Questions tagged [references]

Questions seeking external references (books, papers, etc.) about a particular subject. Always use a more specific tag in addition.

549 questions with no upvoted or accepted answers
Filter by
Sorted by
Tagged with
16
votes
1answer
692 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
0answers
539 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}...
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 ...
10
votes
0answers
853 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 ...
8
votes
0answers
173 views

Is probability fundamentally about reference classes (real or imagined)?

Question: It seems that frequentism and Bayesianism may not really be different as far as the the ultimate basis for what a probability is (relative frequency within a reference class) - it's just ...
7
votes
0answers
461 views

Does using bootstrapped samples improve parameter estimates for a fitted distribution?

The R package retimes has a function for fitting an ex-Gaussian distribution to a set of observations. The method involves taking multiple bootstrapped samples of the observations, and fitting the ex-...
6
votes
0answers
130 views

Bayesian inference via approximate data likelihood

Suppose that we have a very large i.i.d. sample $x_1,...,x_n$ and a data likelihood defined by $$p(x | \theta,\beta) = \prod_ip(x_i | \theta,\beta)$$. Further suppose that $\theta$ is the parameter ...
6
votes
1answer
134 views

is there a book on stats similar to Kallenberg's on probability?

One may find this question a duplicate, but my search through CrossValidated did not give satisfactory result. So I am posting this question and explaining what I want. I need a book such that if one ...
6
votes
1answer
50 views

Reference for the idea that a simpler model can be used when the range of data values is smaller

When we build a statistical-physical model, generally, a simpler model can be justified when the range of data-values is smaller. I can't be the first person to use this idea, but I also can't find ...
6
votes
0answers
239 views

Reference Request: Information Geometry for Ridge Regression

I am reading the book "regression estimators" by Gruber 2010 where he uses this technique to compare Ridge Regressors, however he concentrates on deriving the mathematical results without giving any ...
5
votes
0answers
83 views

French website Providing Instruction/Tutorials on Statistical Theory

This is somewhat of an odd question for CV, but since it's a question about statistical education, I think it falls within the scope of CV. Several years ago I stumbled across a French website that ...
5
votes
2answers
61 views

Computational statistics review

I'm looking for a mathematically rigorous review of key topics in computational statistics, such as numerical integration, EM algorithms, MCMC, and sampling algorithms. Are there any good lecture ...
5
votes
0answers
95 views

Probabilistic upper bounds on importance sampling error

Consider the importance sampling estimation error $$ e_n(f) = \int f d\mu - \frac{1}{n}\sum_{i=1}^n f(x_i) \rho(x_i), \qquad x_i \sim \lambda,\, \rho = \tfrac{d\mu}{d\lambda}, $$ where $\mu$ and $\...
5
votes
0answers
253 views

Suggestions for a recent book on probability

I've been dealing with statistics for a few years now. Up to now, for the probability part I've been referring to my old university book (my edition is even older, by the way), and of course the ...
5
votes
0answers
125 views

Truncated trivariate normal - conditional expectation

I am working on a paper in which I'd need to use the two following conditional expectations: $E(X_{1}|a \leq X_{2} \leq b)$ $E(X_{1}|a \leq X_{2} \leq b, a \leq X_{3} \leq b)$ where $X_{1}, X_{2}, ...
5
votes
0answers
819 views

Proof of Kolmogorov-Smirnov test

Could someone provide me a reference, preferably a book, where I can find detailed proofs and explanations of the Kolmogorov-Smirnov test (including the two-sample variant) and the derivation of the $...
5
votes
0answers
148 views

Compressed sensing: Optimization in $L_1$ norm and total variation with fourier coefficients

I'm reading the article Robust Uncertainty Principles: Exact Signal Reconstruction from Highly Incomplete Frequency Information (Candes, Romberg and Tao, 2004). In this article they are talking ...
5
votes
0answers
1k views

Log-Ratio \ Compositional analysis

I am not a trained statistician but I am trying to improve on my own MBA thesis which was essentially regression analysis of the factors affecting opening cinema box-office in the UK. I am now ...
5
votes
0answers
116 views

