All Questions
Tagged with variance estimation
162 questions
4
votes
0
answers
74
views
Sample Covariance [duplicate]
The sample covariance is defined as $\hat{\sigma}_{xy}:=\frac1{n-1} \sum_{i=1}^n (x_i -\bar{x})(y_i-\bar{y})$. What is the intuition for using the correction term $n-1$ instead of $n-2$. Because we ...
- 363
1
vote
1
answer
80
views
Theoretical foundations of meta-analysis
I am hoping someone can give me some guidance (or references) relating to the mean and variance of the distribution of the mean of sample means.
I am thinking about a large number of populations, ...
- 43
4
votes
1
answer
1k
views
Non-parametric conditional variance estimation
Let $(x_i,y_i)_{1\leq i\leq n}$ some dataset. I want to estimate the conditional expectation $E[Y\mid X=x]$ and the conditional variance $V[Y\mid X=x]$.
I used Nadaraya-Watson's estimator to estimate ...
- 233
4
votes
1
answer
348
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How to implement the sandwich estimator in a semi-parametric situation?
I am trying to implement a sandwich estimator described in Zhang et al. (2012, p. 1012) in very brief terms. The information they give is not enough for me to understand what has been actually done, ...
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2
votes
1
answer
818
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Horvitz-Thompson variance estimation when estimating across strata
I have a sample of Business units, which has been stratified according to two stratification variables (Revenue class and field of Business acitivity). Within the strata, Units were sampled according ...
- 97
0
votes
1
answer
51
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How do you calculate sample variance for the difference between outcomes under two experimental conditions?
Suppose we have a group of volunteers who we each ask to undertake a task under two different conditions. $X_i$ is the outcome for the $i^{th}$ volunteer under the first condition, $Y_i$ the outcome ...
- 103
3
votes
1
answer
49
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estimating variance using only data at the tails without resorting to Gibbs sampling
Suppose we know that the population size is $n=1,000$ but for whatever reason, we only have the bottom $n_1=100$ observations and the top $n_2 = 200$ observations. Furthermore, suppose we know the ...
- 338
1
vote
1
answer
2k
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Variance Estimation of MA(1) with known autocovariance function
I haven't worked with time-series in a while now and stumbled upon them in a different setting.
Given $X_t\sim\mathcal{N}(0,\sigma^2)$ for $t=1,\ldots,n$ and the process $Y_t$ for $t=1,\ldots,n-1$ ...
- 13
1
vote
0
answers
128
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Variance estimation for Levy process
Let $(X_t)$ be a Levy process. It then holds that
$$
E(X_{t+\Delta} - X_t) = \Delta \nu, \\
V(X_{t+\Delta} - X_t) = \Delta \mu,
$$
under sufficient regularity conditions in terms of moments. For ...
- 111
8
votes
1
answer
12k
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what is bias and variance of an estimator?
I know what Variance is. But what is Bias? I just have problems to understand this what is written!
- 85
0
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0
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539
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Gaussian QMLE in estimating CCC-GARCH model
I am having some troubles understanding the estimation of a CCC-GARCH model (where the univariate GARCH models are GJR-GARCH(1,1)) by the means of Gaussian QMLE with the likelihood function of ...
- 173
4
votes
1
answer
1k
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Sampling variance of regression intercept when there is no regressor
Suppose we have a model $y=\beta_0+u$, where $E(u)=0$ and $Var(u)=\sigma^2$. I get the unbiased estimator $\hat\beta_0$ is just $\bar y$. But how can I get the variance of $\hat\beta_0$? Is it correct ...
- 93
3
votes
0
answers
315
views
Average conditional variance
Related to Explanatory power of variable. Given a data for 1d variable $Y$ and multidimensional variable $X$, what is the best way to compute average conditional variance of $Y$ given $X$:
$$
\Bbb V(...
- 419
3
votes
2
answers
10k
views
Why does the parameter variance change when control variables are added to a regression model?
If I add a control variable to my regression, this changes the variances of the parameter estimates. Why is this the case? Is this because SSE(=explained sum of squares) increases and therefore the ...
- 81
2
votes
1
answer
2k
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When would you want to reduce variance?
In a sampling-estimation context, low variance of the estimate is a goal. Several things I've read suggest (though I can't quite connect the dots) that lowering variance in the data will improve the ...
- 517
1
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0
answers
284
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Monte Carlo integration and variance
With the monte carlo integration of a function $f(x)$, what do they mean with the variance? Is it the variance of the function we want to integrate?
$I = ∫^{\infty}_{\infty} f(x)p(x) dx$ (with $p(x)$ ...
- 225
1
vote
1
answer
421
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Questions about unbiased sample variance
I have three related questions:
Is it right to say that an unbiased estimate is close to the true value of population parameter?
If 1) is true, then does the sample variance after correction become ...
