# Questions tagged [self-study]

A routine exercise from a textbook, course, or test used for a class or self-study. This community's policy is to "provide helpful hints" for such questions rather than complete answers.

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### Books for self-studying time series analysis?

I started by Time Series Analysis by Hamilton, but I am lost hopelessly. This book is really too theoretical for me to learn by myself. Does anybody have a recommendation for a textbook on time ...
146k views

### An example: LASSO regression using glmnet for binary outcome

I am starting to dabble with the use of glmnet with LASSO Regression where my outcome of interest is dichotomous. I have created a small mock data frame below: <...
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### How are regression, the t-test, and the ANOVA all versions of the general linear model?

How are they all versions of the same basic statistical method?
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### Pitfalls in time series analysis

I am just starting out self-learning in time series analysis. I have noticed that there are a number of potential pitfalls that are not applicable to general statistics. So, building on What are ...
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### Taking the expectation of Taylor series (especially the remainder)

My question concerns trying to justify a widely-used method, namely taking the expected value of Taylor Series. Assume we have a random variable $X$ with positive mean $\mu$ and variance $\sigma^2$. ...
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I recently came across this identity: $$E \left[ E \left(Y|X,Z \right) |X \right] =E \left[Y | X \right]$$ I am of course familiar with the simpler version of that rule, namely that $E \left[ E \... 9answers 4k views ### What is the relationship between$Y$and$X$in this plot? What is the relationship between$Y$and$X$in the following plot? In my view there is negative linear relationship, But because we have a lot of outliers, the relationship is very weak. Am I right? ... 5answers 4k views ### Will the fact that my Italian son is going to attend a primary school change the expected number of Italian children to be present in his class? This is a question stemming from a real-life situation, for which I have been genuinely puzzled about its answer. My son is due to start primary school in London. As we are Italian, I was curious to ... 5answers 15k views ### LDA vs word2vec I am trying to understand what is similarity between Latent Dirichlet Allocation and word2vec for calculating word similarity. As I understand, LDA maps words to a vector of probabilities of latent ... 3answers 34k views ### How to take derivative of multivariate normal density? Say I have multivariate normal$N(\mu, \Sigma)$density. I want to get the second (partial) derivative w.r.t.$\mu$. Not sure how to take derivative of a matrix. Wiki says take the derivative ... 6answers 4k views ### Why shouldn't the denominator of the covariance estimator be n-2 rather than n-1? The denominator of the (unbiased) variance estimator is$n-1$as there are$nobservations and only one parameter is being estimated. \mathbb{V}\left(X\right)=\frac{\sum_{i=1}^{n}\left(X_{i}-\... 3answers 4k views ### What does the Akaike Information Criterion (AIC) score of a model mean? I have seen some questions here about what it means in layman terms, but these are too layman for for my purpose here. I am trying to mathematically understand what does the AIC score mean. But at ... 4answers 83k views ### Find expected value using cdf I'm going to start out by saying this is a homework problem straight out of the book. I have spent a couple hours looking up how to find expected values and have determined I understand nothing. ... 4answers 2k views ### Is the result of an exam a binomial? Here is a simple statistics question I was given. I'm not really sure I understand it. X = the number of aquired points in an exam (multiple choice and a right answer is one point). Is X binomial ... 2answers 21k views ### What is the difference between censoring and truncation? In the book Statistical Models and Methods for Lifetime Data , it is written : Censoring: When an observation is incomplete due to some random cause. Truncation: When the incomplete nature of ... 