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

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2
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1answer
36 views

Linear Regression with Dummy Predictor

Say there are two groups, each with n=500, with y=weight in pounds. The sample mean and sample standard deviation of weight are given: Exercise(X=1): Mean=170, SD=20 Non-Exercise(X=0): ...
2
votes
3answers
56 views

Beyond the basics: intermediate medical statistics textbooks suggestions

I am a soon-to-be physician. During my studies I have taken a class in biostatistics. I own Martin Bland's "An introduction to medical statistics", which was a required textbooks at the time, and ...
1
vote
0answers
27 views

Bias in lagged dependent variable [duplicate]

$$ y_t = θy_{t−1} + u_t \\ t = 1,...,T; $$ I need to derive a formula for $y_t$ and show that $$ E\left[\frac{\Sigma y_{t-1}u_t}{ \Sigma(y_{t-1})^2}\right] \neq 0 $$
2
votes
1answer
32 views

Unbiased estimator for $P(X_1=1)$

If $ X_1, ... ,X_n$ are IID binomial with parameters $ n$ and $p, $ find an unbiased estimator for $$G(p)=P(X_1=1)=np(1-p)^{n-1}\, .$$ I need to find this estimator so I can apply Lehmann-Scheffé ...
3
votes
1answer
29 views

Use law of total variance to find unconditional variance of overdispersed Poisson?

First, I need to prove that the distribution of a RV X, where X|lambda ~ Pois(lambda), and lambda ~ gamma(a, B), is a negative binomial. I know that it is, but why negative binomial instead of another ...
6
votes
1answer
52 views

Good papers with reproducible analysis requiring only the basics

I'm looking for papers or other examples of research where the statistical analysis done would be within the grasp of someone who has done an introductory stats course. Ideally the datasets would also ...
2
votes
0answers
20 views
+50

Conceptual questions on state and parameter estimation

Parameter estimation of nonlinear systems unscented kalman filter ( paper and many others are categorized under semi-blind identification technique because the Authors say that the dynamics of the ...
2
votes
1answer
40 views

whether Y(employees injured) variation is due to X1(job function) or X2(population)

Here is the actual question- There are 1000 employees in a firm, and the firm has four departments namely D1, D2, D3 and D4 with 100, 200, 300, 400 employees respectively. Now, each employee is ...
6
votes
1answer
104 views

Derivative of order statistics

--For further background into the question, one can refer to equations 2.3 and 2.6 (page 1275 of [0])-- Define: $$g_G(x)=\mbox{med}_Y|x-Y|$$ where $X$ and $Y$ are independent stochastic variables ...
4
votes
0answers
106 views

HPD interval for the mean

Suppose we have iid observation with the following model $ Y_t \sim \mathcal{N}(\mu,1/\mu) , t=1,2,..T$ The question is " Assuming a flat prior on $(0 ,\infty )$ find a 95% HPD interval for $\mu"$ ...
13
votes
4answers
219 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 ...
0
votes
0answers
25 views

Identify the stationary time series

Identify the stationary time series for which $$ \gamma(h) =(-1)^{|h|}+\cos \left(\frac{\pi}{4}h\right)$$ is ACVF. This is a homework problem. Stuck at first level. Please give some hints. Thanks in ...
0
votes
0answers
36 views

Combinatorics: picking 4 numbers such that sum of 2 is equal to sum of other 2

Bus tickets in certain city contains four numbers u,v,w,x. Each of these numbers is equally likely to be any of the 10 digits 0,1,2....,9 and four numbers are chosen independently. A bus rider is said ...
0
votes
1answer
21 views

Getting cointegration vectors using Johansen method

I'm trying to understand better Johansen method so I developed an example 3.1 given by the book Likelihood-Based-Inference-Cointegrated-Autoregressive-Econometrics where we have three processes: ...
1
vote
1answer
35 views

Probability of 4 people placed in 3 rooms

A family consisting of four persons—A, B, C, and D—belongs to a medical clinic that always has a doctor at each of stations 1, 2, and 3. During a certain week, each member of the family visits the ...
2
votes
0answers
20 views

How to nest hierarchical data variances in R

Apologies ahead of time for not having an exact data set as this is more of theoretical question that I stumbled across while working on mixed effects models. Suppose I have the following data ...
3
votes
1answer
43 views

Ancillary statistic: $X_i \sim N(\theta, \theta^2)$

Let $X_1, X_2, ... , X_n$ i.i.d random variables with probability density function $N(\theta, \theta^2)$. Show that $$T(X) = \frac{X_{(1)}-X_{(n)}}{X_{(2)}-X_{(n)}}$$ is ancillary to $ \theta$. My ...
2
votes
0answers
72 views

How many eligible bachelors in a city?