- 11
1
vote
0
answers
42
views
Unbias estimator of the variance when individual observations differ in accuracy?
Experiment
Mother Seeds
Let's say I have a seed. Let's call this seed , a "mother seed". I clone this seed many times, develop the organism and measure some phenotypic trait ...
- 5,182
1
vote
0
answers
10
views
Component variance estimate after taking the difference of normal variables
I have multiple observations $z_i = x_i - y_i$ where $x_i\sim N(0,\alpha^2)$ and $y_i\sim N(0,\beta^2)$, where $\alpha^2$ is assumed known. Under these circumstances, what is a standard method of ...
- 215
1
vote
0
answers
148
views
95% confidence interval for an estimate average
I have a single dataset - from that dataset I have used four methods ($i=1, 2, 3, 4$) to estimate a parameter ($u_i$) and to generate a 95% confidence interval. In other words, I know $V[u_i]$ but not ...
- 11
7
votes
1
answer
358
views
What's the maximum expectation of a conditional variance, $E[\operatorname{Var}(X+Z_1 \mid X+Z_2)]$?
Let $X,Z_1,Z_2$ be 3 mutually independent RV's, with $Z_1, Z_2$ assuming $N(0,1)$ distribution. $X$ is constrained to have unit 2nd moment, i.e. $E[X^2] =1$, but may take arbitrary distribution. The ...
- 856
3
votes
1
answer
4k
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Estimating population variance through simulation in R
I want to estimate the variance of the exponential distribution with a rate of $\lambda=0.2$.
I'm drawing a sample of 5 exponentials 1000 times, and know that the theoretical variance of my '...
- 43
1
vote
0
answers
1k
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Estimation of variance: How to bring Bessel's correction together with degrees of freedom?
I have been considering multiple textbooks to find out the reason that the denominator of the estimation of the population variance is n-1 rather than n. Depending on the book, two reasons are given:
...
- 1,350
3
votes
1
answer
8k
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Variance of the $\hat{\sigma}^2$ of a Maximum Likelihood estimator
Given some normally distributed observations $x_1,x_2,...,x_n$
$\forall i\ x_i\sim\mathcal{N}(\mu, \sigma^2)$
the ML estimator decides that the variance that maximizes the likelihood function is (see ...
- 271
3
votes
1
answer
185
views
Estimating counts from sampled data
I am working on counting events from sampled web logs. To formalize the problem, consider a random process in which we randomly record an event with known probability $r$. Say we have $n$ recorded ...
- 31
6
votes
1
answer
153
views
Error bars on log of big numbers
I am calculating a quantity of the following form:
$\mu = \log( \frac{1}{n} \sum_{i=1}^{n} e^{\phi(X_i)} )$
via MC. $X_i$ are iid and I can sample them. I want to give error bars\ confidence ...
- 2,684
0
votes
0
answers
221
views
Best linear unbiased estimator
I have a sample of N stocks.
I have the following information:
For each stock i, I have an estimate of variance (of returns) $\hat{\sigma}^2_{i}$.
I also have a fitted variance, denoted by $\hat{b}_{...
- 957
2
votes
1
answer
3k
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Estimate of Coefficient Variance in multiple regression
I'm trying to compute an estimate for the variance of the estimated coefficients
in a non-linear regression using the formula described in link.
I can't figure out how to build $F_{ij}$
Let's ...
- 131
5
votes
1
answer
422
views
Conceptual question on estimation : How to calculate the variance of estimation error
EDIT/ UPDATE:
I have understood CRLB & why we need it. But my problem is something else. In book ...
- 787
1
vote
0
answers
55
views
Distribution of sample variance for non-normal random variable [duplicate]
For a sample of size $n$ of non-normal random variables $x_1,...,x_n$. Is it possible to know which distribution the sample variance estimator follows?
Details: The distribution of $x_i$'s is not ...
- 107
2
votes
1
answer
138
views
What is the name of the distribution of unbiased sample variance for a sample from Gaussian distribution?
Suppose $X_i$'s are iid Gaussian random variables with mean $\mu$ and variance $\sigma^2$.
The distribution of $\sum_i (X_i - \bar{X}_i)^2 / (n-1)$ isn't Chi square. What is its distribution called? ...
- 23
0
votes
0
answers
46
views
Can you combined two sources with difference variance to reduce error? [duplicate]
I have two samples of data each estimates of a position x, y with Gaussian noise. One source has a larger variance than the other. Is this source in any way useful ...
- 576
5
votes
1
answer
741
views
Why are Winsorized random variables independent?
While studying trimmed mean I understood that if I have some random variables $X_1, X_2, .., X_n$ by ordering them and trimming, the variables are no longer independent.
However it is said that "by ...
- 7,104
2
votes
0
answers
943
views
Variance of plugin estimator
This question related to my previous question.
