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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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32 views

Determining whether a model with random walk errors is stationary

If we have a model like an AR(1) except the errors are a random walk (i.e. not iid), then is the model itself stationary? So the model is: $$ x_t=kx_{t-1}+\epsilon_t $$ where $k$ is constant and $0<...
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1answer
113 views
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0answers
18 views

Backpropagation formula for simple ANN

I'm trying to solve an exercise. I'm asked to train a 2-layer neural network, given a small dataset. Below is a picture I drew to understand the architecture and derive the formula for backpropagation....
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0answers
25 views

Higher Variance due to Overfitting

This is a homework question. Consider the following two regression models $$\mathbf y=\mathbf X_1\mathbf {\beta_1} + \mathbf {\varepsilon}$$ $$\mathbf y=\mathbf X_1\mathbf {\beta_1} + \mathbf X_2\...
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1answer
28 views
2
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0answers
34 views

Time Series Prediction Model for Home Prices

I am building a time series model to predict the zillow home prices for march 2019.I have data for each zip code from the year 1993 - 2018 and i have prices for every month.I was trying to use ARIIMA ...
1
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1answer
28 views

Number of throws likely to have occurred the most times to get a 6 [closed]

This question has me stumped and I've been trying to figure out how to answer it for a while now - was hoping someone here could share some insight! 'The probability of getting a 6 on any throw of a ...
1
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0answers
19 views

Explain why $df(S_{xx}) = 2$ [duplicate]

Consider $X = \{x_1, x_2, x_3\}$. Then $\bar{x} = \frac{1}{3} (x_1 + x_2 + x_3)$ with degrees of freedom, $df(\bar{x}) = n = 3$. Now consider the total variation in $x$: $$S_{xx} = (x_1 - \bar{x})^2 ...
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1answer
49 views

missing value problem [closed]

I have survival data. However,there are missing values in both categorical and numerical data list. That's, in each column, approximately more than two values are missing. Now, I want to obtain ...
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2answers
26 views

Knowing mean, standard deviation and population size, calculate guaranteed number of elements in range

Knowing the true mean, the true standard deviation and the number of elements of a given population (without knowing the actual values), is it possible to calculate the guaranteed number of elements ...
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0answers
17 views

Trying to find a posterior distribution from non-normal prior and squared loss function

I've been reading an economics paper regarding rational inattention by Sims (link: https://www.sciencedirect.com/science/article/abs/pii/S0304393203000291) and have been trying to implement his ...
1
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1answer
72 views

how to find correlation coefficient when X and Y follows Poisson Distribution?

A bridge is examined for corrosion. It is believed that the corrosion on left side exist is poisson distributed with mean 3 and corrosion on right side is poisson distributed with mean 1.5+0.5X where ...
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0answers
22 views

Interval estimation - sample problem

A random sample of 81 credit sales in a department store showed an average sale of $75.00$. From past data, it is known that the standard deviation of the population is $27.00$. ...
0
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1answer
28 views

How to find the minimum value of c? [closed]

In this book, the answer is not clear. What will be the method to find the value of c?
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0answers
43 views

Measurement error on dependent variable

Could someone help me on the following subject? Calculate the expectation and variance of 'e' knowing that : y* = xB + e* y = xB + e with y = y* + n I have to start from: B^ = B + (X'X)^-1 X'...
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1answer
95 views

Same maximum entropy and measures [closed]

As the author Christian Robert asks about reference measures that are absolutely continuous to one another, and from what I can gather this just means they have the same null set? But would that not ...
1
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1answer
36 views

Interval Estimation questions

I am completely lost at how to do this. My instructor talks so fast i can barely understand her so figuring this out was struggling. This website is my last choice and i hope others can help me out so ...
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2answers
665 views

If I roll a die 25 times what is the probability that the mean outcome is greater than 4?

Consider a problem: You take a fair die to a party and announce that you will roll it 25 times. You will record each outcome and at the end average the 25 outcomes together to get their ...
1
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2answers
131 views

Probability of the sum of cards?

