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.
0
votes
0answers
22 views
ACF proof for ARMA(1,1) model
I need to derive a proof for the autocorrelation function (ACF) of a stationary, invertible ARMA(1,1) model, that shows that the ACF on the first lag depends on both the $\theta_1$ and $\phi_1$ ...
3
votes
0answers
63 views
Complete sufficient statistic
I've recently started studying statistical inference. I've been working through various problems and this one has me completely stumped.
Let $X_1,\dots,X_n$ be a random sample from a discrete ...
2
votes
2answers
60 views
Multiple bivariate normal distributions and conditional expectation
The problem I have is one that ideally seems to be suitable by considering it as a multivariate normal pdf problem however this way seems impossible.
Consider three Normal distributions
$X\sim ...
1
vote
1answer
39 views
Bivariate conditional probability confidence
I have two random variables following normal distributions,
$X\sim N(\mu_{x},\sigma_{x})$
and
$Y\sim N(\mu_{y},\sigma_{y})$
I know the covariance is $\operatorname{Cov}(X,Y) = c$.
And I believe ...
2
votes
2answers
98 views
Unbiased estimator of variance of binomial variable
$Y_{1...n}\sim \operatorname{Bin}(1,p)$, iid, and I need to find an unbiased estimator for $\theta=\operatorname{var}(y_i)$.
I did some calculations and I think that the answer is ...
2
votes
1answer
32 views
How to estimate the parameter of this time series?
The time series is governed by the equation $S(T)=S(0)e^{(\mu-\frac{\delta^2}{2})T+\delta(w(T)-w(0))}$, in which $w(t)$ is a standard Brownian motion. Now given the data $\{S(t)\}_{t=0}^{t=T}$ļ¼ how to ...
4
votes
2answers
91 views
Two normal distributions
I will mark this as homework, even though it's just general interest. The scenario is a little silly, because it's just a real world case for a theoretical problem I've been thinking about.
A man ...
1
vote
2answers
47 views
Understanding and interpreting consistency of OLS
Many econometrics textbooks (e.g. Wooldridge, "Econometric analysis...") simply write something similar to: "If the population model is $y = xB + u$ and (1) $\text{Cov}(X,U) = 0$; (2) $X'X$ is full ...
0
votes
0answers
43 views
Convergence of expression involving $\frac{\phi(t)}{1-\Phi(t)}$ [closed]
The expression is given by
$G(t) = \frac{1}{\frac{\phi(t)}{1-\Phi(t)} - t}\left(\frac{1}{\frac{\phi(t)}{1-\Phi(t)} - t} -t\right)$
$\phi(.)$ is the pdf of standard normal and $\Phi(.)$ the ...
-1
votes
0answers
31 views
find the Null hypothesis in R cmdr
As part of a study on the utilization of biomass power plants, the output average power was observed (in MW) at four Wednesdays and Sundays at 4 comparable installations. The table below shows the ...
1
vote
1answer
47 views
Weibull MLE: what is the method/algorithm used to perform the optimization?
Regarding fitting a Weibull two parameters probability density function (pdf), with the fitdistr from MASS package, in R:
1 - What is the iteration ...
0
votes
1answer
51 views
Find and plot cumulative distribution function
We toss a fair coin.
If a head appears then $X\sim N(0,1)$.
If a tail appears then $X=1$ with probability $1$.
Find the unconditional CDF of $X$ and plot it.
2
votes
0answers
44 views
How to model population growth?
Suppose you are given data about the population of a country from say 1800 to 2010. You are also given some explanatory variables regarding migrations to that country, inflation rate, and other ...
4
votes
1answer
64 views
Question about a marginal distribution
If I observe the following:
$X \sim N(\mu_x,\sigma^2_x)$
$Y|X=x \sim N(x,\sigma^2_y)$
My objective is to calculate the marginal distribution of $Y$.
(Since the variance term does not address some ...
2
votes
1answer
36 views
Can the items measure one underlying construct?
For an assignment I am asked to test whether different items (all dichotomous) can actually measure one concept. The items:
Please tell me whether or not you think it should be possible for a ...
2
votes
1answer
50 views
Statistics wording question
I am reading a statistical procedure trying to figure out and understand what's going on.
The statement says "Compute the posterior on $\mu$."
Does this mean compute $p(\mu)$? Does this mean ...
5
votes
1answer
50 views
Sampling distribution of regression coefficients
I previously learned about sampling distributions that gave results which were for the estimator, in terms of the unknown parameter. For example, for the sampling distributions of $\hat\beta_0$ and ...