Let $$X_1,\dots,X_n$$ are i.i.d. with distribution function $F$ and $$Y_1,\dots,Y_n$$ are i.i.d. with distribution function $G$. Suppose that there ...
- 205
6
votes
2
answers
1k
views
Estimating the error in the average of correlated values
tl;dr I can only generate samples of a random variable $X$ using MCMC. How can I find the error in the estimate of the expected value of $X$ based on this MCMC data?
The problem
I have a "black ...
- 1,408
3
votes
0
answers
260
views
Estimating variance for identically non independent data
Let $X_{ij}$ with $1\leq i<j\leq n$ (that are $X_{12},\dots, X_{1n},\dots,X_{(n-1)n}$) be ${n \choose 2}$ identically normal distributed $N(0,\sigma^2)$ such that
$
\text{corr}(X_{ij},X_{rs})=\rho
...
- 205
4
votes
0
answers
1k
views
Are there efficient estimators for the variance of an exponential family?
Let us consider the Gaussian model $\mathcal{N}(\mu,\sigma^2)$, where both $\mu$ and $\sigma$ are unknown. I have learnt that (for example, from Amari's information geometry book) the exponential ...
- 617
6
votes
1
answer
542
views
Estimate of variance with the lowest mean square error
Regarding estimators of variance from a iid sample of size $n$, Karl Ove Hufthammer says Estimates of variance from an iid sample:
if they do have a normal distribution, dividing by n+1 (sic!) ...
- 19.8k
4
votes
2
answers
44
views
Variance Estimation in case of nonrespondents
I saw in the book of Rubin (1987) that an increase in variance of estimation will occur due to nonresponses. But I wonder the reason behind this. Thanks for your shares!
3
votes
0
answers
385
views
Variance of a difference in marginal proportions in a three-way contingency table
Let a multivariate distribution be given by $P(Y,S_1,S_2)$, where all three variables are discrete, $Y$ is multivalued, $S_1=(0,1)$ and $S_2=(0,1)$, respectively, and all may be dependent. Define the ...
- 6,724
0
votes
0
answers
85
views
Choice of variance estimator [duplicate]
Consider the problem of the choice of estimator of $\sigma^2$ based on a random sample of size $n$ from a $N(\mu,\sigma^2)$ distribution.
In undergraduate, we were always taught to use the sample ...
- 487
4
votes
1
answer
2k
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Unbiased estimator of variance for samples *without* replacement
This is a follow-up question on that one: Could Bessel's correction make sample variance estimation even more biased?
I understand that you need Bessel's correction to get an unbiased estimate of ...
- 6,246
5
votes
2
answers
786
views
Could Bessel's correction make sample variance estimation even more biased?
It is well known that Bessel's correction creates an unbiased estimator of variance. What it basically does is divide by $n-1$ instead of $n$.
Now what I did is that I chose a few number, like $1,2,3,...
- 6,246
2
votes
1
answer
2k
views
How to combine variances from sensors where each observation has its own variance?
I have a set of measurements $x_1$ ... $x_n$. These measurements are normally distributed, measuring the same value. However due to the way the data is measured, each $x$ has its own standard ...
- 123
4
votes
0
answers
101
views
Index of dispersion with approximate distribution
I have an unknown discrete probability distribution $D$ ($D$ is a probability mass function), defined on an interval $[a,b]$ ($a>0$) and an estimation $\hat{D}$ such that, for all $t\in[a,b]$,
$$(...
- 213
2
votes
1
answer
593
views
Estimating the population variance [duplicate]
I'm trying to understand the emphasized phrase in the following passage:
The usual method of determining the probability that the mean of the population lies within a given distance of the mean of ...
- 1,977
1
vote
0
answers
308
views
What coefficient could I use to calculate the relative difficulty of a test in relation to others using only mean and population standard deviation?
I have a series of tests, all of them of different difficulty, and from each of them I get an average score and a population standard deviation; e.g:
...
- 11
2
votes
1
answer
1k
views
Compute the variance of parameter estimates given limited number of samples
I'd like to infer the variance of estimated parameter $\hat\theta$ of the density function of $f(x;\theta)$ given only a limited number of samples $X_1,\cdots,X_n$.
Bootstrapping doesn't perform well ...
- 161
2
votes
0
answers
912
views
Finding the UMVUE of the variance of a gaussian with mean zero
Given $Z_1, ..., Z_n, \sim\mathcal{N}(0, θ^2), θ>0$. Define $X_i=|Z_i|$ and consider estimation of $\theta$ and $θ^2$ on the basis of the random sample $X_1,...X_n$. Find the uniformly minimum ...
- 21
2
votes
0
answers
162
views
How to compute variance of a continuous time sequence?
I am observing two continuous time-series where at every instant in time I may observe a unary event. That is, for each sequence, say $S_1$, I have a data set comprised of $S_1 = (t_0, t_1, ..., t_m)$ ...
- 1,268