Lomax distributions - Kullback Leibler divergence

Does anyone know of a reference for an expression for the Kullback-Leibler divergence between two Lomax (Pareto II) distributions? Not really worried which way the Lomax is parameterized.
5
votes
0answers
286 views

Derivation of prediction intervals for a normally distributed population with unknown population standard deviation

I have via the ISO standard 16269 found the solution to a problem that I've been working on. Based on a couple of independent samples from a normally distributed population, I would like to determine ...
5
votes
0answers
455 views

Sheppard's correction

Is there a good expository account of Sheppard's correction, written in a way that any ordinary mathematician can readily follow? http://mathworld.wolfram.com/SheppardsCorrection.html (I've thought ...
5
votes
0answers
2k views

Examples of spatial generalized linear models

I've been reading some materials on Spatial data analysis, and I've a good background in GLMs. Right now I'm looking to find an example in spatial generalized linear models, but so far I've not found ...
5
votes
0answers
416 views

CIR Process-Variance reduction

I'm trying to evaluate a path dependent function, $f(r_t)$, on a Cox-Ingersoll-Ross process: $$dr_t = \theta (\mu - r_t)dt + \sigma \sqrt r_t dW_t$$ by Monte Carlo simulation. Could anyone suggest ...
4
votes
0answers
21 views

How to combine noisy and noise-free datasets to train a model

Overview Suppose I have two datasets, both of which consist of rows of features and their matching labels. One of these datasets is noise-free and its labels correspond to the ground truth, but the ...
4
votes
0answers
177 views

Why is long-run variance a positive function of the spectral density at frequency zero?

Müller (2014) provides the following definition of the long-run variance $\omega^2$: $\omega^2=2\pi f(0)$ where $f(0)$ is the spectral density of a time series process, evaluated at frequency zero. ...
4
votes
0answers
69 views

Optimal block size for spatial bootstrapping

Take a regression model: $$ y_s = X_s\beta + \epsilon $$ Where $E[\epsilon|X] = 0$, but $cor(\epsilon_s, \epsilon_{near}) > cor(\epsilon_s, \epsilon_{far})> 0$. In other words, $X$ is ...
4
votes
0answers
447 views

Concentration of maximum of subexponential random variables

I'm looking for a concentration bound on the maximum of a collection of sub-exponential random variables, which are not necessarily independent. More specifically, I have the following collection: \...
4
votes
0answers
286 views

Choosing the basis functions in a linear regression

I have two random variables $X$ and $Y$ and I'm trying to model $\mathbb{E}[Y|X]$. To this end, I'd like to pick a collection of functions $f_1, f_2 \dots f_n : \mathbb{R} \to \mathbb{R}$ and then ...
4
votes
0answers
59 views

Analogue of spectral gap but for *smallest* eigenvalues/singular values

The difference between the largest eigenvalue and the next-largest of a graph Laplacian (equivalently, of the random walk Markov chain on the graph) is the spectral gap, related to the Cheeger ...
4
votes
0answers
32 views

Review article for spatio-temporal modelling

I'm currently reading Cressie and Wilke's book on spatio-temporal modelling and I'm curious to know if there are review articles that summarize important tools in spatio-temporal analysis. Can anyone ...
4
votes
0answers
97 views

Combining non-independent priors

I've been working on a stats package that includes Bayesian survival models. The user is allowed to write priors directly for all the parameters involved. However, I think it's pretty difficult for ...
4
votes
0answers
100 views

Valid / invalid moments in Generalized Method of Moments (GMM)

I'm preparing to conduct an estimation procedure using GMM (Generalized Method of Moments), and I'm in the process of selecting my moments. This got me thinking, can I use non-statistical moments as ...
4
votes
0answers
56 views

Processes behind statistical distribution laws: a compendium?

