All Questions
Tagged with estimators normal-distribution
28
questions
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54
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What is the distribution of the unbiased estimator of variance for normally distributed variables?
I must be making some mistake in my derivation of the distribution of the unbiased variance estimator for i.i.d. $X_{i} \sim \mathcal{N}\left(\mu, \sigma^{2}\right)$.
We have $\bar{X} =\frac{1}{n}\sum\...
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1
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1
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78
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Finding the Variance of the MLE Variance of a Joint Normal Distribution
I have a random sampling of $Z_1,...Z_n$ from a normal distribution $N(\mu,\sigma^{2})$. I am considering them within a joint likelihood function.
I know that the MLE ($\hat\sigma^{2}$) of $\sigma^{2}$...
- 13
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1
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539
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Maximum-likelihood estimator for data points with errors
Suppose there are N measurements of a random variable x which has Gaussian p.d.f. with unknown mean $\mu$ and variance $\sigma^2$. Classical textbook solution for estimation $\mu$ and $\sigma$ is to ...
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What is the joint distribution between the sample mean and sample mediant of rounded normal variables?
I am curious about the relationship between the arithmetic mean and the (generalized) mediant. I took $10^4$ samples (each of size $n=3$) of $\operatorname{Round}(X_i,\text{decimals}=3)$ where $X_i \...
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60
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Aproximate maximum of two multivariate Gaussians with multivariate Gaussian
Given two multivariate Gaussians $G_1(\mathbf{x}), G_2(\mathbf{x})$ (not PDFs!) with the same center at the coordinate origin and different covariance matrix $\mathbf{F}_1, \mathbf{F}_2$, where $\...
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1
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0
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47
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Correct approach for combining confidence intervals from multiple estimators
Let's say I have an estimation from 2 different people about human population of a small town. Both are (calibrated) 90% CIs:
Expert 1: 3,000-4,000
Expert 2: 3,000-50,000 (Intentionally much wider ...
- 11
5
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1
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91
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Estimating largest eigenvalue of $N_{d\gg 1}(0,\Sigma)$ from small data
I am trying to estimate the largest eigenvalue of some $d$-dimensional normal distribution $N_d(0,\Sigma)$ from the sample data
$$X_1, \ldots, X_N \sim_{iid} N(0,\Sigma)$$
where $N$ is much smaller ...
- 235
2
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1
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477
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Are moments more robust than MLE?
I am an MBA Student taking courses in Statistics.
We are learning about different ways to estimate the parameters (i.e. coefficients) of a Regression Model. Our professor indicated that there are two ...
4
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2
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3k
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What does asymptotic efficiency mean?
I read some comparison articles, and always find "asymptotic efficiency," "asymptotically less efficient," and "asymptotically normal."
I am really confused about the ...
- 650
2
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1
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40
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Variance Estimator Change if we know Population Mean? (Normal dist. example)
For a normal distribution $N(\mu, \sigma^2)$ a commonly used unbiased and consistent estimator of variance is
$$\hat \sigma^2=\frac{\sum_ix_i^2 + n(\bar x)^2}{n-1}=\frac{\sum_i(x_i-\bar x)^2}{n-1}$$
...
- 154
0
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1k
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Proof Sample Variance is Minimum Variance Unbiased Estimator for Unknown Mean
I am trying to prove that the unbiased sample variance is a minimum variance estimator. In this problem I have a Normal distribution with unknown mean (and the variance is the parameter to estimate so ...
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1
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1
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569
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Variance and expectation of $\frac{1}{n}\sum^n_{i=1}X^2_i$
Let $X = (X_1, . . . , X_n)$ consist of independent and identically Normal $N(0, θ)$ random
variables, with mean $0$ and variance $θ \gt 0$.
The Moment Estimator for $\theta$ is given by $\hat \theta ...
user255658
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940
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Skewed outcome variable, sem model: is it a problem?
My outcome variable is really skewed, and I want to include it in a SEM model (I am using lavaan - R). It is measured with a 7-points Likert scale (agreement) and consists of 5 items.
If the model ...
- 21
3
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48
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variance estimator for a symmetrical two-sides censored normal distribution
Suppose to draw a sample of $n$ observations from $X \sim \mathcal{N}(0,\sigma)$, with observations outside the interval $(-c,+c)$ censored; $c$ is known and one can conveniently set $c=1$, for ...
- 1,090
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3
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958
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How to find maximum likelihood estimates of an integer parameter?
H.W. Question:
$x_1,x_2,\ldots,x_n$ are independent Gaussian variables with mean $\mu$ and variance $\sigma^2$. Define $y = \sum_{n=1}^{N} x_n$ where $N$ is unknown. We are interested in ...
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