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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0answers
9 views

DCCA clustering algorithm understanding

I try to understand the step 2.5 of the DCCA clustering algorithm pasted below. The original reference is here and the PowerPoint presentation is here. I have the following questions: Do we perform ...
0
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0answers
44 views

Statistics Test Question - Help needed! [on hold]

I am really terrible at statistics and basically don't even know where to begin on answering these. Any help would be appreciated. I've googled but there is some much info that it confuses me and I ...
1
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0answers
20 views

Allocation of design points in an experiment

I would like some hints with the following problem. Thanks for any help in advance. An experimenter wants to design an experiment for estimating the rate of change in a dependent variable Y as an ...
2
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1answer
23 views

How to compare two reviews, when one has more participants than the other

Hi I only did some basic stats at school but now I need to rank some data for a project, and I've run into this kind of scenario Game A: 1000 Reviews, 900 Positive and 100 Negative, so 90% positive. ...
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1answer
31 views

Conditional probability: how do i find the conditional probability given two parameters?

It is known that 25% of full time workers are also students. It is also known that 64% of the population work full-time and that 22% of the population are students. If a member of the population is ...
0
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1answer
31 views

How to introduce the error bars in text?

I want explictly to state in my written text that the error bars in the current plot and all of the following ones represent the 95% percent of the calculated mean. However, the metric changes in the ...
0
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1answer
19 views

Two-step Engle and Granger's procedure

If I want to check if there is cointegration between $X_t$ and $Y_t$ in the following model, is it enough to check p-value of Breusch-Godfrey test? The maintained hypothesis in this test is no ...
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0answers
16 views

the powerful LR-based solutions [on hold]

could you please tell me what are the powerful LR-based solutions (more powerful than linear regression as the baseline )? i want to perform them on my dataset in scikit
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0answers
20 views

Specifying integration level of time series

How to specify the level of integration of $X_t$ in such case? I am familiar with testing integration in R, cointegration strategies, but which method to use in such case? In brackets there are ...
2
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1answer
33 views

Can we estimate a missing Y value from a three factor experiment?

In preparation for an examination I'm looking at some old questions, and I could use a little help with figuring out what to do here: In a three-factor experiment the researchers lost the results ...
0
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1answer
28 views

Generate random number with normal distribution?

I encountered this question, where given it is a normal distribution, how do we go about it to generate a series of random numbers beside Monte Carlo? The clue given was using exponential function.
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0answers
37 views

Likelihood ratio test for two independent poisson distributions

Suppose that $X_1, X_2, ..., X_n \sim Pois(\mu)$ and $Y_1, Y_2, ..., Y_n \sim Pois(\theta)$. $X$ and $Y$ are independent. Derive the likelihood ratio test of $H_0: \theta = \mu$ versus $H_a: \theta ...
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0answers
37 views

Very Basic Question on Sampling [on hold]

For determining sample size , why is to focus on the unbiasedness and accuracy of the estimates ? In a simulation study , authors chose that sample size for which they get unbiased and accurate ...
1
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1answer
34 views

Projection Matrix Help

I'm having trouble understanding the following in a review textbook I'm using, particularly the long equality with inverses and transposes, and the subsequent conclusion regarding the rank and trace ...
2
votes
1answer
32 views

Standard Deviation of a sum of identical random variables

In a variation of the famous "how many chips are in a bag of Chips Ahoy" inference investigation, I am asked to make a confidence interval for the number of chips in 50 cookies (the amount in a bag) ...
1
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1answer
30 views

Probability homework question with specifity, sensitivity and prevalence

Assume that a diagnostic test for EPM (equine protozoal myoeloencephalitis) has a sensitivity of 89% and a specifity of 92%. The prevalence of the disease is 1% What is the probability that ...
1
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0answers
17 views

Restricted Maximum Likelihood Estimation for Linear Mixed Model

The maximum likelihood estimation procedure for linear mixed model is described in this link. It seems to me that something is wrong there. In their Restricted Maximum Likelihood section the first ...
2
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1answer
17 views

