Tagged Questions
2
votes
2answers
100 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
33 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 $\{S(t)\}_{t=0}^{t=T}$， how to ...
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
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 ...
0
votes
2answers
31 views
Combined Individual Error
This is from my college project management course. Reading through an example question here it says:
When estimating in parts, the total error will be less than the sum
of the part errors.
...
6
votes
2answers
158 views
How to find MLE when samples depend on the estimated parameter
Can you show me what I'm doing wrong here? This is the homework problem:
Consider a random sample $Y_1, \ldots , Y_n$ from the pdf $f_Y(y;\theta) = 2y\theta^2$ where $0\le y \le \frac{1}{\theta}$. ...
0
votes
0answers
18 views
Can the kernel-smoothed hazard rate be defined for times greater than the largest death time?
I am trying to follow the book "Survival Analysis", and here's a summary of the concepts on hazard rate estimation from sas.com
For the ALL group, the largest observed time was $t_D=662$, while an ...
1
vote
0answers
132 views
Finding the UMVUE of the variance of a gaussian with mean zero
Given $Z_1, ..., Z_n, \sim\mathcal{N}(0, θ^2), θ>0$. Define $X_i=|Z_i|$ and consider estimation of $\theta$ and $θ^2$ on the basis of the random sample $X_1,...X_n$. Find the uniformly minimum ...
0
votes
0answers
37 views
Show that the slope estimate can be written as a sum
I am stuck on a homework question for a graduate level linear models class. The question is to show that for simple linear regression the slope estimate $ \hat{\beta_1} = ...
2
votes
1answer
222 views
How do I use student's-t distribution without the sample size?
Here is my question (homework obviously):
A sample from a normal population produced variance 4.0.
Find the size of the sample if the sample mean deviates from the population
mean by no more than 2.0 ...
3
votes
1answer
59 views
Is it worth to take another sample?
There is a random normal variable, with unknown mean and std. I want to estimate the mean by sampling. After several samples, I have an estimate, which I can make more precise by taking more samples, ...
3
votes
1answer
497 views
What are complete sufficient statistics?
I have some trouble understanding complete sufficient statistics?
Let $T=\Sigma x_i$ be a sufficient statistic.
If $E[g(T)]=0$ with probability 1, for some function $g$, then it is a complete ...
2
votes
1answer
103 views
Help computing asymptotic variance of a weird first difference estimator in a fixed effects model
I'm working on an econometrics problem set, and I'm having some major problems computing asymptotic variance for this estimator. I'm considering a fixed-effects model
$$
Y_{it} = \beta_1 X_{it} + ...
1
vote
1answer
224 views
Maximum likelihood estimation and the n-th order statistic
Let $X_1, ..., X_n$ be a sample of independent,
identically distributed random variables, with density
$$ f_{\theta}(x)=e^{ (\theta -x)}$$.
$x \ge \theta$, otherwise $f_\theta = 0$
The question ...
2
votes
2answers
478 views
Why doesn't the Cramer-Rao lower bound apply?
Let $X_1, X_2, \dots, X_n$ be a sample of i.i.d. random variables, with density $$f_\theta=\frac{2}{3\theta}\left(1-\frac{x}{3\theta}\right) $$ for $0 < x < 3\theta$. And
$f_\theta=0$ if $ x ...
2
votes
2answers
149 views
Interval estimation of $\sigma^2$ with the reliability of $95\%$
I got these values from the measurement by a telescope:
20.1, 20.2, 19.9, 20, 20.5, 20.5, 20, 19.8, 19.9, 20.
I know that the actual distance is 20 km and the error of the measurement is not affected ...
-1
votes
1answer
126 views
Maximum likelihood estimator (Gaussian errors, known SD)
Suppose that the random variables $Y_1, ..., Y_n$, satisfy $Y_i = \beta \cdot x_i + \epsilon_i$ for $i = 1,...,n$
where $\beta$ is a constant, $x_1,...,x_n$, are constants, and ...
-2
votes
1answer
358 views
Finding uniform minimum variance unbiased estimators
$X_1, X_2, X_3, \ldots{}, X_n$, i.i.d., follow $\mathcal{N}(0, \theta^2)$, $\theta > 0$.
What are the UMVUEs (Uniform Minimum Variance Unbiased Estimators) of $\theta$ as well as ...
0
votes
0answers
365 views
Cramer-Rao Lower Bound Questions
I've been reviewing questions from a statistics exam of the last year. There is a question with the probability density function below
$$\displaystyle f(x,\theta) = \frac 1{2\theta^3}x^2e^{-\frac ...
8
votes
2answers
486 views
What kind of distribution is $f_X(x) = 2 \lambda \pi x e^{-\lambda \pi x ^2}$?
What kind of function is:
$f_X(x) = 2 \lambda \pi x e^{-\lambda \pi x ^2}$
Is this a common distribution? I am trying to find a confidence interval of $\lambda$ using the estimator ...
1
vote
1answer
159 views
Expected number of shipments and its standard deviation
Recent history suggests that one supplier fails to meet this new specification 20% of the time. Assume that the next 15 batches of this alloy are a random sample.
How can I find the expected number ...
-2
votes
1answer
189 views
How do I deduce the SD from regression and ANOVA tables?
This is a Minitab printout. I want to find the value of A5, or S.
I think S is supposed to be the sample standard deviation, but I don't know how to calculate it. Any tips on how I should go about ...
