All Questions

Although this question is somewhat subjective, I hope it qualifies as a good subjective question according to the faq guidelines. It is based on a question that Olle Häggström asked me a year ago and ...

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, ...

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) ...

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 ...

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: ...

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 + ...

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 ...

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 ...

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},\cdots,\frac{X_{...

Xavier initialization seems to be used quite widely now to initialize connection weights in neural networks, especially deep ones (see What are good initial weights in a neural network?). The ...

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 ...

Most of the time, sticking to a pure Bayesian approach to statistics with proper priors, leads to admissible estimators. Nevertheless, there is a good reason to use Empirical Bayes in many cases, and ...

I am interested in estimation of ARMA models. I understand that a popular approach is to write the model down in the state space form and then maximize the likelihood of the model using some ...

I am modelling invertebrate.biomass ~ habitat.type * calendar.day + habitat.type * calendar.day ^ 2, with a random intercept of ...

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 ...

I have a multivariate dataset that changes over time. I have extracted (and normalised) some features and used k-means to generate clusters over the entire span of the dataset. Now I want to see ...

In "3 Things That Bother Me" (1988), Ed Leamer writes: Bootstrap estimates of standard errors are based on the assumption that the observed sample is the same as the true distribution, ...

I am aware it is common practice to standardize the features for ridge and lasso regression, however, would it ever be more practical to normalize the features on a (0,1) scale as an alternative to z-...

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'...

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 ...

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 ...

I made a model using repeated measures univariate ANOVA in R. ...

Suppose that $k$ experts are each asked to rank a set of $n$ objects in order or preference. Let allow ties in the rankings. John Kemeny and Laurie Snell in their 1962 year book "Mathematical models ...

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 $P(|\sum_1^n x_iy_i|\ge nt) \leq e^{(?)}$ for $t>1$. ...

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 ...

I am working with some survey data that uses probability weights. A number of sources explain that likelihood-based tests and fit statistics like likelihood-ratio, AIC, and BIC are not valid in the ...

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 ...

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 ...

I am reading a Springer title from 1997 called Applied Generalized Linear Models by James K. Lindsey. In the preface, Lindsey writes For this text, the reader is assumed to have knowledge of basic ...

Suppose $X\sim N_3(0,\Sigma)$, where $\Sigma=\begin{pmatrix}1&\rho&\rho^2\\\rho&1&\rho\\\rho^2&\rho&1\end{pmatrix}$. On the basis of one observation $x=(x_1,x_2,x_3)'$, I have ...

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 ...

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 ...

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 \...

I have several intermittent data. Based on those data, I would like to compare several forecasting methods (Exponential Smoothing, Moving Average, Croston, and Syntetos-Boylan), and decide whether ...

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, ...

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. ...

Being recently interested in Kalman filters and Recurrent neural networks, it appears to me that the two are closely related, yet I can't find relevant enough litterature : In a Kalman filter, the ...

I want to use CNN architectures for classification of multivariate time-series, where we apply one label to each sequence. I searched the net for the available designs in the literature and i found ...

Sibisi and Skilling (1996, also mentioned in the 1997 paper) define Bayesian kernel density as $$ f(x) = \int dx' \,\phi(x')\, K(x, x') \tag{2} $$ Here the kernel $K$ is an assigned smooth ...

I am trying to prove or disprove that the difference between Spearman's Correlation and Kendall's Correlation is no more than 1 (or less, the tighter the merrier). I am assuming there are no ties. ...

What are the eigenfunctions and the eigenvalues of the exponential kernel? The exponential kernel is defined as $$k(x,x')=\sigma^2\exp\left(\frac{||x-x'||}{l}\right)$$ where both $\sigma>0$ and $l&...

I am new to gam, and most of my knowledge comes from this document http://www3.nd.edu/~mclark19/learn/GAMS.pdf. Now I am using generalized addictive model with random effects to model some data, where ...

I am just trying to implement the scaled Baum-Welch algorithm and I have run into a problem where my backward variables, after scaling, are over the value of 1. Is this normal? After all, ...

Suppose that I have two distance matrices for the same set of items. By a distance matrix I mean a square matrix whose (i,j)th entry holds the distance (in terms of cosine similarity) between ith and ...

I am analyzing the performance of a predictive model with the AUC, area under the ROC curve. I repeat several times cross-validation, and I have different estimations of the AUC in each folder. For ...

I have two endogenous variables $x_1$ and $x_2$ and am trying to estimate the following model: $$y = \theta_0 + \theta_1 x_1 + \theta_2 x_2 + \theta_{12} x_{12}$$ where $x_{12} = x_1\times x_2$. I'm ...

Considering an SDE of the form $$dX_t = \mu(X_t, t)dt + \sigma(X_t, t)dW_t ,$$ where $W_t$ is a Wiener process, is there a set of necessary and sufficient conditions on the structure of the functions $...

Consider a time series: $X_1,X_2,...X_{n-1},X_n$ This series can also be written as a function of time $X(t)$, so that: $X_1,X_2,...X_{n-1},X_n = X(t_1),X(t_2),...X(t_{n-1}),X(t_n)$ Most ...

Consider an ordinary least squares model, $$y = \beta X + \epsilon \qquad \epsilon\sim N(0, \sigma)$$ The Gauss-Markov theorem tells us that the ordinary least-squares (OLS) estimator is the minimum-...

I know there are many topics(1,2,3), papers(1,2,3) and websites(1) that discuss this topic at length. However for the past two days I am reading all I can find about the subject and seems I hit a ...