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Questions tagged [self-study]

A routine exercise designed to test one's knowledge; often 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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Have I constructed the Neyman-orthogonal score correctly?

I am trying to construct a Neyman-orthogonal score for the Poisson m-estimator, using section 2.2 of Chernozhukov et al. (2018). Have I done this correctly? If so, can somebody please help me show/...
Nick Green's user avatar
1 vote
1 answer
46 views

Rao-Blackwell Theorem

I'm having problems on understanding the Rao-Blackwell theorem. In particular I don't understand why the resulting estimator is the one with minimum variance between ALL unbiased estimators of the ...
Onofrio Olivieri's user avatar
2 votes
0 answers
44 views

No Existence of Efficient estimator

I need to prove that given $(X_1,...,X_n)$ from the density $$\frac{1}{\theta}x^{\frac{1}{\theta}-1}1_{(0,1)}$$ no efficient estimator exists for $g(\theta)$=$\frac{1}{{\theta}+1}$. I have shown that ...
Onofrio Olivieri's user avatar
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0 answers
20 views

Equivalence of $\sum_{i=1}^3 \sum_{j=1}^3 k_j Cov[y_i, x_j]$ and $\sum_{i=1}^3 k_j\sum_{j=1}^3 Cov[y_i, x_j]$ [duplicate]

We define two correlated random variables $Y_i$ and $X_j$ and say we have this sample, $Y_i:\{y_1,y_2,y_3\}$ and $X_j:\{x_1,x_2,x_3\}$ for the convenience of illustration. I want to calculate $Cov[\...
Roger Jia's user avatar
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0 answers
9 views

Question on ARCH effect Test

I try to conduct ARCH effect test. I have a time series (Global price of Brent crude oil) which follows AR(3). First of all, I estimate AR(3) model for the Oil price. $$Y_t = \alpha_0 + \alpha_1 Y_{t-...
1190's user avatar
  • 1,140
2 votes
1 answer
280 views

With $X$ and $Y$ being two independent $\text{Bernoulli(1/3)}$ rvs, show whether $U = |Y-X|,~V = X+Y$ are independent or not

Let $X$ and $Y$ be two independent $\text{Bernoulli(1/3)}$ random variables. Define random variables $U$ and $V$ as $$U = |Y-X|, \hspace{5mm} V = X+Y$$ Are $U$ and $V$ independent? I am new to the ...
Samar's user avatar
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2 votes
2 answers
471 views

Methods for Detecting outliers in a time series

I have a question on detecting the outliers in a time series like PPI, CPI, inflation,...etc.) Which method should I use? How can I precisely detect these outliers in a test or a method? Please ...
0 votes
0 answers
17 views

derivative of Logistic Regression with sigmoid func [duplicate]

I am having difficulty figuring out, why I get different answer from the professor. we are tasked with finding the deriative of the logistic regression cost function with the sigmoid function: $$L(w│D)...
Ofek nourian's user avatar
2 votes
0 answers
49 views

derivative of Logistic Regression (sigmoid) [closed]

I am having difficulty figuring out, why I get different answer from the professor. we are tasked with finding the deriative of the logistic regression cost function with the sigmoid function: $$ L(w│...
Ofek nourian's user avatar
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0 answers
29 views

How to derive GEE from GLM?

I am now reading the lecture note from: https://dept.stat.lsa.umich.edu/~kshedden/Courses/Regression_Notes/gee.pdf Why do we have $V_{i}^{-1}(y_{i}-\mu_{i})$? I cannot link the last equation on page ...
doraemon's user avatar
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1 vote
0 answers
43 views

Probability of leaving with $20

You play a game with a coin. You may place a bet; if Heads is flipped then you receive your bet back plus the same in winnings. If Tails is flipped then you lose your bet. You have 20 dollars and you ...
Yuna's user avatar
  • 11
3 votes
1 answer
44 views

Rough answer for the maximum of absolute value of $n$ standard gaussians (Computer Age Statistical Inference Problem 1.3)

I am working through "Computer Age Statistical Inference" as a self-study and am stuck on the follow exercise (1.3): The details of equation 1.6 are unimportant for the exercise, so far as ...
naveace's user avatar
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3 votes
1 answer
98 views

Is it true that R(k+1, n+1) < R(k, n)?