6answers 15k views ### What's the difference between logistic regression and perceptron? I'm going through Andrew Ng's lecture notes on Machine Learning. The notes introduce us to logistic regression and then to perceptron. While describing Perceptron, the notes say that we just change ... 4answers 4k views ### Self study vs a taught education? There is a question with similar intent on programmers.SE. That question has some quite good answers, but the general theme seems to be that without self study, you get no-where. Obviously there are ... 4answers 85k views ### McFadden's Pseudo-R2 Interpretation I have a binary logistic regression model with a McFadden's pseudo R-squared of 0.192 with a dependent variable called payment (1 = payment and 0 = no payment). What is the interpretation of this ... 3answers 4k views ### Which hospital should be chosen? One has a higher success rate, but the other has a higher overall success rate I have a question about something that my statistics teacher said about the following problem. My question isn't even about the occurrence of Simpson's paradox in this situation. My question is simply ... 5answers 20k views ### Why does the variance of the Random walk increase? The random walk that is defined as Y_{t} = Y_{t-1} + e_t, where e_t is white noise. Denotes that the current position is the sum of the previous position + an unpredicted term. You can prove that ... 1answer 1k views ### What are the classical notations in statistics, linear algebra and machine learning? And what are the connections between these notations? When we read a book, understanding the notations plays a very important role of understanding the contents. Unfortunately, different communities have different notation conventions for the formulation ... 7answers 24k views ### Two dice rolls - same number in sequence I am currently studying Statistical Inference class on Coursera. In one of the assignments, the following question comes up. ... 2answers 50k views ### How to know if a data follows a Poisson Distribution in R? I am an undergrad student and I have a project for my probability class. Basically, I have a dataset about the hurricanes that impacted my country for a series of years. In my probability Book, (... 8answers 52k views ### Looking for a good and complete probability and statistics book I never had the opportunity to visit a stats course from a math faculty. I am looking for a probability theory and statistics book that is complete and self-sufficient. By complete I mean that it ... 3answers 6k views ### Functions of Independent Random Variables Is the claim that functions of independent random variables are themselves independent, true? I have seen that result often used implicitly in some proofs, for example in the proof of independence ... 3answers 21k views ### Interpreting plot of residuals vs. fitted values from Poisson regression I am trying to fit data with a GLM (poisson regression) in R. When I plotted the residuals vs the fitted values, the plot created multiple (almost linear with a slight concave curve) "lines". What ... 3answers 6k views ### Neyman-Pearson lemma I have read the Neyman–Pearson lemma from the book Introduction to the Theory of Statistics by Mood, Graybill and Boes. But I have not understood the lemma. Can anyone please explain the lemma to ... 3answers 31k views ### Why is nls() giving me “singular gradient matrix at initial parameter estimates” errors? I have some basic data on emission reductions and cost per car: ... 4answers 25k views ### How to test if my distribution is multimodal? When I plot a histogram of my data, it has two peaks: Does that mean a potential multi-modal distribution? I ran the dip.test in R (... 4answers 635 views ### What is the intuition behind the independence of X_2-X_1 and X_1+X_2, X_i \sim N(0,1)? I was hoping someone could propose an argument explaining why the random variables Y_1=X_2-X_1 and Y_2=X_1+X_2, X_i having the standard normal distribution, are statistically independent. The ... 9answers 2k views ### Reference Request: Generalized Linear Models I am looking for an introductory to intermediate level book on Generalized Linear Models. Ideally, in addition to the theory behind the models, I would want it to include applications and examples in ... 2answers 1k views ### Advantages of the Exponential Family: why should we study it and use it? So here I am studying inference. I would like that someone could enumerate the advantages of the exponential family. By exponential family, I mean the distributions which are given as \begin{align*} f(... 