This is a very simple question posed to me by a friend of mine. I know it's a statistical analysis problem, but I suck at math. Given the total population of $x$ within a metropolitan area, what ...
1
vote
0answers
42 views

Should I use independent samples t-test?

I need to analyse if there's a difference between poor and rich European countries (using a GDP per capita index variable) and look if it has an effect on the variable environment. The GDP per capita ...
0
votes
0answers
10 views

Express Multinomial as vector sum of bernoulli trials?

So we know we can think of the binomial as a sum of iid bernoulli. Can we similarly express the multinomial as a vector sum of dependant bernoulli's and get the asymptotic distribution that way? I ...
2
votes
0answers
25 views

Sample probability for binomial distribution

$X\sim B(40, 0.3), \bar X$ is the sample mean, and $n$ is number of observations. I need help in finding $P(\bar X\ge13)$ for a sample of $49$. I have tried the following, please guide. $\mu=40 ...
2
votes
1answer
37 views

Show that a statistic is ancillary

Let $X_{i} \sim U(0, \theta) $ and $X=(X_1,\dots,X_n)$. Show that $$ \frac{X_{(1)}}{X_{(n)}}$$ Is ancillary for theta I coulxnt find a way of doing it that looks convenient. Any idea? P.s: ...
5
votes
1answer
71 views

Exponential Family: Observed vs. Expected Sufficient Statistics

My question arises from reading reading Minka's "Estimating a Dirichlet Distribution", which states the following without proof in the context of deriving a maximum-likelihood estimator for a ...
0
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0answers
61 views

GLM, Regression analysis, or other

I need to resolve a question with the use of SPSS, but don't really know what model to use. The question talks about the environment (scale variable (from not at all concerned - very concerned)), I ...
0
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0answers
32 views

$R^2$ equal square of sample correlation [duplicate]

I?m having a hard time proving that $R^2$ is equal to the square of the sample correlation between $Y$ and $\hat{Y}$. Every book I search tells me that's very easy, like verbeek. They just state that ...
2
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1answer
42 views

Rejection-Sampling of Exponential Distribution

Consider the following question. Consider the generation of random numbers following an exponential distribution with some known mean. Give three reasons why the rejection-acceptance method would ...
1
vote
3answers
119 views

ROC graph shape

Could you explain to me how the shape of a ROC curve is determined? From the following illustration, it seems that for every time the actual class (C) is positive, it goes up and when it's negative, ...
1
vote
0answers
25 views

How to find the variance for a mean response in a multiple linear regression model

The question is the following: Our regression model can be written as $y_i = \beta^Tx_i + \epsilon_i, 1 \leq i \leq n$. Find the $100(1- \alpha)\%$ confidence interval for the mean response ...
2
votes
2answers
46 views

Derivation of Regularized Linear Regression Cost Function per Coursera Machine Learning Course

I took Andrew Ng's course "Machine Learning" via Coursera a few months back, not paying attention to most of the math/derivations and instead focusing on implementation and practicality. Since then I ...
0
votes
2answers
37 views

Evaluating predictive models

I am looking for ways of evaluating the performance/success of predictive (classification) models for economic purposes. I know of: Direct accuracy percentage AUC score Net profit Rate of return ...
1
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0answers
22 views

Document classification problem

Assume we have $L$ labelled documents, and $U$ unlabeled ones, where all the documents from class $k$ were generated from a multinomial or Naive Bayes distribution with parameter $\theta_k$, and ...
1
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0answers
57 views

Effective Sample Size for posterior

I am trying to implement unsuccessfully a function in matlab, to compute the effective sample size after a MCMC chain, with a posterior with 3 coefficients. Source: Sims MCMC $ VAR(1) / Y_t=\mu ...
1
vote
2answers
108 views

Multivariate Bayesian formula

I got there example graphs bishop's PRML (8.2.1) 1. a <- c -> b $$ p(a,b,c) = p(a|c)p(b|c)p(c) --(1)\\ p(a,b) = \sum_c p(a|c)p(b|c)p(c) --(2) $$ Q1: Can I use a new graph to represent the ...
0
votes
1answer
28 views

Rank of a matrix in regression hypothesis test?