G-Means: Learning K in K Means

I am currently trying to understand the paper 'Learning K in K-Means' by Hamerly & Elkan (2004), which is the paper implementing G-Means, an automated way in selecting K for K-Means. There is one ...
0
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1answer
40 views

Why is multiple regression to be preferred over simple linear regression? [closed]

How does a multiple regression differ from a simple linear regression and why is the use of a multiple regression generally preferred over a simple linear regression?
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3answers
48 views

Learning material for regression analysis

I found a lecture notes from regression analysis but it was quite hard to learn from it. Those notes were aimed for students who had read just basics of statistics beforehand. I have a background in ...
0
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1answer
28 views

mean and standard deviation from rnorm(5, mean = 0, sd = 1)

I am trying to figure out a good way to find mean and standard deviation from sampling rnorm(5, mean = 0, sd = 1) 1,000 times. I thought about using a for loop and combining the result of rnorm as a ...
0
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1answer
24 views

Chi Square Statistic - Which variable should be defined as the dependent variable?

I am stuck with this very basic question which I need to answer using SPSS for the problem set pasted in cursive below. Any pointers in the right direction would be very much appreciated. Thank you. ...
0
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1answer
20 views

Addition Rule and Conditional Probabilities

My question comes from part of an assignment question that I am having difficulty understanding. I have a community of people, males and females split into three age categories (A, B, and C), so ...
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0answers
14 views

Some difference in notation in a project report

I am focusing on a specific model in my study. When I am writing my project paper, for describing the estimation procedure, can I describe it more generally with some difference in notation than my ...
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0answers
7 views

MLP with hidden layer units more than input layer

What is an acceptable scenario in multi-layer perceptron when the number of neurons in the hidden layer is more than input layer neurons. What changes to the cost function should be made for such a ...
0
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0answers
36 views

Restricted Maximum Likelihood Estimates of Multilevel Regression Model

A two-level regression model : $$Y_{ij} = \gamma_{00} + \gamma_{10}X_{ij} + \gamma_{01}Z_j + \gamma_{11}X_{ij}Z_j + u_{0j} + u_{1j}X_{ij} + e_{ij}$$ where $e_{ij}\sim N(0,\sigma^2_e)$ and , $$ ...
3
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2answers
60 views

How does the proportion of X > a compare to the proportion of Y > a?

I am completing CS109 Data Science class available online for free. I'm not quite sure what they are asking for. In general, if group A has larger values than group B on average, does this ...
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0answers
9 views

What is negative reconstruction error for Deep Belief Network?

I was studying Deep Belief Networks and started testing a small example. For the sake of these question consider the one at deeplearning tutorials Observation 1: I noticed that my reconstruction ...
5
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5answers
295 views

Standardizing a Standard normal Variable

If I standardize a standard normal random variate , will it be still standard normal ? That is, if $X\sim N(0,1)$ , then can I do $$X^*=\frac{x-\bar x}{sd(x)}$$ ? and will $X^*\sim N(0,1)$ ? In ...
2
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1answer
46 views

Calculating Overall Relative Bias

I am in some trouble to understand how is to calculate the overall relative bias. In this link, there are results of overall relative bias in "Parameter estimates" sub-section under "Results" ...
1
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0answers
31 views

Multilevel Model in Matrix Form

A two-level model, with one explanatory variable at the individual level $(X)$ and one explanatory variable at the group level $(Z)$ : ...
1
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1answer
43 views

Underestimated Coverage probability

Let $U0$ denotes intercept variance and $U1$ denotes slope variance. Given that the coverage rate for the intercept variance is $91$% $(U0)$ , and the coverage rate for the slope variance is $91.2$% ...
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1answer
20 views

An unbiased and consistent estimator [closed]

An unbiased and consistent estimator is said to be efficient if it has? a. minimum variance b. maximum variance c. both a and b d. none of these
0
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1answer
16 views

Posterior predictive distribution - dirichlet multinomial model

i saw this derivation of the posterior predictive distribution of a dirichlet multinomial model. Is one always allowed, or are there special circumstances, in which one can split the integral in ...
0
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1answer
19 views

