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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Do Neural Networks tend to have Zero Mean Errors in each Output?

My NN (a few linear layers with ReLUs + batch normalization, no activation in the last layer) learns to approximate vector-valued labels $y_z$ from data $z\sim\rho_z$ in a supervised way, i.e. net$(z)=...
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Are the method-of-moments-based normal confidence intervals asymptotically valid and optimal?

A common way of getting confidence intervals for the mean of a normal random variable is to estimate the mean and variance by the method of moments and then compute a confidence interval based on ...
4 votes
2 answers
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How to reference lm function in R? [closed]

Hopefully a quick and easy question for somebody on here. I'm a masters student using R to interpret data for my thesis. I want to reference the type of linear regression that I have used in my ...
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0 answers
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Gaussian white noise model for beginners

It is a classical result that the "Gaussian white noise model" is asymptotically equivalent to nonparametric regression and density estimation [1,2]. While this is clearly an important ...
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What test should be used to see if recall is the same in production as estimated ion testing set? [closed]

I am curious how machine learning models are supposed to be evaluated in the real world environment comparing to the recall estimated on the testing set? Any suggestions?
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1 vote
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Spatial Statistics (for mathematicians) lecture notes request

I'm currently doing a master's in mathematics, and I'm interested in spatial statistics, mainly for a project. Unfortunately, it seems impossible to find lecture notes on this topic. I have seen some ...
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What is a good dissimilarity on rooted ordered labeled trees with probabilities on the leaves?

Consider a rooted ordered labeled tree that is "binary" in that there are at most two children of any vertex and whose leaves are decorated with probabilities (the sum of the leaf ...
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Bayes update rule studied as an operator

The bayes rule can be understood as a nonlinear map from the space of probability measures to itself. Are there any reference/books which study it from this perspective? For eg. can we say something ...
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0 answers
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How to run cosinor analysis in R? [closed]

I'm working on a research project for which I've collected google trends data and need to do cosinor analysis to study seasonality. This project is similar to this previous work. However, I'm not ...
1 vote
0 answers
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Learning materials about Time Series Forecasting? [duplicate]

I am a beginner in Time Series Forecasting meaning I have created some simple forecasting models and used them and I am also familiar with Stats and Probability but not that good just some basic ...
1 vote
1 answer
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Differences between variations of GARCH (EGARCH, APARCH, ...)

I want to know the differences between EGARCH, APARCH, TGARCH, QGARCH, GJRGARCH, IGARCH, AVGARCH, PGARCH, GARCH-M and the standard GARCH. I tried to find the information by myself but I cannot find ...
0 votes
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OLS Autoregressive Distibuted lag models

Could anyone suggest a book or a paper about the asymptotic behaviour of OLS in an autoregressive distributed lag (ARDL) model, or at least an ARX(p) model, with clearly stated underlying assumptions? ...
1 vote
1 answer
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Fractional Factorial Design when some factors have more than 2 levels

Let's say I was conducting an experiment with 4 factors. Three of them have qualitative settings, so I can simply designate one as +1 and one as -1. But one of the factors is numeric, and I would like ...
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Online courses for advanced statistics/econometrics with Python? [duplicate]

I am searching for intermediate/advanced online courses in statistics/econometrics that employ python. Exploring the main platforms (i.e. Coursera, Edx, etc..) I found either very basic courses that ...
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0 answers
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What are some good books for causal inference? [duplicate]

I am looking for a book(s) on causal inference for a beginner. I mostly want to know about the mathematics behind techniques and models in causal inference. However, a good book on the intuition ...
user avatar
0 votes
0 answers
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Online courses/resources for panel data analysis in python?

I am keen to learn more about panel data models using python, but I do not find related courses or many resources online. In particular, I usually find general statistics courses with Python or, ...
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Partial adjustment model with negative adjustment/inertia?