The problem is basically as follows There are four cards with points [1,2,3,4], every time I draw one card randomly and then put it back to the deck. As I keep ...
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0answers
46 views

Generalized Least Squares

A simple linear regression model satisfies all Gauss-Markov conditions except for white noise, is known I am wondering how to find the matrix Ω = Euu′ for this model. Any suggestions are welcome. ...
1
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0answers
61 views

Normal max entropy

In the following link, at the bottom of the page. https://www.dsprelated.com/freebooks/sasp/Maximum_Entropy_Property_Gaussian.html The Gaussian maximum entropy is derived. I have a question about ...
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0answers
25 views

Marginal Log Likelihood of Count Data to Simplify MLE

My question concerns the calculation of a marginal likelihood given some priors for my underlying exponential mixture distribution. Background My data is the (orderd) set of integers $\{N_\ell\}$. ...
1
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0answers
19 views

Beginner in R programming [closed]

I face a problem when dealing with the question on the image and the value given was $n=7$, $m=11$, $t=18.72$. The detail of the question is on the picture attached. Thanks a lot
3
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1answer
42 views

Deriving Bayes risk for squared error loss function

I think I must be doing something wrong here because my derived Bayes Risk is incredibly long and cumbersome... Let $X|p \sim Bin(n,p)$ and $p \sim Beta(a,b)$. Then $p|X \sim Beta(a+x,b+n-x)$ and ...
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0answers
23 views

Expected Value of Cross Validation approximates Predictive Square Error

In the context of Smoothing Splines, Im trying to show that the expected value of the cross-validation can approximate the predictive square error. More specifically, I want to show that $$E[(y_i - \...
3
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1answer
179 views

Some Questions about reference measures and maximum entropy priors (from The Bayesian Choice)

I am relatively new to statistics and Bayesian theory but I am trying to understand it by working through a few books. There are some things I am confused about. ( As I believe my analysis and such is ...
2
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0answers
57 views

How to prove variance of Spearman's Rho

How does one derive the variance of Spearman's Rho? The result is $\frac{1}{n-1}$. I simplified the formula into the last line shown in the picture but how does one proceed from then? ($R(X_i)$ and $R(...
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1answer
434 views

If both prior and likelihood are Gaussian what can we say about the posterior? [closed]

If X is a random variable that has Gaussian prior and Gaussian likelihood. What can be inferred about the posterior? As posterior is proporional to prior*likelihood which are Gaussians, the posterior ...
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1answer
26 views

How to quickly apply an algorithm with enough understanding

Let me take an explicit example.(the answer should be universal for any algorithm) I want to group cities with similar average income together I want to use dbscan to do this.(R/python/javascript/...
3
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1answer
47 views

Finding MLE of $p$ where $X_1\sim\text{Bernoulli}(p)$ and $X_2\sim\text{Bernoulli}(3p)$

Let $X_1\sim\text{Bernoulli}(p)$ and $X_2\sim\text{Bernoulli}(3p)$ be independent Bernoulli random variables where $p\in[0,1/3]$. Derive the MLE of $p$. We have that $$L(p\mid \vec{x})=p^{x_1}(1-...
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0answers
79 views

Finding MLE and MSE of $\theta$ where $f_X(x\mid\theta)=\theta x^{−2} I_{x\geq\theta}(x)$

Consider i.i.d random variables $X_1$, $X_2$, . . . , $X_n$ having pdf $$f_X(x\mid\theta) = \begin{cases} \theta x^{−2} & x\geq\theta \\ 0 & x\lt\theta \end{cases}$$ where $\theta \...
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2answers
78 views

A book on solved Probability problems

I was looking for a book to practice Probability problems with solutions to get intuition of Probability and I see Schaum's series is kind of most respected on solved problems. But I wonder which on ...
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0answers
19 views

Example of an non-symmetrical Wilcoxon Rank Sum test statistic value

I have been given a homework in a subject called "Non-Parametric Statistics" and I'm a bit stuck with it. I would be very thankful if you could give me any advice or help, which would lead to a ...
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0answers
38 views

Notation confusion in likelihood question [closed]

Asking this question based on an equation I found in my homework: "Given a training set, $\mathcal{S}$, find an expression for the likelihood, $p_\mathcal{D}(\mathcal{S}\mid w)=\mathbb{P}[\mathcal{S}...
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2answers
48 views

Good vs Bad Trial in Probability

I am watching this video on Probability, around the end there is a problem to be solved: I can't understand how a summation which extends from 1 to infinity can be equal to $\frac{1}{1-4/6}$
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0answers
43 views

