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)
1,974 questions
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Makeham's Law Parameter Approximation Using Broyden's Method
I am trying to estimate the parameters for Makeham's Law of Mortality using Broyden's method for my actuarial studies, and I'm having trouble implementing it in R.
Makeham's Law of Mortality
$$
\mu_x =...
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Unbiased estimator assumption for delta method
The following is described as Univariate Delta Method:
Let $(X_n)_{n\ge1}$ be a sequence of random variables such that $$\sqrt{n}(X_n - \mu) \xrightarrow{d} \mathcal{N}(0,\sigma^2) $$ for
some ...
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The method of moments and maximum likelihood estimator for exponential distribution $\lambda^2 + \lambda$
Let $X_1,...,X_n$ be a random sample with exponential distribution Exp$(\lambda^2+\lambda)$
What is the method of moments estimator of $\lambda$?
So PDF is $F(x;\lambda) = (\lambda^2+\lambda)\exp(-(\...
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Expectation under true distribution with mixture samples
Let $X_1, X_2, \dots , X_n$ be an i.i.d. sample from the mixture distribution
\begin{equation} \label{eqn:mixture distribution}
p_{\epsilon,\theta} = (1 - \epsilon)p_{\theta} + \epsilon \delta,
\end{...
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Uniqueness of the function $\tau(\theta)$ in the Cramér-Rao inequality
Theorem (Cramér-Rao inequality).
Consider a sample from a parametric model satisfying regularity conditions.
Let $\theta^*$ be an unbiased estimator of $\tau(\theta)$. Then for any $\theta \in \Theta$,...
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Transfer of strong consistency
Consider a sequence of i.i.d. random variables $X_1,\, \dots,\, X_n$ whose mean is denoted as $x_0$ and variance $\sigma^2 < \infty$.
From the Strong Law of Large Numbers, the empirical mean $\bar ...
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Identifiability & estimation: $d$ and $\underline c$ from $\lvert S \rvert = 6$
The scalar target $z$ is modeled as $$f(x,y) = \underline c^T \underline b, \qquad \underline b=\begin{bmatrix} 1 \\ x \\ ln(y+d) \\ x \cdot ln(y+d) \end{bmatrix},$$
with unknown parameter $d$ and ...
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Reference request for theory of estimation
I am trying to learn the theory of estimation, primarily from a mathematical (measure-theoretic/probabilistic) perspective. More specifically, I'm looking for resources that cover one-parameter and ...
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Show that powers of an MVUE is an MVUE
Question is in the title. Given that $\delta:=\delta(\mathbf X_n)$ is MVUE (minimum variance unbiased estimator) of a scalar parameter $\theta$, we are asked to show that for all natural numbers $k$, $...
- 15k
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Robust Method to Fit an Ellipse in $\mathbb{R}^{2}$
Summary
I am looking for a convex and robust formulation to fit an ellipse to a set of points.
Specifically, can handle an extreme condition number of the Scattering Matrix.
Full Question
The ...
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Does it make sense to consider situations where the MLE exists only for infinitely many $n$?
Does it make sense to study statistical models in which the maximum likelihood estimator (MLE) $ \hat{\theta}_n $ exists only for infinitely many $ n $, but not necessarily for all $ n $?
Suppose, for ...
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Intuition behind matrix form of Fisher information
Throughout mathematical statistics, the Fisher information comes up quite frequently as a measure of information. I understand that in the case where you have a single parameter, the Fisher ...
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Proving completeness for a statistic [duplicate]
Let $X_1, X_2,...,X_n$ be $iid$ continuous uniform
$\mathcal{U} (0,\theta)$ and let $T=Max(X_i)$ Show that the family of
distributions of T is complete.
Step I: Find the CDF (using independence ...
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Is a linear model an instance of a parametric model?
In All of Statistics, chapter 6.2, it states "a parametric model takes the form $F=\{f(x; θ) : θ ∈ Θ\}$ ...". Then, in chapter 13.1, it states, "The Simple Linear Regression Model
$Y_i =...
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Existence of unbiased efficient estimators
Let $X_1,X_2,...,X_n (n\geq 2)$ be a random sample from a distribution
with probability density function:
$$ f(x;\theta) = \begin{cases}
\theta x^{\theta-1}, \hspace{1 cm} 0\leq x \leq 1 \\
...
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