Is the following statement correct or not: The probability of having at least k+1 successes in n+1 trials is less than the probability of having at least k successes in n trials. That is, is it true ...
user413516's user avatar
3 votes
1 answer
27 views

Question on decomposition plot (seasonality)

I cannot really understand the presence of seasonality by looking at the decomposition plots. Therefore, I attach two decomposition plots. Is there any seasonality in the series? First one is CPI ...
1190's user avatar
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2 votes
1 answer
62 views

UPDATED: Very unstable model and mostly insignificant variables in fixed effects regression model

I have been trying to create a regression model for my master thesis for the last week and I am stuck with the following issue. Currently seeking any help I can get, so greatful for any input you ...
DataScience-Student's user avatar
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0 answers
26 views

Is there an additive property for hypergeometric random variables?

I know that for binomial and negative binomial RVs there is an additive property where if $X_1\sim bin(a, p)$ and $X_2\sim bin(b, p)$ then $X_1+X2 \sim bin(a+b, p)$ if $Y_1\sim NB(c, p)$ and $Y_1\sim ...
BadAtMaff's user avatar
0 votes
0 answers
33 views

Exam P Sample Problems # 30

The question: A company establishes a fund of 120 from which it wants to pay an amount, C, to any of its 20 employees who achieve a high performance level during the coming year. Each employee has a ...
BadAtMaff's user avatar
2 votes
3 answers
158 views

Conditional probability, who's right?

i need help with a math problem. Me, and at least two teachers have all done it and gotten different results, so now I'm asking the wise people of the internet for help settling the debate. Here's the ...
Azrael's user avatar
  • 21
4 votes
1 answer
232 views

Exercise about Order statistics from uniform distribution

I'm trying to solve an exercise about order statistics. The exercise is the following: Let $U_{(1)}< \ldots <U_{(n)}$ be the order statistics from Uniform distribution U(0,1). Show that $(-\log[...
MLe's user avatar
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0 votes
0 answers
40 views

Likelihood function for data with random censoring

The following is from Klein and Moeschberger, p. 76. Let $(T,\delta)$ be a tuple with $T = \min(X,C_r)$ and $\delta = 0$ if the lifetime X is censored and $\delta = 1$ if it is not; $C_r$ denotes the ...
Montresor's user avatar
  • 101
0 votes
1 answer
66 views

How to solve this "easy" probability problem

I'm struggling on how can I solve the following problem. I tried with a lot of calculus without success, but i think that the way to solve is: $$P(\text{at least one failure})=1−P(\text{no failures in ...
Ga13's user avatar
  • 280
1 vote
1 answer
89 views

Understanding the Logistic regression formula

Logistic regression aims at transforming the linear regression formula and fitting the s curve or logistic function to a particular dataset in order to calculate the probability of a categorical ...
Amelia Nicodemus's user avatar
0 votes
0 answers
45 views

Sufficient Statistic for Truncated Normal

I am doing exercise 3.18 of "The Bayesian Choice": Give a sufficient statistic associated with a sample $x_1,...,x_n$ from a truncated normal distribution $$ f (x|\theta) \propto \exp(-(x ...
daniel's user avatar
  • 155
0 votes
0 answers
24 views

Computing Bayesian model averaged posteriors

The Bayesian model averaged posterior predictive distribution for new data $\tilde{y}$ given training data $y$, across a set of $M$ models $\mathcal{D} = \{D_{1}, ..., D_{M}\}$, is defined as: \begin{...
user_15's user avatar
  • 185
2 votes
1 answer
41 views

Bayes Theorem and Total Probability

I'm back for more help....I'm terrible with conditional probability. Here's a problem from an assignment in a stats course I'm taking: A U.S. Army Corps of Engineers (USACE) study focused on DDT ...
jerH's user avatar
  • 235
1 vote
1 answer
43 views

Unsure about assumptions of linear model with time series variables, spurious regression and periodic patterns

Background I'm learning about time series in context of linear regression. The goal of this question is to understand how seasonality of either X or Y can affect the model. Linear model assumptions $...
Brzoskwinia's user avatar
1 vote
1 answer
53 views

What is the distribution of the unbiased estimator of variance for normally distributed variables?