I am fitting a partial adjustment model of the form $$ y_t = \alpha_0 + \alpha_1 y_{t-1} + \beta_0 x_t $$ and encountered for the first time a negative $\alpha_1$. I am intrigued and a little bit ...
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Selecting ARIMA orders by ACF/PACF vs. by information criteria

We keep on getting questions here about selecting ARIMA model orders based on ACF/PACF plots. This is the older methodology proposed by Box and Jenkins. More modern tools like the ...
1 vote
1 answer
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Visualisation of a relationship between families of stochastic processes

I am looking for a diagram of stochastic processes like the Univariate Distribution Relationship Chart Maybe someone know a visualisation of a relationship between families of stochastic processes ?
2 votes
2 answers
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Sensitivity vs. specificity vs. recall

Given a binary confusion matrix with true positives (TP), false positives (FP), true negatives (TN), and false negatives (FN), what are the formulas for sensitivity, specificity, and recall? I'm ...
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Can I have two different specifications in the two stages of a control function?

I want to estimate some bilateral flows between countries using a Poisson Pseudo Maximum Likelihood (PPML). The empirical setting I have is something like: $$ Y_{ijt} = exp(\beta_1 Endog_{jt} + \...
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7 votes
1 answer
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How competitive is stepwise regression when it comes to pure prediction?

When we want to do inference on parameters or nested models, stepwise variable selection causes a number of problems, discussed by Frank Harrell and others. However, if we validate the stepwise model-...
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Gathering Resources to Learn Statistics from the Ground Up [duplicate]

I am a math grad student who recently decided to do a research study in statistics in Winter 2023. I took AP Stats in high school over ten years ago. I have a solid background in pure math and have ...
1 vote
1 answer
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Source needed: Why vector representation are ideal for statistical models

I am just looking for a scientific source, either a paper or book, that I can refer to when talking about the fact that the ability to represent data in vectors is a desired property. Reasons can ...
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2 votes
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Proof of identification of causal effect in high dimensional mediation analysis

I'm studying this paper for high-dimensional mediation analysis for a class project. Section 2 of this paper talks about different assumptions being made for identifying causal effects. But my ...
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0 answers
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Continuous Time Markov Chain Generator Matrix

I'm looking for references on Continuous Time Markov Chain, with clearer explanation on generator matrix. Also, if there's large amount of examples that would be very helpful. Ross's book is very good....
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1 vote
1 answer
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Benchmarking a clustering algorithm

Intro I built a clustering algorithm for a specific problem I have. The clustering algorithm wasn't my main goal, I just had to be able to separate the data into clusters prior to further processing, ...
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5 votes
1 answer
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Derivative of the Backshift Operator?

Is there any meaningful sense in which the backshift operator can be said to have a derivative? Here's my attempt at constructing one. Based on some helpful threads on this site, I represent the ...
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3 votes
0 answers
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Applications of Canonical Correlation Analysis in real-life problems?

I have been exposed to Canonical Correlation Analysis (CCA) a few years ago and I still find it mathematically elegant and beautiful. On Cross Validated there are several interesting posts on CCA, ...
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Where to find proof of theorems in Probabilistic Graphical Models by Koller and Friedman?

I am self-studying Probabilistic Graphical Models by Koller and Friedman. Though the text is good, I am getting stuck with a few exercises, particularly the proofs of theorems that are given as ...
1 vote
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Interpreting IV for continuous treatment and continuous instrument

Most standard IV framework looks at cases when both treatment (let's denote by $D$) and instrument (let's denote by $Z$) is binary. Let $Y(D)$ be the potential outcome (by using this notation, I'm ...
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Parameter estimation of a communication channel (conditional probability distribution)

I am trying to find literature in statistics that deals with the following problem. Given a parameter-dependent communication channel, mathematically described as a conditional probability $p_{\vec{\...
0 votes
0 answers
12 views

References for choosing Welch's over Fisher's 1W-ANOVA

I learned that the Welch test is equivalent to, or better than, 1-Way ANOVA. I read about this in this blog, which in turn cites a minitab report. I also found similar arguments in other private-...
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1 answer
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What multivariate GARCH model is this?

