Finding the Minimum Mean Square Estimator for Scalar Parameter w

In summary, the conversation is about finding the minimum mean square estimator for a scalar parameter based on a scalar observation. The problem involves using the functions f(w) and f(n) to calculate the estimator, and there is a discussion about the correct calculations for the mean square error.
  • #1
sant142
2
0
I am not able to understand how to go about this problem:

Find the minimum mean square estimator for the scalar parameter w based
on the scalar observation z = ln w + n where
f(w) =1 if 0<=w<=1;
0 else:

and
f(n) =e^-n if n>= 0;
0 else

I did f(z/w) = (f(n)) /g'(n) at n = z- ln w

Am i wrong?
 
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  • #2
Hey sant142 and welcome to the forums.

Can you show us what estimator you got (as a function of a random sample I.I.D) and the calculations you obtained for the MSE (and proof that it is MMSE)?
 

Related to Finding the Minimum Mean Square Estimator for Scalar Parameter w

1. What is the minimum mean square estimator for scalar parameter w?

The minimum mean square estimator for scalar parameter w is a statistical method used to estimate an unknown scalar parameter based on a set of observations. It minimizes the expected value of the squared difference between the estimated parameter and the true parameter, making it an unbiased and efficient estimator.

2. How does the minimum mean square estimator for scalar parameter w work?

The minimum mean square estimator for scalar parameter w works by calculating the expected value of the squared difference between the estimated parameter and the true parameter. It then minimizes this value to find the best estimate of the true parameter.

3. What are the benefits of using the minimum mean square estimator for scalar parameter w?

The minimum mean square estimator for scalar parameter w has several benefits, including being unbiased and efficient, meaning it is not affected by random errors and produces estimates with minimum variance. It is also a well-established and widely used method in statistical inference.

4. When is the minimum mean square estimator for scalar parameter w used?

The minimum mean square estimator for scalar parameter w is often used in situations where the true value of a parameter is unknown, but a set of observations is available. It is commonly used in fields such as engineering, economics, and social sciences.

5. Are there any limitations to the minimum mean square estimator for scalar parameter w?

One limitation of the minimum mean square estimator for scalar parameter w is that it assumes the underlying data follows a normal distribution. If this assumption is not met, the estimator may not provide accurate results. Additionally, it may not be the best estimator to use if the true parameter is known to have a large variance.

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