3
votes
2answers
103 views
Covariance Matrices
I was wondering if anyone knows of any really productive ways to graph/map/plot/visualize covariance matrix data. I am currently using levelplot() in ...
0
votes
0answers
25 views
Binary classification of gene sequence data
I'm working on an older competition on Kaggle purely for self-study. The competition is to predict HIV progression given 2 nucleotide sequences, viral load (numeric), and CD4 count (numeric). The ...
0
votes
2answers
48 views
Generalization for interpreting a test?
At my college I am doing a lot of testing, such as testing for autocorrelation, White , DW, $t$, $F$ etc.
However, I always have to look up, when to reject and when to accept for example $H_0$
...
2
votes
1answer
71 views
Inverting a hypothesis test: nitpicky detail
First timer here. I'm reviewing a section of Casella and Berger on inverting a hypothesis test to get a Confidence Interval (CI), and came across a proof which I believe is missing a tiny piece. ...
1
vote
1answer
65 views
Somers' D (contingency table) in R
I need to compute the Somers' D for a contingency table (choosing between R|C and C|R), but I can't find any function to do this. I know there is the somers2 ...
1
vote
0answers
49 views
6-sided die roll average value [duplicate]
A die is rolled 100 times. Find the probability that the mean value would
be between 3 and 3.5.
I've found the expected value which is 3.5 without idea what to do next.
0
votes
0answers
36 views
Changepoint Analysis on differenced data
I was told to run a changepoint analysis in R on my data. But the data shows a decreasing trend, so the changepoint analysis won't be of help (I don't think?). If I differenced the data, to get rid of ...
0
votes
0answers
56 views
Statistics problem travel distance [closed]
I've tried to solve this but I have no idea; I tried it several times but I still didn't manage to get a correct solution.
For a sample of 10 students, the following bivariate data represents the ...
0
votes
0answers
11 views
regarding Two level full factorial design coefficient's variance
Assuming that the observations are independent with variance $\sigma^2$ and there are no repetitions, what it the variance of each influence as calculated from the experiment?
what is the variance of ...
2
votes
0answers
33 views
Outliers in importance sampling
I'm working on a HW question in which I'm using importance sampling method to estimate E(X) where X is distributed as standard Laplace. To do so, I choose my proposal density to be standard normal. I ...
3
votes
1answer
55 views
Understanding the two-stage choice paradigm
In Manski - The structure of random utility models the following example is proposed:
Consider the alternative set space a = $(\alpha,\beta,\gamma)$ with the attribute representation: $X = ...
1
vote
0answers
20 views
Two level full factorial design question
I need to prove the following identities for a factorial design experiment of the form $2^k$.
$\overline{Y}(AB+)-\overline{Y}(AB-)=0.5[A(B+)-A(B-)]$
$A(B+)=A+AB$
$A(B-)=A-AB$
$A=[A(B+)+A(B-)]/2$
...
0
votes
0answers
27 views
Estimating Change in Mean (Linear Regression Example)
A question states: Estimate the mean change in the number of flycatchers killed when the nest box tit occupancy increases by 10%.
The slope for this regression is .10766X. Hence, says the answer, ...
0
votes
1answer
90 views
Proving $\text{Var}{(\hat{y}_h)} = \sigma^2 \left(\frac{1}{n} + \frac{(x_h-\bar{x})^2}{S_{xx}}\right)$
I have asked in another question how $\text{Var}{(\hat{y}_h)} = \sigma^2 \left(\frac{1}{n} + \frac{(x_h-\bar{x})^2}{S_{xx}}\right)$. Note that $\hat{y}_h$ = $b_0 + b_1X_h$ which is a regression line ...
1
vote
1answer
50 views
Proof: Linear Regression
I am at a loss how might one prove $\text{Var}{(\hat{y}_h)} = \sigma^2 \left(\frac{1}{n} + \frac{(x_h-\bar{x})^2}{S_{xx}}\right)$. Note that $\hat{y}_h$ = $b_0 + b_1X_h$ which is a regression line ...
1
vote
1answer
56 views
Showing that $s^2$ is an unbiased estimator of $\sigma^2$ [duplicate]
$s^2 = \sum \frac{(x_i - \bar{x})^2}{n-1} $ which apparently equals $ \frac{\sum(x_i^2) +n\bar{x}^2 - 2n\bar{x}^2}{n-1}$. Does this just come from expanding the numerator and using the fact that ...