I read a paper a few years ago that specifies a multivariate GARCH model with a particular form of rolling correlations. The GARCH literature is full of abbreviations and differing terminology which ...
3 votes
1 answer
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What are some good books for Computational Bayesian Statistics?

There is already a community wiki on introductory textbooks for Bayesian statistics. However, I am looking for a book(s) on Computational Bayesian Statistics for intermediate learner who already has a ...
1 vote
0 answers
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Fitting a regression model with both binary and continuous responses

It is well known that Probit regression can be formulated as transformed linear model in the following sense: Suppose that $Z = X\beta + \epsilon$ for some normally distributed $\epsilon$ and let $Y = ...
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1 vote
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Looking for a textbook on mathematical statistics at the same level of Casella but with the language of linear algebra

Is there any textbooks on math stats that's at the level of Casella but uses the language of linear algebra and covers the multivariate cases? Casella is a great book, but he dose not talk about the ...
0 votes
0 answers
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Can anyone provide me with reference to some lecture notes or an online lecture on Multiplicative Error Models?

As the title says, I am looking for some lecture notes or an online class going over Multiplicative Error Models. I have found a number of academic papers on the topic, but I am having trouble ...
10 votes
4 answers
621 views

Introductory material on splines

I am looking for a basic, step-by-step introduction into modelling with splines. (I have encountered splines while teaching another topic. The textbook I am using does not cover splines in sufficient ...
1 vote
0 answers
29 views

Exercises for Linear Regression Models

I am looking for exercises (more theoretical than applied) about linear regression models. Maybe you can advice me where I can find such exercises. Here is what my linear models course deals with if ...
0 votes
0 answers
22 views

good book/course on sample size calculation [duplicate]

could you please recommend a good book/course on sample size calculation? Ideally it should include adaptive designs and mixed models Thanks!
1 vote
0 answers
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Update to Box and Jenkins Air Passenger data? [closed]

A textbook example of a time series is the Box and Jenkins Air Passenger data. In R you can get it with the command data(AirPassengers). It has the number of ...
0 votes
0 answers
4 views

Within-Between Mixed or Hybrid panel data model

I am looking for references to work with hybrid (or mixed) within-between panel data model from an econometrics perspective. Slides, book chapters as well as R examples would all be helpful.
1 vote
1 answer
47 views

Is this a known measure of "effective degrees of freedom" in regression?

Suppose $x,y$ are I.I.D random variables in $d$ dimensions. Consider the following quantity: $$R=\frac{(E\|x\|^2)^2}{E\langle x, y\rangle^2}$$ equivalently for empirical distribution with data matrix $...
2 votes
1 answer
62 views

Derivation of Box-Cox and Yeo-Johnson Log-Likelihood Functions

The scipy documention lists expressions for the Log-likelihood functions for the Box-Cox and Yeo-Johnson transformations here and here. I'm looking for a source ...
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Recommend a research-level book on econometrics, particularly for the theory of linear regression for random regressors X

Can anyone suggest a research monograph (with proofs or at least detailed references) for econometrics? Specifically, I'm looking to learn about the theory of linear regression and all the usual ...
2 votes
0 answers
20 views

Recommendation for books about statistical data analysis with sparse data ( a lot of zeros)

Evident from the title, i am looking for books about the general statistical data analysis techniques such as hypothesis testing, etc but for large and sparse dataset.
0 votes
0 answers
23 views

Global forecasting with Random Forests

The global approach for forecasting a group of time series involves training a single univariate model across all series, see Montero-Manso and Hyndman. Regression trees, e.g., Random Forests, perform ...
20 votes
8 answers
2k views

What are some good blogs for Mathematical Statistics and Machine Learning?

I am looking for blogs that focus on the mathematical theory of Statistics and Machine Learning, ideally at a research or "advanced" level. The blog doesn't have to be solely about these ...
0 votes
0 answers
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Nonlinearly-Correlated Brownian motions across different times and representation with independent processes

This is a more wide-net question of https://mathoverflow.net/questions/430053/two-increasingly-correlated-brownian-motions-and-williams-decomposition. I posted this in MO, but I thought perhaps stats-...

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