I must be making some mistake in my derivation of the distribution of the unbiased variance estimator for i.i.d. $X_{i} \sim \mathcal{N}\left(\mu, \sigma^{2}\right)$. We have $\bar{X} =\frac{1}{n}\sum\...
YEp d's user avatar
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1 vote
0 answers
22 views

What is the formula to compute the height of significance line on autocorrelation plot?

Autocorrelation of a time series can be plotted in R with use of acf function. For example: acf(ldeaths) # built-in series I ...
Brzoskwinia's user avatar
0 votes
1 answer
30 views

Gaps (misinterpreting perhaps) between chi square sig and Cramer’s v

I did chi square test for independence and Cramer’s V test. I’m having problems with interpret the results. I checked if there is a connection between gender and dropping out of school (in SPSS). My ...
Shir's user avatar
  • 3
2 votes
1 answer
47 views

MLE of $\beta$ and $\sigma^2$ in linear regression with Laplace errors

Say we have a linear regression model $$ y_i = x_i^T\beta + \sigma\varepsilon_i $$ for $i = 1, \dots, n$, and $\varepsilon_i$ is distributed according to a Laplace distribution $\mathcal{L}(0, 1)$ ...
timeinbaku's user avatar
0 votes
0 answers
39 views

Complete second-order model with 2 quantitative and 1 qualitative variables

I want to check if what I have for the equation for the second-order model relating y to 2 quantitative and 1 qualitative variables (3 levels) is correct: $\mathbb{E}(y)= \beta_0 + \beta_1x_1 + \...
DragonFruit's user avatar
0 votes
0 answers
61 views

Usage of Sufficient statistic for a Gamma distribution

I need some help to understand how to utilize sufficient statistic from a data. Suppose I observe some random process that produces $x\in X$, where all elements have a gamma distribution. As far as I ...
tessob's user avatar
  • 11
0 votes
0 answers
51 views

Find $E[Y]$ when $f(x,y) = \frac{x}{3}e^{-xy}$

Truth be told, I don't really have an issue with this problem in general, but in it's calculation. Let me explain. We need to find $E[Y]$ when $f(x,y) = \frac{x}{3}e^{-xy}$, $1<x<4$ and $y>0$...
Anweshan Goswami's user avatar
3 votes
2 answers
183 views

Long-run average cost for uniform distribution

The lifetime of a device is a continuous random variable having the continuous uniform distribution $\mathrm{Unif}(0,15)$. Suppose that under an age replacement strategy a planned replacement at age $...
waterr's user avatar
  • 41
0 votes
0 answers
21 views

Lasso Regression Problem [duplicate]

$\operatorname*{argmin}_\beta\{\|y-X\beta\|^2 + \lambda\|\beta\|_1$, where $X$ is orthonormal. $\beta \in \mathbb R^d$. $X = [x_1,\ldots,x_n]^T$ and $y=(y_1,\ldots,y_n)^T \in \mathbb R^n$. $X^TX=I_{d\...
Harry Lofi's user avatar
0 votes
0 answers
67 views

Posterior distribution of shape & rate parameter in Poisson-Gamma Mixture

Currently I'm struggling to handle the following question. Suppose $x_i,(i=1,2,\dots,n)$ follows Poisson distribution: $$p(x_i|\theta) = \frac{\theta^{x_i}e^{-\theta}}{x_i!}, \quad x_i\in\mathbb N,\...
jason 1's user avatar
  • 311
0 votes
1 answer
40 views

question about outliers in a 5 term data set

the question states that no data set with only 5 terms has an outlier, and I'm stumped you're given a set of 5 numbers in ascending order $$ x_1, x_2, x_3, x_4, x_5 $$ I started by finding the IQR, ...
Bongo 186's user avatar
5 votes
2 answers
288 views

Expected value of decreasing function of random variable versus expected value of random variable

Given two random variables $X_1$ and $X_2$ (same sample space $\mathcal{X}$) that $$\mathbb{E}[X_1]=\int_{\mathcal{X}}xf_1(x)dx > \mathbb{E}[X_2]=\int_{\mathcal{X}}x f_2(x)dx$$ Can we say that $\...
Rokai's user avatar
  • 51
2 votes
2 answers
82 views

How to find probability from $E[X^n]$?

