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Unanswered Questions

28
votes
0answers
1k 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 ...
25
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 ...
24
votes
0answers
536 views

State of art streaming learning

I have been working with large data sets lately and found a lot of papers of streaming methods. To name a few: Follow-the-Regularized-Leader and Mirror Descent: Equivalence Theorems and L1 ...
23
votes
1answer
432 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,...
21
votes
0answers
9k views

The cross validation (CV) and the generalized cross validation (GCV) statistics

I have found possibly conflicting definitions for the cross validation (CV) statistic and for the generalized cross validation (GCV) statistic associated with a linear model $Y = X\boldsymbol\beta + \...
20
votes
1answer
483 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 ...
19
votes
2answers
1k 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 ...
18
votes
0answers
17k views

Choosing optimal alpha in elastic net logistic regression

I'm performing an elastic-net logistic regression on a health care dataset using the glmnet package in R by selecting lambda values over a grid of $\alpha$ from 0 ...
18
votes
0answers
497 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, ...
17
votes
0answers
359 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
926 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 ...
15
votes
0answers
881 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 ...
15
votes
1answer
592 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 ...
14
votes
1answer
1k 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 ...
14
votes
0answers
450 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 ...

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