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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.

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Independent Study Statistics/Probability Grad Level [duplicate]

I am trying to decide on topics for my independent study this semester. I am a Pre-Doctoral Mathematics student, so looking for a more math based text rather than engineering based (which I have found ...
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1answer
68 views

What can we say about distributions of random variables $X$ such that $X$ and its inverse $1/X$ have the same distribution?

What can we say about random variables such that it and its inverse have the same distribution? One example is Cauchy distributed random variables, easily proved via the fact that if $X, Y$ are IID ...
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1answer
15 views

Derivation of the Mann Whitney U normal approximation

The normal approximations for the Mann Whitney U statistic are given by wikipedia but there are no refrences mentioned. What are the actual derivation steps of the untied and tied case approximations? ...
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20 views

Asymptotic equivalence between cross validation and bayesian information criteria

I heard that Bayesian information criteria and cross validation are asymptotically equivalent when the size of validation set is large enough similar to the relationship between Akaike information ...
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2answers
88 views

Regression as mutual information minimization

I am trying to see if mutual information can be used as an objective function in a generalized formulation of the linear regression without the normal distribution assumption for the residual error. ...
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1answer
61 views

Most powerful test for deciding probability mass function

Let $X$ be an integer valued random variable supported on $\{0.1.2...,12\}$ whose pmf is either $g(x)=1/13; x=0,1,...,12$ or $ f(x)=\dfrac x {36} 1_{\{0,1,...,6\}} + (\dfrac 13 - \dfrac x{36})1_{\{7,...
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What are most recent research work on the problem of key phrases extraction from a text corpus?

I am interested in the problem of extracting key phrases from a text corpus. This is different from the keyword extraction problem, which is only for a particular document. This problem helps us, for ...
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34 views

Now that I've theoretical foundation in ML, where can I find simple, already solved, practice exercises to better my understanding of data science?

I've studied and understood well quite a bit of theoretical concepts of Machine Learning (except Deep Learning): e.g. the mathematics behind several classification and clustering algorithms, SGD and ...
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1answer
26 views

Books on Bayesian inferential analysis of GARCH models

Do you know books about Bayesian inferential analysis of GARCH models with the analysis of these models in R and JAGS? Here is a list of the books I already have: [Ardia] - Financial Risk Management ...
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0answers
10 views

What are some resources to learn about Bayes Optimal Classifier?

I am in need of some resources to learn Bayes Optimal Classifier. I am searching for some texts or tutorials which explain this topic without, mostly, rigorous mathematical notations, and in a ...
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1answer
12 views

Does using random minibatchs give more resilance against local minima, vs full batch gradient descent

It was my believe that one of the advantages of using minibatches, when training a neural network via gradient descent (be it "vanilla" or the latest flavour of AdaGrad), was an increased resiliance ...
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16 views

Convergence in total distribution distance in the Random Walk Metropolis-Hastings algorithm

I'm searching for a proof of the convergence in total distribution distance of the transition probabilities of a Markov chain generated by the Random Walk Metropolis-Hastings algorithm to its ...
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24 views

PCA used for regression

Can anybody point me to a thorough example where PCA was used for predictive purposes and it compared favorably to regular linear regression (i.e., perhaps a lower RMSE using the PCA components ...
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0answers
32 views

Is there a statistical journal that publishes such a kind of papers?

Just out of curiosity, I find it interesting to know if there is a statistical journal potentially considering publishing articles of this type to be introduced in the following. As far as I am aware, ...
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1answer
45 views

Typo or change of interpretation in loss function in the Bayesian Choice textbook?

