# unbiased estimator

1. ### Mean-square error question with lengthy calculus.

I got the alpha in 9a which is 2 and 9b mse is infinity. Then I cannot continue.
2. ### Mean Squared Error explained in a visual manner (method case)

Dear all. I would like to share with you the video I have develop in which people can understand the concepts of Bias and Efficiency of an estimator from a total practical point of view and using a simulated case (method case). If you want understand this concepts, above all for people who don't...
3. ### Parametric vs. Nonparametric.

Suppose a researcher estimated a parameter in parametric way with correct distributional assumption. Another researcher estimated the same parameter in non-parametric way. Will there any difference of accuracy (bias) in estimation in these two situations?
4. ### Are Unbiasedness and Accuracy of the estimates, all to determine the sample size?

For determining sample size , why is to focus on the unbiasedness and accuracy of the estimates ? Are this two properties, unbiasedness and accuracy of the estimates, all to determine the sample size ? In a simulation study of multilevel model, authors chose that combination of sample size...
5. ### Biased and un-biased estimators.

I am working with the Rayleigh-distribution and note that on Wikipedia they say that s^2 = 1/(2N) sum x_i^2 is an unbiased estimator of sigma^2. Now they also say that s = sqrt(s^2) is a biased estimator of sigma. How can this be?? If one is unbiased, why isn't the other one? I mean, you...
6. ### Is that the correct procedure to showing unbiasedness.

I want to modify the following program to show unbiasedness using r x <- c(10,12,14,13,10,11,9,15,8,14) mu=mean(x) T=0 #the statistic for(i in 1:210){ r = sample(x,size=4,replace=F) T[i]=mean(r) } MSE <- (1/209)*sum(T-mu)^2 #mean square error MSE
7. ### Unbiased Estimator.

the radius of a circle is measured with an error of measurement which is distributed normal with mean 0 and variance \sigma^2,\sigma^2 unknown.Given n independent measurements of the radius , find an unbiased estimator of the area of the circle. By using *Maximum Likelihood Estimator* I found...
8. ### Why is the mean of sample variances not equal to the population variance?

Several texts say that the mean of all values of an unbiased estimator is equal to the parameter it is estimating. They also say that the sample variance using Bessel's correction is an unbiased estimator of the population variance. Here's what I'm confused about: Consider a population...
9. ### Question about normally distributed estimator with a constant

Hi all i'm having serious difficulties with the following problem :shakehead any help would be much appreciated. _________________________________________________ Assume that some random variable x is normally distributed with mean μ and variance σ². consider the following estimator where ci...
10. ### Help with unbiased estimators and efficiency

Suppose that Y1, Y2, ..., Yn constitute a random sample from the density function f(y|t) = e^-(y-t), y>t where t is an unknown positive constant a. Find an estimator t1(hat) for t by the method of moments b. Find an estimator t2(hat) for t by the method of maximum likelihood c...
11. ### I need help

I need help I have this homework that I cant solve it Show that s^2=(1|n-2)∑(y-y^) is unbiased estimator for sigma^2 in linear regression model can you help me??????
12. ### E[MSE] simple linear regression

Hi All- I am trying to figure out how to prove that MSE = SSE/n-2 is an unbiased estimator of sigma^2 in simple linear regression. I have that (1/(n-2))E{SUM[Yi^2-2Yib1Xi-2boYi+bo^2+b1^2Xi^2]} Are bo and b1 random variables? Am I going about this the right way? Thanks!