# 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)

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### Average Rank versus Ranked Average in Parameter Estimation

I have the following problem: In a cricket tournament, the eleven batsmen of a team play 100 matches before the final. The runs scored by each are available. Determine the average rank of the batsmen ...
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### Calculating the bias of the inverse of a sample covariance matrix

It's standard in a stats class to calculate the bias of the sample covariance matrix (or lack thereof), but I'm having trouble finding any exact results on how the inverse of the sample covariance ...
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### Calculating Standard Error (SE) of a Nonlinear Function Using SE of Its Parameters

I'm working with a nonlinear function, specifically a beta weighting scheme, which generates weights that can vary in shape (e.g., decaying, hump-shaped, U-shaped). I have estimates for the parameters ...
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### Maximum Likelihood Estimation for Poisson Mean with Given Observations

You have a sample of $n$ i.i.d. realizations of the random variable $X$ distributed as a Poisson with parameter $\lambda$. It is known that: $n_1$ values are greater than or equal to $2$; $n_2$ ...
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### Minimum MSE Estimator among all possible estimates. Sheldon Ross Exercise 59 in Chapter 7 [duplicate]

In Sheldon Ross' Introduction to Probability and Statistics for Engineers and Scientists, the problem $59$ in chapter $7$ asks us that if $X_{1},...,X_{n}$ denote a sample from a population whose mean ...
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### Non-linear parameter optimization using Python

I have a model that generates the curve represented by the red squares the data represented by the black circles. The model curve (red squares) depends on some parameters to fitting. Is there any ...
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### Predicting simulated data for a known curve

I am a newbie here seeking advice on a mathematical problem I am currently having in my research. I have a pre-existing curve created by extrapolating known fitted experimental data. As shown below, ...
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### Method of Moment for Normal mixtures $p\cdot N(0, 1) + q\cdot N(\eta, 1)$

Setup Let $X_1,\ldots , X_n$ be random variables according to $$p\cdot N(0, 1) + q\cdot N(\eta, 1),\ p\in (0, 1), q:=1-p.$$ We use method of moments to obtain the needed starting $\sqrt{n}$-...
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### Determining Parameter Values for a Set of Solutions Involving Absolute Value Equations

The problem in the textbook asks the following: At what values of the parameter "$a$" does the set of solutions to the equation $|x - 1| + |x - a| = 1 - a$ consist of three integers? I ...
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### Estimating the parameters of an ellipse (part 2)

This post is a follow up of this previous one. I would like to clarify why the angle estimator works and how to estimate the axes length. Unfortunately, I still have some trouble with this problem. I ...
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### How can an estimator be consistent and asymptotically normal at the same time?

I can't work out why the asymptotic distribution of an estimator matters if it is consistent? My understanding is: An estimator, $\hat{\theta}$, is consistent if it converges in probability to the ...
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### Let $Y_1, \dots, Y_n \sim \; \textrm{iid}$ with pdf $f_Y(y)$. Show that the UMVUE of $\theta$ is given by $\frac{n-1}{\sum_{i=1}^n Y_i}$ [duplicate]

I'm having a difficult time figuring out where to go here. Question: Let $Y_1,\dots, Y_n$ be iid random variables with pdf $f_Y(y) = \theta e^{-\theta y} \;,\; y >0\;,\;\theta >0.$ Show that the ...
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### How to estimate the best variance-proxy of a sub-Gaussian distribution from data?

Suppose we have $N$ independently identically distributed (i.i.d.) samples $X_1,\cdots,X_N$ generated from a sub-Gaussian random variable $X \sim \mathbb{P}$. Then by definition there exists the ...
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In Statistical Inference, we were taught this theorem, Consider an estimator $T_n$ of population parameter $\theta$, using $n$ samples. $T_n$ is a Consistent Estimator of $\theta$ if E[T_n] \to \...