Linked Questions
25 questions linked to/from Why shouldn't the denominator of the covariance estimator be n-2 rather than n-1?
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Degrees of freedom in covariance calculation [duplicate]
When calculating the sample covariance, why do we divide by $n-1$ instead of $n-2$? Don't we lose two degrees of freedom since we need to calculate two sample means? For example, when estimating the ...
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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 ...
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Understanding "we lose degrees of freedom in product deviations"? [duplicate]
I'm having a tricky time understanding the statement:
we lose $n−1$ [degrees of freedom] by computing the product
deviations [in $cov(x,y)$]
I'm not necessarily looking for an overview of ...
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Why does computing product derivations eliminate degrees of freedom? [duplicate]
I'm trying to get an intuition as to why degrees of freedom is n - 1 when calculating sample covariance. This is what I found:
1) Start with 2n degrees of freedom from the bivariate data
2) Lose 2 ...
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30
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10
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Sample two numbers from 1 to 10; maximize the expected product
Assume you sample two numbers, randomly drawn from 1 to 10; you could choose two strategies: 1) pick with replacement and 2) pick without replacement. Which strategy would you prefer to maximize the ...
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Covariance of two sample means
I am trying to derive the covariance of two sample means and get confused at one point. Given is a sample of size $n$ with paired dependent observations $x_i$ and $y_i$ as realizations of RVs $X$ and $...
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Variance and covariance in the context of deterministic variables
Questions:
Can we talk about:
variance of a deterministic variable?;
covariance between a deterministic variable and a stochastic variable?;
covariance between two deterministic variables?
Are these ...
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Why is Covariance Useful?
There are a number of topics related to covariance on this site. What I am having trouble grasping: why is covariance a useful thing to calculate?
As far as I see it, covariance is not a helpful ...
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2
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Variance of the sum of random vectors
Let $X_1, X_2, \dots , X_n \sim G$ where $G$ is some distribution and the samples are not independent. If $X_i \in \mathbb{R}$, then I know that
$$\text{Var}\left(\sum_{i=1}^{n} X_i \right) = n\text{...
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1
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Efficient way to compute distances between centroids from distance matrix
Let us have square symmetric matrix of squared euclidean distances $\bf D$ between $n$ points and vector lengthed $n$ indicating cluster or group membership ($k$ clusters) of the points; a cluster may ...
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2
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When are OLS linear regression parameters inaccurate?
Q1: Show quantitatively that OLS regression can be applied inconsistently for linear parameters estimation.
OLS in y returns a minimum error regression line for estimating y-values given a fixed x-...
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2
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Standard Deviation is to variance as ____ is to covariance?
I'm looking at the bivariate relationships among a set of time-series data that have the same units. I have computed the covariance matrix and am working on interpreting it. My hunch is that it would ...
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1
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formula for sample covariance: Bessel's correction
Two options for the sample covariance between X and Y:
1)(with Bessel's) COV(X,Y) = $1/(n-1)$ * $\Sigma$ $(Xi - mean(X))$*$(Yi - mean(Y))$
2)(without) COV(X,Y) = $1/n$ * $\Sigma$ $(Xi - mean(X))$*$(...
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1
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Uncorrected sample standard deviation in correlation coefficient
There seems to be a common use of the uncorrected sample standard deviation in calculating the correlation coefficient:
https://www.experts-exchange.com/articles/2728/Covariance-and-Correlation-in-MS-...
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1
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Dividing by degrees of freedom [duplicate]
When estimating parameters such as (I don't care about this specific instance particularly) Variance of a random variable X, one usually adopts Bessel's correction, i.e. using the formula $\hat{Var}{(...
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