How can I improve my understanding of Maximum Likelihood estimators?

In summary, Maximum Likelihood estimation is a statistical method used to estimate the parameters of a probability distribution by maximizing the likelihood of the observed data. It differs from other estimation methods by considering all available information from the data. The assumptions of Maximum Likelihood estimation are that the data follows a specific distribution and that observations are independent and identically distributed. The formula for Maximum Likelihood estimation is L(θ|x) = ∏ f(x|θ). Some advantages of using Maximum Likelihood estimation include efficient and unbiased estimates, its versatility in different statistical models, and its robustness to small sample sizes.
  • #1
benji84
2
0
Can anyoe help with likelihood estimtor problems?
:cry:
 
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  • #2
It goes like this:

Let X be a continuous r.v with pdf:

f(x;theta)=theta(1+theta)x^(theta-1).(1-x)

Show that the maximum likelihood estimator of theta satisifies:

a.(theta)^2+ (2+a)theta+1=0
 
  • #3
What is 'a'? What values is f nonzero for? And be clearer with your notation please. Also, where are you having trouble?
 
Last edited:

1. What is a Maximum Likelihood estimator?

A Maximum Likelihood estimator is a statistical method used to estimate the parameters of a probability distribution by choosing the values that maximize the likelihood of the observed data.

2. How is Maximum Likelihood different from other estimation methods?

Maximum Likelihood is different from other estimation methods because it takes into account all the available information from the data, instead of just relying on a few summary statistics.

3. What are the assumptions of Maximum Likelihood estimation?

The assumptions of Maximum Likelihood estimation are that the data follows a specific probability distribution and that the observations are independent and identically distributed.

4. What is the formula for Maximum Likelihood estimation?

The formula for Maximum Likelihood estimation is L(θ|x) = ∏ f(x|θ), where L(θ|x) is the likelihood function, x is the observed data, and θ is the parameter being estimated.

5. What are the advantages of using Maximum Likelihood estimation?

The advantages of using Maximum Likelihood estimation include its ability to provide efficient and unbiased estimates, its applicability to a wide range of statistical models, and its robustness to small sample sizes.

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