2answers 411 views ### Suppose Y_1, \dots, Y_n \overset{\text{iid}}{\sim} \text{Exp}(1). Show \sum_{i=1}^{n}(Y_i - Y_{(1)}) \sim \text{Gamma}(n-1, 1) What is the easiest way to see that the following statement is true? Suppose Y_1, \dots, Y_n \overset{\text{iid}}{\sim} \text{Exp}(1). Show \sum_{i=1}^{n}(Y_i - Y_{(1)}) \sim \text{Gamma}(n-1, ... 1answer 13k views ### Difference between Hidden Markov models and Particle Filter (and Kalman Filter) Here is my old question I would like to ask if someone knows the difference (if there is any difference) between Hidden Markov models (HMM) and Particle Filter (PF), and as a consequence Kalman ... 4answers 3k views ### Can anyone clarify the concept of a “sum of random variables” In my probability class the terms "sums of random variables" is constantly used. However, I'm stuck on what exactly that means? Are we talking about the sum of a bunch of realizations from a random ... 3answers 1k views ### Why are “time series” called such? Why are “time series” called such? Series means sum of a sequence. Why is it time Series, not time sequence? Is time the independent variable? 1answer 13k views ### A proof for the stationarity of an AR(2) Consider a mean-centred AR(2) processX_t=\phi_1X_{t-1}+\phi_2X_{t-2}+\epsilon_t$$where \epsilon_t is the standard white noise process. Just for sake of simplicity let me call \phi_1=b and \... 1answer 7k views ### Proof of LOOCV formula From An Introduction to Statistical Learning by James et al., the leave-one-out cross-validation (LOOCV) estimate is defined by$$\text{CV}_{(n)} = \dfrac{1}{n}\sum\limits_{i=1}^{n}\text{MSE}_i$$... 1answer 1k views ### Quiz: Tell the classifier by its decision boundary Given are the 6 decision boundaries below. Decision boundaries is violett lines. Dots and crosses are two different data sets. We have to decide which one is a: Linear SVM Kernelized SVM (Polynomial ... 2answers 6k views ### Hidden Markov Model vs Markov Transition Model vs State-Space Model…? For my master's thesis, I am working on developing a statistical model for the transitions between different states, defined by serological status. For now, I won't give too many details into this ... 1answer 503 views ### Second moment method, Brownian motion? Let B_t be a standard Brownian motion. Let E_{j, n} denote the event$$\left\{B_t = 0 \text{ for some }{{j-1}\over{2^n}} \le t \le {j\over{2^n}}\right\},$$and let$$K_n = \sum_{j = 2^n + 1}^{2^{2n}} ... 1answer 7k views ### Question on how to normalize regression coefficient Not sure if normalize is the correct word to use here, but I will try my best to illustrate what I am trying to ask. The estimator used here is least squares. Suppose you havey=\beta_0+\beta_1x_1$, ... 8answers 28k views ### How is interpolation related to the concept of regression? Explain briefly What is meant by interpolation.How is it related to the concept of regression? interpolation is art of reading between the lines of a table and in elementary mathematics the term ... 1answer 4k views ### Construction of Dirichlet distribution with Gamma distribution Let$X_1,\dots,X_{k+1}$be mutually independent random variables, each having a gamma distribution with parameters$\alpha_i,i=1,2,\dots,k+1$show that$Y_i=\frac{X_i}{X_1+\cdots+X_{k+1}},i=1,\dots,k$,... 3answers 1k views ### Why do we need Bootstrapping? I'm currently reading Larry Wasserman's "All of Statistics" and puzzled by something he wrote in the chapter about estimating statistical functions of nonparametric models. He wrote "Sometimes we ... 4answers 2k views ### Expected value of sample median given the sample mean Let$Y$denote the median and let$\bar{X}$denote the mean, of a random sample of size$n=2k+1$from a distribution that is$N(\mu,\sigma^2)$. How can I compute$E(Y|\bar{X}=\bar{x})$? Intuitively, ... 2answers 107k views ### How do I calculate the variance of the OLS estimator$\beta_0$, conditional on$x_1, \ldots , x_n\$?

I know that $$\hat{\beta_0}=\bar{y}-\hat{\beta_1}\bar{x}$$ and this is how far I got when I calculated the variance: \begin{align*} Var(\hat{\beta_0}) &= Var(\bar{y} - \hat{\beta_1}\bar{x}) \\ &...
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### Probability theory books for self-study

Are there any good books that explain important concepts of probability theory like probability distribution functions and cumulative distribution functions? Please, avoid referring books like "...