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Questions tagged [references]

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

574 questions with no upvoted or accepted answers
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16
votes
0answers
3k 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 ...
14
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0answers
584 views

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

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_{...
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908 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
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77 views

What is the “direct likelihood” point of view in statistics?

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 ...
8
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0answers
189 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
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0answers
500 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
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0answers
132 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
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0answers
73 views

How to justify a “complicated” regression model over a simpler model to a non-technical audience?

I find myself in the position of advocating for a linear mixed-effects model to estimate a trend to a non-technical audience. The subject of the regression model is a somewhat contentious topic and my ...
6
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1answer
158 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
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1answer
52 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
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0answers
249 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
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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
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2answers
68 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
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0answers
519 views

Under what conditions will a Bayesian posterior fail to converge to a point mass?

Let's say you have a Bayesian model: $$\theta' \sim g(\theta|\mu) $$ $$ y \sim p(y|\theta')$$ And we have some data ($n$ data points) $\mathbf{y}_n$, which we will use to perform inference on $\...
5
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0answers
112 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
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313 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
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0answers
207 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 $d = \sqrt{n}$. ...
5
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0answers
130 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
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0answers
863 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
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0answers
151 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
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0answers
2k 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
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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
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0answers
302 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
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0answers
494 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
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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
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0answers
419 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
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0answers
17 views

First historical references on auto-correlation and cross-correlation

Although the origin of Pearson's correlation coefficient is well documented (see wikipedia), I have trouble to find some of the first and historical papers introducing the motivation, the benefits and ...
4
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0answers
79 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 ...
4
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0answers
31 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
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0answers
22 views

What can I use to compute a similarity (or diversity) index for a sample with “multidimensional” attributes?

Current problem: We have a batch of $n$ items for which we capture their details with $m$ attributes. It could look something like this: The goal is to compute an "index" that says how "similar" this ...
4
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0answers
38 views

Best textbook on philosophical background of interpretations (for beginners)

I'm looking for the best textbook teaches basics of statistics for a general researcher (undergraduate) without totally ignoring the mathematical proofs and theories while the main emphasizes is on ...
4
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0answers
47 views

Choosing the number of hidden layers and nodes in a Deep Belief Network

What are the recent advances and current best practices in choosing the number and size of stacked Restricted Boltzmann Machines in Deep Belief Networks ?
4
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0answers
217 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
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0answers
87 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
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0answers
548 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
1answer
106 views

Most powerful test bounds in differential privacy setting

I am interested in the setting of differential privacy- let's say a random function $\mathcal{D}:X\to\mathbb{R}$ discriminates between (distinct) $x, y \in X$ in a differentially private way if $$ \...
4
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0answers
127 views

Time varying (auto)correlation estimation

I would need to estimate a time varying autocorrelation of a variable. Do you have any references or examples? I've tried to search for a package in R but I wasn't ...
4
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0answers
413 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
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0answers
71 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
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0answers
37 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
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0answers
105 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
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0answers
116 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
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0answers
57 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
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0answers
187 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
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0answers
146 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
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0answers
514 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
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0answers
461 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
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0answers
127 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
73 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
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0answers
75 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-...