1
vote
1answer
57 views
Questions on Definitions and Notation (MSE, SSE, Sxx)
It is said that $S_{xx} = \sum_{i=1}^n(x_iā\overline x)^2 = \sum_{i=1}^n x_i^2 ān\overline x^2$.
I suspect this is simple algebra but I am missing something still. How does this work?
Further, ...
2
votes
1answer
43 views
Penalty value in changepoint analysis
I'm working with the changepoint R package in R and I understand everything but the penalty value. I know it changes the units of change in the mean, but I still don't know how to interpret it. How do ...
0
votes
0answers
42 views
A question on the exponential distribution [closed]
I am wondering if you could help me with the following:
Charlie and Bella and their friends Mark and Leonard each have a toy. Each toy breaks at a time that is exponentially distributed with ...
1
vote
0answers
31 views
The meaning of translation completeness w.r.t a random variable
I stumbled upon this term in McFadden - Analysis of qualitative choice behavior (page 111).
It is said that
"A random Variable $X$ is translation complete if for a function h
of bounded ...
2
votes
1answer
65 views
Joint distributions for uncorrelated varibles
Can someone think of joint distribution of random variables X, Y such that the following three
conditions are satisfied:
$E[X] = 1$,
$E[Y] = 1$, and
$E[XY] = 0$?
A friend of mine asked me this, ...
0
votes
0answers
46 views
Linear regression intercept proofs
Consider that $b_{0} = Y_1 - b_1X_1$ where $Y_1$ and $X_1$ here are the mean values for each. How would I derive the variance and other properties for $b_0$?
I'm not very good at doing proofs in ...
3
votes
1answer
52 views
Maximum likelihood estimate for a parameter $a$
How to find maximum likelihood estimate for a parameter $a$ in distribution:
$$f(x)=\begin{cases} \frac{\left| x\right| }{a ^{2} } &\text{for } x \in\left[ -a;a\right] \\0 &\text{for } x ...
1
vote
0answers
29 views
Some help on genome analysis
I have an exam tomorrow about statistics for genome analysis and I'm having some troubles with some questions from an example exam. All help would be very welcome!
These are the questions:
The ...
-4
votes
0answers
25 views
Please show me that with which formula, I can calculate pooled variance for unequal population variance? [closed]
I know it not legal and valid for faq but I cannot put a photo here because of reputation and not logged in here. Sorry. This is last question. After this, I never put link here. Sorry.
My question ...
-2
votes
1answer
54 views
What is the sample standard error formula?
What is the sample standard error formula?
I know only $s$ but I guess this is not it.
I am confused about its formula. Please help me. Thank you.
0
votes
1answer
31 views
Consistent estimator with var=0
I'm trying to think of an example of a consistent estimator with var=0 but I'm having a hard time.
I pretty sure it exists but I'm unable to find one.
Any help\hints would be much appreciated.
-3
votes
0answers
31 views
regression f test [closed]
y=3+0.86x_1-3.16x_2+10.3x_3+0.73x_4
F=30.85 ; P<0.05
Which of the following is correct?
A)There is a strong relationship between the dependent variable and ...
1
vote
1answer
119 views
Questions on linear regression
I had a few true / false questions on a practice test that I would like to discuss if possible.
A value $R^2$ close to 1 indicates the linear regression is a good fit to data
Yes, but I am not ...
0
votes
0answers
43 views
regression and correlation analysis [closed]
I. The main objective of regression analysis is to predict the dependent variable by the help of one or more independent variables.
II. The main objective of correlation analysis is to determine ...
-3
votes
0answers
60 views
multiple regression analysis [closed]
$$y = 3 + 0.86x_1-3.16x_2+10.3x_3+0.73x_4 \\
F = 30.85,~ p <0.05$$
Which of the following is correct?
A) There is a strong relationship between the dependent variable and independent variables.
...
1
vote
1answer
36 views
Proving stationarity with difference equations
This is exercise 2.9.b from Time Series Analysis ā With Applications in R (Cryer, Chan). First of all, for $m\in\mathbb N+2$, let us define the $m$-th difference of a discrete time series ...
2
votes
2answers
73 views
How do you explain 'co-integration' to determine spurious regression to a fairly new time series student?
I would appreciate it if someone could explain the concept of spurious regression intuitively / without it being too technical.
So far the student understands that spurious regression is basically ...
