All Questions
Tagged with bias self-study
31
questions
2
votes
1
answer
62
views
Data taken from survey where survey-takers self report a continous variable
I have a problem with some health data that I'm trying to analyze. The main issue originates from a census variable is derived from self reported times. The variable is sleep duration, which is ...
4
votes
1
answer
188
views
Proving that the bias of the derivative of Parzen-Rosenblatt (kernel density) estimator is of order $O(h^2) $ and $O(h)$ when $h$ approaches $0$
I came across this property that I don't get and I couldn't find the proof anywhere:
Suppose we have a density $K$ of the standard normal distribution and $K'$ its derivative. Suppose that the density ...
- 241
1
vote
2
answers
227
views
How to find MLE, probability distribution, and bias?
Suppose the data consist of a single number $X$, from the following probability density:
$$f(x|θ) = \begin{cases}
\frac{1+xθ}{2} & & \text{for } -1 \leqslant x \leqslant 1, \\[6pt]
0 & &...
- 19
0
votes
1
answer
66
views
Baseline carried forward missing data assumptions
Researchers assessed the effectiveness of a range of weight management programmes for weight loss. A randomised controlled trial study design, incorporating eight treatment arms, was used. Each ...
- 67
2
votes
1
answer
181
views
Bias of MLE of simple PDF
Given a sample $x_1, x_2, \cdots x_n$ from the pdf:
$$
f(x ; \theta) = (\theta + 1) x^\theta
$$
where $0 < x < 1$ and $\theta > -1$ is unknown. What is the bias of the MLE of $\theta$?
I'...
- 2,831
7
votes
0
answers
377
views
Can an asymptotically efficient estimator be biased?
In "Theory of point estimation" by Lehmann and Casella (1998) there is the following definition:
It is also said that
So terms of the asymptotically normal sequence of estimators can be ...
- 1,008
4
votes
1
answer
94
views
How would I calculate the bias of the estimator Û=(X₂+X₃+...+Xn)/(N+10)
The observations $X_1,\dots, X_n$ form an IID sample from a probability distribution with unknown mean $U$. Let
$$ \hat{U}=\frac{X_2+X_3+\dots+X_n}{n+10}$$
be an estimator used to estimate $U$. (I....
- 41
1
vote
1
answer
1k
views
Consistent estimator - bias and variance calculations
Working through some homework problems for a Mathematical Statistics course and I'm having a hard time finding good examples in the text to explain some details. This particular problem is:
$Y_1 ... ...
- 1,158
0
votes
1
answer
3k
views
How to get an unbiased estimator
Defining the sample mean as $\bar{x} = \frac{1}{N}\sum_{n=0}^{N-1}x_n$, and having $N$ realizations of a random variable $x$ with mean $\mu$ and variance $\sigma^2$
Defining $\bar{x}^2=\hat{\mu^2}$, ...
- 43
0
votes
0
answers
45
views
Finding Variance and Bias of a Function
First time using this website hopefully you guys could help me out.
I'm in an Econometrics class and I am having great difficulty with practice questions as I've been away for a year and a half from ...
- 21
0
votes
1
answer
46
views
Simple variance of estimator calculation question
I'm trying to solve a question about finding bias and variance of an estimator, but I'm having trouble with the variance calculation.
Say we have an IID sample of n points $y_i \sim N(\mu,1)$.
If ...
- 113
5
votes
2
answers
3k
views
Testing whether a die is biased, reasoning about the approach
Question :
A die is marked on one side, and the number of times that the mark appears is
recorded.
The mark appears once from 25 rolls, is the die biased?
working
$H_0 : $ The die is not biased
$...
- 946
4
votes
1
answer
228
views
Significance versus the bias-variance trade off
I'm taking an online course. In one of the lessons about methods to select explanatory variables, it is said that you can use the t-test or F-test to add/remove a single or group of terms to/from a ...
- 637
0
votes
1
answer
63
views
How to find the variance and bias to obtain MSE?
Considering $MSE[\hat{\mu}|{\mu}*]= Var [\hat{\mu}|{\mu}*] + Bias (\hat{\mu}|{\mu}*)^2$ and the following givens $\hat{\mu}= 112$, ${\mu}*= 112$, ${\mu}_0 = 100$, ${n = 10}$, $\bar{y}=113$, and ${\...
- 1
1
vote
2
answers
4k
views
Why we use Ridge regression instead of Least squares in Multicollinearity?
Why do we use Ridge regression instead of Least squares in Multicollinearity?
Which one is correct:
a. lower bias and higher variance
b. lower bias with the same variance
c. higher bias with a ...
- 21