The simple processes that "explain" the binomial, Gaussian or Poisson distribution are relatively well-known. Johnson or shot noises may be known in restricted area of science. Sometimes, a ...
4
votes
0answers
177 views

Central Limit Theorem when the dimension size increases with the sample size

Let $X_1, X_2,\ldots, X_n \in \mathcal{R}^d$ and be zero-mean, unit variance random variables. Here the dimension ($d$) is a function of the sample size($n$) i.e, $d=f(n)$. For example $d = \sqrt{n}$. ...
4
votes
0answers
183 views

Fisher - Neyman dispute over weak and strong null hypotheses

I am trying to find information on one of the many exchanges between Fisher and (I believe, but cannot be sure) Neyman. I believe the exchange took place at one of the Royal Statistical Society ...
4
votes
0answers
139 views

Video Lectures on Design and Analysis of Experiments

Where can I find video lectures or tutorials on design and analysis of experiments? E.g. something similar in scope and depth to Montgomery's Design and Analysis of Experiments?
4
votes
0answers
497 views

Paper showing that logistic regression intercept biased in rare events

I'm studying the logistic regression for estimate the Probability of Default of SME's. Fortunately the event (firm's default) is a rare event. King and Zeng tell us that "logistic regression can ...
4
votes
0answers
427 views

Generalization of Fisher information for a discrete parameter

This is mainly a reference request. There must be some generalizations of the concept of Fisher information for discrete (say, integer-valued) parameters, and of related results such as the Cramer-...
4
votes
0answers
125 views

Where to start to learn about pricing models?

I have a situation at my work that I want to take as a chance to learn more about pricing and stats. In a nutshell, I work for a company that buys several products and then charges a margin (we have ...
4
votes
1answer
70 views

What are best practices for visualizing/selecting visualizations for continuous data?

There appear to be a large number of rules of thumb for histogram bin size and kernel selection for density plots. Are histograms and/or density plots really the best visualization for a single ...
4
votes
0answers
73 views

literature on small samples and parametric survival models

I have an abundance of small data sets with right-censored data. There are different groups in each data set and I'd like to get confidence intervals for the regression parameters. Each data set has 3-...
4
votes
0answers
105 views

Coverage rates of confidence intervals in reality

One proves mathematically that if assumptions of a model are satisfied, then the coverage rate of a $100p\%$ confidence interval is $100p\%$. But then statistics gets applied to the world, where ...
4
votes
0answers
300 views

The distribution of the scalar product of multivariate complex normal vectors

Assume two independent random complex vectors (with real and imaginary parts): $$ \vec{\dot{Z}}=(\dot{z}_1,\dot{z}_2,\ldots,\dot{z}_n)~~~~~~~~~~ \begin{cases} \Re(\dot{z}_i)&=x_i \\ \Im(\dot{z}_i)...
4
votes
0answers
81 views

Tutorials / examples for multiclass boosting

I want to learn the multiclass boosting technique. I have a basic understanding of binary boosting and also have seen some working examples on this. I have also read about the basics of multiclass ...
3
votes
0answers
64 views

What are some examples of reversed usage of “percentiles”?

The technical definition of a "percentile" in statistics is taken from the quantile function; it is the value below (or below or equal to) which a given percentage of values falls. For example, the ...
3
votes
1answer
33 views

Sufficient statistic for Gaussian $AR(1)$

Question Does the Gaussian $AR(1)$ model, with a fixed sample size $T$, have nontrivial sufficient statistics? The model is given by $$ y_t = \rho y_{t-1}, \, t = 1, \cdots, T, \; \epsilon_i \...
3
votes
0answers
49 views

What are the main approaches to the foundation of statistics without probability

The frequentist, likelihood and, to an even greater extent, Bayesian approaches to statistics are all based on probability. Without probability, it seems difficult to use a data sample ("seen" cases), ...
3
votes
0answers
40 views

Looking to identify a book by a top statistician with a chapter on Simpson's Paradox

It was more than 20 years ago. I had just gotten acquainted with Simpson's paradox. I was browsing in a bookstore and saw a book by an eminent statistician -- eminent in the sense that I had come ...
3
votes
0answers
24 views

Are there extant deep learning analogs to random coefficient (aka mixed) models?

Random coef models, applied to longitudinal data, capture response heterogeneity by cross-sectional unit. I've got a longitudinal prediction problem, in which I know that some "features" (or ...
3
votes
0answers
95 views

Biased estimates of Hurst exponent in R/S analysis

I've used the standard R/S algorithm for estimating the Hurst exponent in Mathematica*, and tested it on fBm and fGn for $H\in\{0.05,0.1,\ldots,0.95\}$, generating 1000 time series for each $H$. The ...