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/...
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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 ...
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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 ...
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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[\...
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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.
$$Y_t = \alpha_0 + \alpha_1 Y_{t-...
- 1,140
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With $X$ and $Y$ being two independent $\text{Bernoulli(1/3)}$ rvs, show whether $U = |Y-X|,~V = X+Y$ are independent or not
Let $X$ and $Y$ be two independent $\text{Bernoulli(1/3)}$ random variables. Define random variables $U$ and $V$ as $$U = |Y-X|, \hspace{5mm} V = X+Y$$ Are $U$ and $V$ independent?
I am new to the ...
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Methods for Detecting outliers in a time series
I have a question on detecting the outliers in a time series like PPI, CPI, inflation,...etc.)
Which method should I use? How can I precisely detect these outliers in a test or a method?
Please ...
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derivative of Logistic Regression with sigmoid func [duplicate]
I am having difficulty figuring out, why I get different answer from the professor. we are tasked with finding the deriative of the logistic regression cost function with the sigmoid function:
$$L(w│D)...
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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│...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
