Mathematics Stack Exchange
Mathematics Stack Exchange

Questions tagged [parameter-estimation]

Questions about parameter estimation. Estimation theory is a branch of statistics that deals with estimating the values of parameters based on measured/empirical data that has a random component. (Def: http://en.m.wikipedia.org/wiki/Estimation_theory)

Questions about parameter estimation. Estimation theory is a branch of statistics that deals with estimating the values of parameters based on measured/empirical data that has a random component. Reference: Wikipedia.

The parameters describe an underlying physical setting in such a way that their value affects the distribution of the measured data. An estimator attempts to approximate the unknown parameters using the measurements.

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Estimation Theory - Maximum Likelihood Estimation

The below homework question comes from Larsen and Marx, 4th edition. Is the maximum likelihood estimator for $\sigma^{2}$ in a normal pdf, where both $\mu$ and >$\sigma^{2}$ are unknown, asymptotically unbiased? I think I understand the notion…
PatternMatching
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Parameter Bias of an OLS Estimation

True Model: $$Y = \alpha + \beta \bf{X} + \gamma W + V$$ Model to be regressed on: $$Y = \alpha + \beta \bf{X} + U $$ Where: $$U + \gamma \bf{W} + V$$ So, in this model, if Cov(X,W) $\neq 0$ then $\hat{\beta}$ will be biased, assuming $\gamma \neq…
user43395
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Finding the maximum likelihood estimator of theta

The question reads : Find the maximum likelihood estimator for theta based on the sample of size n from a distribution with density $$f(x|\theta)=\frac{2\theta^2}{x^3};x>\theta.$$ According to my calculations it is observed that the maximum is not…
Dr. NGILAZI BANDA
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How to find the maximum likelihood estimator of $f(y;\alpha)=5\alpha^5y^{-6}$?

How to find the maximum likelihood estimator of $$f(y;\alpha)=\frac{5\alpha^5}{y^6}$$ for $$0<\alpha\leq y<\infty.$$ Otherwise, $$f(y;\alpha)=0.$$ I have tried, but my result is $\hat{\alpha}_{MLE} = +\infty$. Am I right?
MaxGaussian
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Finding an maximum likelihood estimator (Bernouilli problem)

Could someone point me in the right direction? Suppose we compare 2 treatments. For each patient we observe $(Y_i,R_i)$ where $Y_i$ denotes if the treatment was succesfull ($Y_i=1$) or not ($Y_i=0$), and $R_i$ denotes the treatment group 1 or 2. In…
dietervdf
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Method of Moment

In this lecture on method of moment, we have: why is gradient of psi inverse a dxd matrix? K-th moment $m_k$is defined as $ \mathbb E[X^k] $ and can be estimated by the average using Law of Large Numbers which here is represented by $\hat m_k$ My…
Mina
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MOM for uncommon distribution (using Gamma function)

I'm stuck understanding this question where we are trying to get the MOM for a RV, IID, with a density function as: $$f(x|α) = {Γ(3α)/Γ(α)Γ(2α)} * x^{α-1} * (1-x)^{2α-1}$$ Where alpha is the perimeter. These are also given: $$E(X) = 1/3,…
sofarsophie
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