It is given that $E[X^n] = \frac{2}{5}(-1)^n + \frac{2^{n+1}}{5}+\frac{1}{5}$, where $n=1,2,3,\ldots.$ I need to find $P(|X-\frac{1}{2}| > 1)$. What my approach is : I have opened the modulus ...
Anweshan Goswami's user avatar
1 vote
2 answers
47 views

Interpretation of incidence rate ratio

The incidence rate ratio (and 95% confidence interval) of rotavirus gastroenteritis for the vaccine group compared to the placebo group is $0.67 (0.55, 0.82)$. I want to know approximately how many ...
Happy Cretine's user avatar
3 votes
0 answers
89 views

Posterior Distribution using Jeffreys prior

I'm trying to show that if $X_1, \cdots, X_n \stackrel{iid}{\sim} N(\mu, \sigma^2)$ with unknown $\mu$, $\sigma$ and the prior $\pi(\mu, \sigma^2) \propto 1/\sigma^2$ then the posterior distribution ...
S10000's user avatar
  • 183
0 votes
1 answer
59 views

Hastie "statistical learning" 2.28. Least squares and covariance

In Hasties book "statistical learning", just above equation 2.28, it says that $\mathbf{X}^T\mathbf{X} \rightarrow NCov(X)$ (when $N$ is large and $E(X)=0$). Why is this true? $Cov(X)$ is ...
Science Guy's user avatar
0 votes
0 answers
25 views

PDF of difference of uniform distributions [duplicate]

Main questions are in bold but feel free to correct me if I'm wrong somewhere else. As far as possible, I need both intuition and formal explanation. Let $X \sim Uniform(a,b)$ and $Y \sim Uniform(c,d)$...
White1Hun's user avatar
1 vote
1 answer
43 views

FInding a complete and sufficient statistic

I am attempting to learn how to find a complete and sufficient statistic. So, I am working on this problem for class: Let $X_1, \cdot\cdot\cdot,X_n$ be a random sample from the pdf $f(x_i|u)=e^{-(x-\...
Harry Lofi's user avatar
1 vote
0 answers
41 views

Understanding Schoenfeld Residuals

I'm reading the original paper by Schoenfeld from 1982. It is very laconic. Few parts that I don't understand: Why can we substitute $\hat \beta - \beta$ with the Score, and why is the score equal to ...
Maverick Meerkat's user avatar
0 votes
0 answers
36 views

GLM link function, variance Function, and dispersion for linear regression

we were recently introduced in class to GLM's and I am still trying to wrap my head around link functions, variance functions and dispersion paramters. In particular we were asked re-write the linear ...
Harry Lofi's user avatar
2 votes
0 answers
49 views

What to do in Box-Jenkins framework when time series has deterministic trend and seasonality?

I'm self-studying time series and I'm puzzled by apparent lack of consistency between : the "classical" decomposition of time-series and the Box-Jenkins methodology. Concerning the ...
Johannes Konrad's user avatar
0 votes
0 answers
43 views

BIvariate Normal and Conditional Expectation

I am working on a problem where I must show that the conditional distribution of Y given X follows the distribution with mean and variance shown below. In the previous question, we were given that X ...
Harry Lofi's user avatar
1 vote
1 answer
43 views

F-distibution only depends on degrees of freedom

I am reading ISLP Chapter 3.2 on multiple linear regressions. They define the F-statistic as $S_1$, the variance of sample 1 from population 1, divided by $S_2$, the variance of sample 2 from ...
amineh's user avatar
  • 87
0 votes
0 answers
52 views

Two-proportion hypothesis test with variances unknown

"A group of test subjects are split into two groups. 1000 people are given a vaccine, and 15 of them get the disease. 800 people are given a placebo, and 60 of them get the disease. Test the ...
Forklift17's user avatar

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