Variance of Wilcoxon Rank-Sum Test (no ties)

$\newcommand{\E}[1]{\mathbb{E}\left[#1\right]} \newcommand{\r}[1]{r\left(#1\right)} \newcommand{\P}[1]{\mathbb{P}\left(#1\right)} \newcommand{\Var}[1]{\text{Var}\left[#1\right]}$ Given two sets of ...
1
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1answer
16 views

Wilcoxon Rank-Sum Test $H_1$ notation

This notation is from Nonparametric Statistical Inference, 5th ed., by Gibbons and Chakraborti. On p. 290, it states: Wilcoxon (1945) proposed a test where we accept the one-sided location ...
1
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0answers
21 views

Notation in two-level regression model

In this pdf, formula of two-level regression model is written as : $$Y_{ij}=\beta_{0j}+\beta_{1j}X_{ij}+e_{ij}$$ and in the pdf $e_{ij}$ is referred as individual level Residual . But I am not ...
4
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1answer
118 views

Statistical Significance Issue in Mixed Model

A multilevel model, with one explanatory variable at the individual level (X) and one explanatory variable at the group level (Z): ...
1
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1answer
47 views

Find confidence interval via pivotal quantity?

Suppose $X_1, X_2, ..., X_n$ is a random sample from a population with pdf $$f(x|\theta) = \dfrac{1}{2\theta}e^{-|x|/\theta},x\in \mathbb{R}$$ The pivotal quantity is $\frac{2}{\theta}\sum_{i=1}^n ...
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3answers
110 views

Central Limit Theorem for Normal Distribution of Negative Binomial

The question is: Explain why the negative binomial distribution will be approximately normal if the parameter k is large enough. What are the parameters of this normal approximation? I have ...
3
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0answers
30 views

Convergence Criteria in R's lmer

In this article , it is written in the Convergence and estimation bias para that : It is important to consider the minimum number of cases needed to ensure the model converges and that sample ...
-1
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1answer
37 views

Expectation of a random variable and the indicator random variable proof

I need to show that $E[T 1_A] = E[T|A]P(A)$. What I've got so far is $E[T1_A] = \int_{\Omega}T.1_A dP = \int_AT dP$. Now I know that $\int_AdP = P(A)$ however I'm lost as to how do I get the ...
6
votes
4answers
808 views

How to Prove that an Event Occurs Infinitely Often (Almost Surely)?

Exercise: There is a fair 6-sided die and a biased coin that has probability p > 0 of coming up heads on each toss. The die gets rolled infinitely often, and whenever you roll a 6, you then ...
4
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1answer
128 views

Maximum Likelihood Estimator for Negative Binomial Distribution

The question is the following: A random sample of n values is collected from a negative binomial distribution with parameter k = 3. Find the maximum likelihood estimator of the parameter ...
1
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1answer
22 views

Polya Urn - formulas

i am trying to understand Dirichlet processes and Polya's Urn, following the excellent article ...
0
votes
0answers
11 views

dirichlet process - formula explanatation

i am self-studying the Dirichlet process, from among others http://www.stat.ubc.ca/~bouchard/courses/stat547-sp2011/notes-part2.pdf, and struggling with the following basic question: I understand ...
1
vote
0answers
35 views

How to determine stationarity, mean and covariance?

I'm having some trouble with some questions for an assignment that I need to do. The question asks to determine whether or not a process is stationary and if it is, what is its mean and covariance. ...
1
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1answer
37 views

Is it possible to get a null hypothesis from this? If so, what would it be?

I have been working on this for the past 4 hours.. sadly. I need to get the null and alternative hypothesis from an article that states a p value, and I chose this one. ...
3
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2answers
40 views

The mean shifted outlier model

In the OLS setting, the mean shifted outlier model connects two behaviors: delete the $i^{th}$ observation adding a variable In other words, assume the original model, $\omega$ ,is: $$ Y = X\beta ...
0
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0answers
12 views

Argmax of transformed RV

Does performing a (nonlinear) transformation to a random variable, finding the value in that space that maximizes the PDF, and transforming that value back to the original space yield the same maximum ...