Using Leibniz integral rule when minimizing Expected Absolute Loss [duplicate]

Consider choosing $\theta^*$ that minimizes the expected absolute loss: \begin{align} \tag{1} \int_{\Theta}|\theta-\theta^*|\pi(\theta|\mathbf{x})d\theta= \int_{-\infty}^{\theta^*}(\theta^*-\theta)\...
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1answer
26 views

Drawing Gloves from a drawer — Finding Probability

Probability of drawing white glove on first attempt P(B1) = 1/5. For finding white glove at 2nd attempt means fist one was not white and hence was discarded and now 4 are left. Therefore probability ...
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0answers
34 views

Z Score and Percentile

Suppose Brandon's age is converted to a z-score, is 1.50. The distribution of age is very closely approximated by a normal distribution. What is Brandon's percentile compared to other people in the ...
1
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1answer
95 views

Likelihood - estimation on parameters

I make confusions in the using of (1) Maximum Likelihood to find (approximately) the original signal knowing the data observed and (2)the using of Maximum Likelihood to find estimations of parameters ...
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0answers
6 views

Low t Values Multicollinearity

I'm studying a model which has large datasets of empirical data and analysis available. In the particular dataset that I consideted (with a few a priori expectations) I tried out a simple linear ...
0
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1answer
61 views

P-value from sum of bootstrap vs ttest are different [closed]

I am learning about bootstrapping and I am calculating the correlation between x and y, between two independent groups with each size n=8 and n=24, respectively. Their distributions are non-Gaussian ...
4
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2answers
113 views

Is this actually an example of selection bias?

In Lesson 3, Chapter 3 of Miguel Hernán's edX course on causal diagrams, he presents this DAG: It represents a study on the effect of hormone therapy on lung cancer (whether hormone therapy causes ...
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1answer
40 views

How is to maximize a function $f(x,y)$ for values of $y$?

Maximum Likelihood Method: Likelihood function asks what value of parameter, $\theta$, makes the data set most probable. Let the distribution is $$f(x;p)=\binom{3}{x}p^x(1-p)^{n-x},\quad x=0,1,2,3.$...
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0answers
62 views

Finding the pdf of the posterior distribution and the corresponding Bayes Estimate of $\theta$

Suppose that we observe i.i.d random variables $X_1, X_2, \ldots , X_n$ having pmf $$f_{X}(x\mid\theta) =\theta(1−\theta)^{x−1}I_{\{1,2,3,\ldots\}}(x)$$ where $\theta\in(0,1)$. Consider the ...
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0answers
27 views

Zero Intercept Model Interpretation [duplicate]

I am supposed to run a regression of Medical Expenditure on several explanatory variables like income, no of illnesses, age and also some dummy variables like gender differentiating dummy, dummy for ...
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0answers
13 views

Estimability of 2way ANOVA

Consider the model, yijk = µ + Ai + Bij + eijk ; i, j, k= 1,...,5 I tried testing for estimability by trying to reducing the coefficient matrix. But the matrix is really big that it's getting ...
2
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1answer
41 views

How to prove two models beta variances' relationship

I have two models: 1. $y=bx$ ($a=0$) 2. $y=\alpha+\beta x$. I have to calculate the variance of $b$ and then show that $\operatorname{var}(b)\leqslant \operatorname{var}(\beta)$. The estimate of b is ...
2
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1answer
59 views

Deriving marginal pdf from joint pdf

Problem setup: $X \sim \Gamma(\alpha,\beta)$, $f_{Y|X}(y|x)= \tau xy^{\tau-1}e^{-xy^\tau}$ for $y>0$ and $f_{Y|X}(y|x)=0$ for $y\leq0$, where $\tau\geq1$ is a constant. I am asked to derive the ...
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1answer
34 views

Find the mean, variance and others of a “RV = Gaussian RV + Discrete RV + ”?

Since I am solving a preparatory examen to study, it is not clear to me how to approach the question because I don't know what is the specific topic to study rigorously in order to know how to do it. ...
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0answers
44 views

Bibliography recommendation for PhD in Statistics

I have a graduate degree in Economics, and I've always been fascinated by the data analysis and the statistics in general, that's why I decided that I want to pursue a PhD in Statistics. But I am ...