All Questions

32
votes
0answers
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 ...
26
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 ...
22
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 + \...
18
votes
0answers
294 views

Did Deborah Mayo refute Birnbaum's proof of the likelihood principle?

This is somewhat related to my previous question here: An example where the likelihood principle *really* matters? Apparently, Deborah Mayo published a paper in Statistical Science refuting Birnbaum'...
18
votes
0answers
524 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, ...
16
votes
0answers
371 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 + ...
16
votes
0answers
955 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
0answers
581 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) ...
15
votes
0answers
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
424 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: ...
14
votes
0answers
732 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?
14
votes
0answers
481 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 ...
13
votes
0answers
238 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 ...
13
votes
0answers
588 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 ...
13
votes
0answers
956 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 ...
12
votes
0answers
484 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}...
12
votes
0answers
5k views

How do I interpret the covariance matrix from a curve fit?

I'm not too great at statistics, so apologies if this is a simplistic question. I am fitting a curve to some data, and sometimes my data best fits a negative exponential in the form $a * e^{(-b * x)} +...
12
votes
0answers
607 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 ...
11
votes
0answers
633 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 ...
11
votes
0answers
761 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
4k views

How to compute confidence interval in ANOVA with repeated measures?

I made a model using repeated measures univariate ANOVA in R. ...
10
votes
0answers
866 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 \...
10
votes
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 ...
10
votes
0answers
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 ...
10
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 ...
10
votes
0answers
303 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. ...
10
votes
0answers
387 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 ...
10
votes
0answers
921 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 ...
10
votes
0answers
297 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
2k 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 ...
9
votes
0answers
81 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=\...
9
votes
0answers
158 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 ...
9
votes
0answers
352 views

Compute partial $\eta^2$ for all fixed effects anovas from a lme4 model

Disclamer: I wasn't sure where to post this question: CV or SO, but eventually decided to try here first I've been asked by one of the reviewers to add effects sizes (preferably $\eta^2_p$ which is ...
9
votes
0answers
173 views

Intuitive understanding of the Halmos-Savage theorem

The Halmos-Savage theorem says that for a dominated statistical model $(\Omega, \mathscr A, \mathscr P)$ a statistic $T: (\Omega, \mathscr A, \mathscr P)\to(\Omega', \mathscr A')$ is sufficient if (...
9
votes
0answers
484 views

What are multivariate orthogonal polynomials as computed in R?

Orthogonal polynomials in an univariate set of points are polynomials that produce values on that points in a way that its dot product and pairwise correlation are zero. R can produce orthogonal ...
9
votes
0answers
1k 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 ...
9
votes
0answers
591 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 ...
9
votes
0answers
172 views

What is tantile regression?

My question follows on this discussion of medials and tantiles vs medians and quantiles from earlier this year: When would we use tantiles and the medial, rather than quantiles and the median? As ...
9
votes
0answers
464 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 ...
9
votes
0answers
764 views

Understanding Sequential Probability Ratio Test (SPRT) Likelihood Ratio

I am a software developer looking to develop an alternative for the simple hypothesis testing scheme described here. In short, the test works as follows: Two URLs are compared for their ability to ...
9
votes
0answers
360 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'...
9
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>...
9
votes
0answers
765 views

What is Shannon's source entropy?

Suppose that ${X_n; Y_n}$ is a random process with a discrete alphabet, that is, taking on values in a discrete set for $n$ data length. They correspond to the input and output of a communication ...
9
votes
0answers
509 views

Variance of the Kaplan-Meier estimate for dependent observations

Can someone help me find a way to estimate the variance of the Kaplan-Meier estimate with dependent observations? Specifically, I have failure time data from patients with several different ...
8
votes
0answers
144 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+...
8
votes
0answers
185 views

Conditions for cyclic behaviour of ARIMA model

I'm trying to model and forecast a time series that is cyclic rather than seasonal (i.e. there are seasonal-like patterns, but not with a fixed period). This should be possible to do using an ARIMA ...
8
votes
0answers
343 views

No-U-Turn Sampler (NUTS) for Hamiltonian Monte Carlo (HMC): how do I understand the doubling process?

I'm reading the original NUTS paper by Hoffman and Gelman, but couldn't fully understand the recursively doubling process. The following figure is taken from the paper. The NUTS process starts ...
8
votes
0answers
2k views

Backpropagation on a convolutional layer

Online tutorials describe in depth the convolution of an image with a filter, etc; However, I have not seen one that describes the backpropagation on the filter (at least visually). First let me try ...
8
votes
0answers
168 views

Correlation between two binary variables within one categorical variable

The Problem: I have measured two binary variables within 1 categorical variable with 5 levels. Initially, I thought I'd be able to use Fisher's Exact test or some N x M x K version of it. However I ...
8
votes
0answers
650 views

Is sparsity of topics a necessary condition for latent Dirichlet allocation (LDA) to work

I have been playing with the hyper-parameters of the latent Dirichlet allocation (LDA) model and am wondering how sparsity of topic priors play a role in inference. I have not performed these ...

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