In going over some example problems from class notes, I came across the following problem: "Suppose we have a regression model $y=\beta_0+\beta_1x_1+\beta_2x_2+\beta_3x_4+\beta_4x_4+\epsilon$. We ...
0
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0answers
39 views

Large regression models and multivariate model

Large Regression models says that a regression model is large if the signal dimension $p$ is greater than number of observations $n$. In AR(2) model $y_t = a1y_{t-1} + a2y_{t-2}$ the parameter is a ...
0
votes
2answers
19 views

What is signal dimension

Estimating Unknown Sparsity in Compressed Sensing is a paper about sparse signal. I am just learning the concepts. In the first paragraph, it says that when the number of observation data samples $n$ ...
4
votes
1answer
60 views

Sample Mean of AR(1) model

Consider the AR(1) model with iid innovations with finite mean and variance. Also, let $X_0 = 0$. \begin{align} X_t = \phi X_{t-1} + \epsilon_t \end{align} The goal is to derive the asymptotic ...
0
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0answers
31 views

Let F be a distribution function. Prove that X is a RV

Let $F$ be a distribution function on $(\Omega,\, \mathfrak{F},\, P)=\left((0,1),\ \mathfrak{B}(0,1),\ \lambda\right)$ where $\lambda$ denotes Lebesgue measure. Define $X:\Omega \to \mathbb{R}$ by ...
2
votes
1answer
23 views

How do we perform a two-tailed z-test when we *do* know the population mean of the intervention sample?

I am in the process of working through the Udacity course Intro to Inferential Statistics. In Lesson 9: Hypothesis Testing, the following example is given. Say that we record survey data from all ...
1
vote
1answer
67 views

Support Vector Machine Question

I need help with the following problem. I provided my current (partial) solution, and I hope someone can correct me and/or give me suggestions as to how I should solve the parts that I've left out. ...
0
votes
0answers
28 views

Web Videos that can provide me with a better understanding of statistical concepts

I have an exam coming up and I would like to know are there youtube videos/playlist or any videos online that can explain the following concepts below in a simple manner. The concepts are: ...
2
votes
0answers
31 views

Haar prior for von Mises distribution

Ok, Let me tell you that this is the very first time that I have no idea with the question below. I can not find a solution or anything that will lead me to it. I say this to prevent comments "what ...
0
votes
0answers
26 views

Testing association between exposure and disease

In a particular example from the book Epidemiologic Research by Kleinbaum [example 15.1], I have three problems. Consider the data in table 01. These data pertain to a follow-up study concerning the ...
3
votes
1answer
93 views

Proof/Derivation of Residual Sum of Squares (Based on Introduction to Statistical Learning)

On page 19 of the textbook Introduction to Statistical Learning (by James, Witten, Hastie and Tibshirani--it is freely downloadable on the web, and very good), the following is stated: Consider a ...
1
vote
1answer
25 views

Out-of-sample vs. test set

Someone asked me if I did out-of-time testing (which I assume is just out-of-sample testing but with a timeline element). But if I have a test set, is that not essentially the same as out-of-sample ...
0
votes
0answers
8 views

Intuition related to standard deviation as threshold

I have a set of input output training data, few samples are Input output [1 0 0 0 0] [1 0 1 0 0] [1 1 0 0 1] [1 1 0 0 0] [1 0 1 1 0] [1 1 0 1 0] and so on. I ...
1
vote
1answer
33 views

Trying to figure out a formula and answer to probability question

If I go to a certain establishment 12 times in one year (let's just say once a month), and there's a 6.25% chance each time that I go in there that I would run into a person I know, what is the ...
1
vote
1answer
37 views

Is it necessary to plot histogram of dependent variable before running simple linear regression?

I was working on an assignment. The data set was really simple, only consisting one independent variable $y$ and dependent variable $x$. Someone suggested me plot a histogram of $y$ before running ...
0
votes
1answer
30 views

Conceptual question on optimization

What is the intuition and the physical meaning of the mathematical expression in convex optimization? When using optimization algorithms like particle swarm or genetic algorithm, do they have ...
4
votes
2answers
202 views

What are the properties for independence

For 2 variables to be independent of each other, should the correlation = 0 or mutual information = 0 or covariance = 0. I have seen different conditions and all these are really confusing.