Estimate Function w/ Parameter: Bias & Differentiability?

  • Thread starter EvLer
  • Start date
In summary, we discussed estimating a function of a parameter using the plug-in method. We learned that the estimate, P', can be used to estimate f(p), but there may be bias associated with this estimation. However, this bias is not always present, as shown by the example of f(p) = Ap + B for any constants A and B. Additionally, we explored how to show that e-x' is not an unbiased estimate of e-lambda, where lambda is a parameter and x' is an estimation for a Poisson random variable.
  • #1
EvLer
458
0
If I am trying to estimate a function of a parameter by a plug-in method:
let's say p is a parameter then P' is an estimate of it
so then f(p) can be estimated by f(p').
So, my question is whether I will ALWAYS have a bias associated with this estimation... even if the estimate function is infinitely differentiable...
prof in class gave reasons why you have bias with Normal distribution and Bernouli but not the general case...
Thanks
 
Physics news on Phys.org
  • #2
No, you don't ALWAYS have bias.

For example f(p) = Ap + B for any constants A and B.
 
  • #3
AlephZero said:
No, you don't ALWAYS have bias.

ok, then how can I show (hint, not solution) that e-x' is not an unbiased estimate of e-lambda, where lambda is a parameter and x' it's estimation for Poisson rv
thanks
 

1. What is the purpose of estimating a function with parameters?

The purpose of estimating a function with parameters is to determine the relationship between variables and make predictions based on that relationship. This allows for a better understanding of the underlying process and can help in decision-making.

2. What is bias in the context of function estimation?

Bias in function estimation refers to the difference between the expected value of the estimated function and the true value of the underlying function. A biased estimate may over or underestimate the true value, leading to inaccurate predictions.

3. How does bias affect the accuracy of function estimation?

Bias can affect the accuracy of function estimation by leading to incorrect predictions. If the estimated function is consistently biased, it may not accurately reflect the true relationship between variables, resulting in inaccurate predictions.

4. What is differentiability and why is it important in function estimation?

Differentiability refers to the ability of a function to be differentiated at a certain point. In function estimation, differentiability is important because it allows for the use of calculus to find the optimal parameters that minimize the bias and improve the accuracy of the estimated function.

5. Can a function be both biased and differentiable?

Yes, a function can be both biased and differentiable. The differentiability of a function does not necessarily guarantee that it is unbiased, and vice versa. It is important to consider both bias and differentiability when estimating a function to ensure accurate predictions.

Similar threads

  • Set Theory, Logic, Probability, Statistics
Replies
1
Views
347
  • Set Theory, Logic, Probability, Statistics
Replies
7
Views
337
Replies
1
Views
588
  • Calculus and Beyond Homework Help
Replies
7
Views
135
  • Calculus and Beyond Homework Help
Replies
18
Views
1K
  • Set Theory, Logic, Probability, Statistics
Replies
7
Views
369
  • Set Theory, Logic, Probability, Statistics
Replies
3
Views
700
  • Set Theory, Logic, Probability, Statistics
Replies
9
Views
1K
  • Calculus and Beyond Homework Help
Replies
1
Views
171
  • Calculus and Beyond Homework Help
Replies
19
Views
3K
Back
Top