In the proof of the following proposition, the posterior loss depends on a prior distribution $\pi$, while in the derivation it depends on the parameter $\theta$. Should the posterior loss function be ...
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0answers
14 views

Reference request: Least Squares Concentration Bounds

I've recently become interested in parameter estimation for regression and time-series type models and I often encounter, and indeed need to understand, results using concentration of measure-type ...
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0answers
14 views

Best estimator for the variance of the empirical median

Let $X_i$ be $n=2k+1$ IID continuous random variables with distribution function $F$ and quantile function $F^{-1}$. Let $m$ be their empirical median. It is well known that: If the $X_i$ were ...
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0answers
27 views

Books for data sources

There are many books on data science that describe in detail learning algorithms and methods. But another important step in data science is data collection and feature engineering. Are there books ...
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26 views

Tail probability of minimum to maximum ratio among $n$ i.i.d. half-normal random variables

I have $n$ i.i.d.$\sim\mathcal{N}(0,1)$ random variables $X_1,\cdots,\ X_n$. For my research, I am interested in finding bounds (upper and lower) of the tail probabilities of the ratio $\frac{|X|_{(1)}...
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0answers
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$\mathbb{R}^m\to\mathbb{R}^n$ regression

The naive approach to a $\mathbb{R}^m\to\mathbb{R}^n$ regression problem is simply to solve $n$ distinct $\mathbb{R}^m\to\mathbb{R}$ regression problems. However, suppose that the output of the ...
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1answer
34 views

(Online) intuitive explanation of state space models

I have a similar question to the one in the link below: Intuitive explanation of state space models In the link they recommend the book by Commandeur and Koopman. I have this book already. I was ...
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0answers
12 views

Fractional Brownian motion with additional terms

Fractional Brownian motion seems fairly a straight forward random process with a kind of auto-correlation function, $$ \mathbb{E}\left[ B^H_t B^H_s \right] = \frac{1}{2} \left( |t|^{2H} + |s|^{2H} - |...
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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 ...
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4answers
176 views

Is it mandatory to subset your data to validate a model?

I'm having a hard time getting on the same page as my supervisor when it comes to validating my model. I have analyzed the residues (observed against the fitted values) and I used this as an argument ...
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0answers
30 views

Statistics in medicine, any literature recommendations?

I work in the field of medicine as Ph.D. student. My primary work right now is modeling. And the more I get into it, and its statistics, I can see that I lack a lot, and what I have done, and others (...
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27 views

Econometrics of demand for substitute goods

I've got a problem that seems to be exposing a fairly fundamental hole in my econometrics training. I'm looking for a canonical reference for how to deal with the following sort of problem: For ...
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0answers
20 views

Statistics for Market research [duplicate]

I'm looking for some sources in order to learn about Market Research (a statistical approach with R/Python). You know, the kind of things you must know if you wanna work for Nielsen Kantar, etc.
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1answer
88 views

Who invented the hazard function?

The hazard function or instantaneous failure rate is very popular in survival analysis: https://en.wikipedia.org/wiki/Failure_rate $$\lambda(t) = \dfrac{f(t)}{1-F(t)}.$$ However, I cannot find a ...
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0answers
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Answers to exercises in Pinhiero and Bates' book

Can anyone tell me where to find the answers to the Exercises in Pinhiero and Bates' book Mixed Effects Models in S and S-Plus? I want to check my answers against someone who knows better.
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0answers
43 views

Understanding the outputs of tar (Threshold Autoregressive model estimation, TSA package) command in R

I'm using the TSA::tar command to estimate threshold autoregressive model coefficients. There are a few parameters I would like to know the function of: rss1, rss2, std.res, rms1, rms2 (rms of what?) ...
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0answers
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How do you manage provenance metadata and licence conditions for the data and software packages you use in your research?

In spatial analysis (and no doubt, any research field) we often work with a broad range of data and software libraries, increasingly open source. These are all associated with various licence ...
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27 views

Terminology for a “studentized” random variable?

Let $X_{1}, \dots, X_{n}$ be i.i.d. ramdom variables having mean $\mu$ and standard deviation $\sigma$. I wonder if the "studentized" $X_{i}$, the sample version of standardized $X_{i}$ where $\mu$ is ...
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Reference for implementation of LDA in sklearn

Is there a reference explaining the implementation of sklearn.discriminant_analysis.LinearDiscriminantAnalysis._solve_svd? More specifically, I am curious about ...
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1answer
25 views

Best way to compare several cases to a null model

At the moment I am doing analysis in some data that is (currently) divided by number of individuals in a group. More or less like: Groups w/ two individuals: Value_1, Value_2, ..., Value_N Groups w/ ...
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1answer
34 views

