated that non-square Latin Hypercube experimental design is not well defined (I assume that for higher dimensions that means ...
10
votes
0answers
175 views

Maximum Entropy with bounded constraints

Assume we have the problem of estimating the probabilities $\{p_1,p_2,p_3\}$ subject to: $$0 \le p_1 \le .5$$ $$0.2 \le p_2 \le .6$$ $$0.3 \le p_3 \le .4$$ with only the natural constraint of $p_1+...
10
votes
0answers
184 views

Empirical Bayes (In)Admissibility

Sticking to a pure Bayesian approach to statistics with proper priors most of the time leads to admissible estimators. Nevertheless there is good reason to use Empirical Bayes in many cases, and the ...
10
votes
0answers
350 views

Time series modeling of circular data

I'm building ARIMA models for some wind/waves data. I'm building a separate model for each variable. Two of the variables that I need to model are wave and wind direction. The values are in degrees (...
10
votes
2answers
8k views

Interpreting negative cosine similarity

My question may be a silly one. So I shall apologize in advance. I was trying to use the GLOVE model pre-trained by Stanford NLP group (link). However, I noticed that my similarity results showed ...
10
votes
1answer
401 views

Adjustments to (Linear Regression) Forecast

Full disclosure: I am not a statistician, nor do I claim to be one. I am a lowly IT administrator. Please play gentle with me. :) I am responsible for collecting and forecasting disk storage use ...
10
votes
0answers
2k views

Gamma hurdle model for continuous response

I am modelling invertebrate.biomass ~ habitat.type * calendar.day + habitat.type * calendar.day ^ 2, with a random intercept of transect.id (50 transects were repeated 5 times) My response is zero-...
10
votes
0answers
609 views

Picking block length in a block bootstrap

I am using the Mann-Kendall test to assess trends in a data time-series. I believe there is autocorrelation in my data and therefore need to use a block bootstrap to correct for it. I have plotted ...
10
votes
1answer
395 views

Visualizing many left-skewed distributions

I have a series of left-skewed/heavy tailed distributions that I would like to show. There are 42 distributions across three factors (labeled as A, ...
10
votes
0answers
384 views

Asymptotic property of tuning parameter in penalized regression

I'm currently working on asymptotic properties of penalized regression. I've read a myriad of papers by now, but there is an essential issue that I cannot get my head around. To keep things simple, I'...

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