Machine learning books covering neural networks / cnn / GAN [duplicate]

I'm not an expert in machine learning. Is there any textbook (with a decent amount of mathematical rigor) that cover the subjects neural network / convolutional neural network / GAN network? I've the ...
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1answer
28 views

Books for data science applications on graphs

Application of data science especially ML algos on complex structures that can be represented as graphs has risen tremendously. Research work in recent times in this area focus on topics like:- ...
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0answers
15 views

Estimation of infinitesimal generator/transition rate matrix from proportion data

Suppose I have a collection of data $\{\boldsymbol x_t \in \mathbb S^d\}_{t = 1,\dots,T}$ where $\mathbb S^d$ is the $d$-dimensional unit simplex, i.e. the elements of $\boldsymbol x_t$ sum to $1$. ...
0
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1answer
29 views

Best Clusterizing Techninque for 7 points Likert scale

What is the best clustering method seven points Likert Scale. When what I am looking to answer is if there are groups of people behavior on it. For example. I have around 30 questions with this scale....
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0answers
5 views

Statistical meaning of $\mathbb E_P[score_\theta(Z)]^T\operatorname{Cov}_P[score_\theta(Z)]^{-1}\mathbb E_P[score_\theta(Z)]$

Consider a random vector $Z$ with distribution $P$ having mean $\mu$ and covarance matrix $\Sigma$. Question Statistically what is the meaning of the quadratic quantity $\mu^T\Sigma^{-1}\mu$ ? More ...
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0answers
41 views

Asymptotic properties for LASSO in logistic regression

I am trying to find a paper or book that gives the asymptotic properties for the LASSO for logistic regression. Anyone has any suggestions please?
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0answers
22 views

Benchmark data sets for anomaly detection algorithms in multivariate time series

as per title, which datasets are commonly used to benchmark novel methods to detect anomalies in multivariate time series? I'm particularly interested in moderately high-dimensional (10-40 components),...
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2answers
78 views

A book on solved Probability problems

I was looking for a book to practice Probability problems with solutions to get intuition of Probability and I see Schaum's series is kind of most respected on solved problems. But I wonder which on ...
2
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2answers
65 views

Looking for books about causal discovery

I am new in causal discovery. I am reading papers and other stuff about causal discovery, but couldn't get any good books or good information. Can anyone recommend the best book for causal discovery?
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0answers
19 views

Sum of correlated non-Gaussian random variables with same distribution as individual terms

Let's say there is a sum $s$ of $N$ zero-mean correlated random variables $\{x_i\}$: $$ s = x_1 + x_2 + \ldots +x_N, $$ where the correlations $C_{ij} = \mathbb E[ x_i x_j]$ are known. Assume that ...
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0answers
24 views

Master's-level Quantitative Methods / Statistics textbook for Management, Marketing, Economics students

What are some good textbooks for a master's (or upper undergraduate) level course in Quantitative methods / Statistics for students in Management, Marketing or Economics?
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Proof of multivariate Cramer Rao bound?

The Cramer-Rao lower bound is a presented in most statistical textbooks, but they tend to provide a proof for the univariate case, and let the multivariate case to the reader. I wonder if there is any ...
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0answers
79 views

What is a good book for learning about time series analysis?

I am a junior in college and am looking for a book to self study time series analysis. I am a math student and have taken upper level probability and statistics courses, so a mathematical background ...
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1answer
63 views

Matrix Profile vs. Deep Learning

I've been reading about Matrix Profiles and how they can be used for anomaly detection in time-series. However, I'm a bit confused how they compare/relate to typical Deep Learning approaches. I would ...
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0answers
8 views

Formalised analysis of questionnaires

I have given a dataset that resembles a questionnaire and I am requested to write a statistics paper on it. I have little to no experience dealing with cross section categorical data. While I have ...
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1answer
35 views

Asymptotic Normality of Posterior distribtuion

I am trying to understand asymptotic Normality of posterior distributuions. Specifically, what are the (regularity) conditions that allow us to use this approximation? The problem is that the ...