**2.384 variance questions.**

I am following the Hunter-Schmidt method for a meta analysis of Pearson r values.
I am wondering if there is a way in which to create 95 % credibility intervals when I have a negative value for ...

I had to translate several given statistics equations into code, and I came across this formula:
Variance of a simple random sample $= \frac{p(1-p)}{n-1}$
The sample in question are test letters ...

In baseball, Bill James suggested using, to predict next season's winning percentageruns_scored^2/(runs_scored^2 + runs_allowed^2), rather than this season's ...

I am comparing two temperature control devices both designed to maintain body temperature at exactly 37 degrees in anaesthetised patients. The devices were fitted to 500 patients forming two groups. ...

I am using KPSS test to verify if my process has constant variance around the mean, but I am not sure if this is the correct test for my case. In KPSS the null hypothesis is that the process is ...

When conducting a (variance-based) sensitivity analysis, should I set the range of a specific parameter to its maximum allowable range, or restrict it to something more appropriate for my specific ...

Consider a normal vector $Y \sim \mathcal N(\mu, V)$ with $\mu \in\mathbb R^n$ and $V\in\mathbb R^{n\times n}$. I am interested in the expected value of
$$ {1\over n-1} \left( Y'Y - {1\over n} (\...

I want to run a two-way ANOVA. I have unequal sample size and equal variance. Can I run the analysis?

I need to calculate $\text{VAR}[\bar X]$ where $X_i$ are random sample of size $n$ from a normal distribution with mean $\theta$ and variance $\sigma^2$.
So I do $\text{VAR}[\bar X] = E[\bar X^2] -(...

I want to add noise to a given time series of data. The noise is to be generated using a distribution technique. For example for an interval of 10 min I have 60 entries which sum upto say 13643Kw. ...

More generally, if $\{X_n\}_{n\in\mathbb{N}}, X$ are real random variables with finite variance such that $X_n\xrightarrow{d}X$, what are some sufficient conditions to assure that $\operatorname{Var}(...

Consider a set of distinct numbers. After removing both the max and the min from the set and adding the median to the set, the set of numbers obviously becomes less dispersed and the variance should ...

Given that the median seems to be a more robust statistic than the mean/average, I was wondering if there is a solution of the maximum entropy distribution given the median (or the median and some ...

Assume that I trained a nonlinear model , one feature of the training data has very low variance, because of this, the same feature of the test could be quite different, at least in scale, from the ...

I am trying to derive the ridge approximation formula for the lasso variance, but I am stucking at one point.
As statet in the originial paper of tibshirani the penalty term can be transformed to $\...

Suppose that $X$ and $Y$ are scalar random variables that are jointly normally distributed:
$$
\begin{pmatrix} X \\ Y \end{pmatrix} \sim N \left(
\begin{pmatrix} \mu_x \\ \mu_y \end{pmatrix}, \begin{...

I'm quite a newb at statistics and interpolation, and I cannot understand how to interpret the error estimation computed by Kriging.
For example, I performed kriging on temperature values (Celsius ...

Consider three time series x, v, w
The distribution of the values that x,v,w take are zero-mean Gaussian, stationary and independent of time (no temporal colleration) and of each other. We know the ...

I am conducting a meta analysis of Pearson's r correlations. As there are two correlations , sometimes three , for the same study and dependent variable I have averaged the correlations via fishers z ...

Suppose I have a matrix
$$ \hat X = \begin{pmatrix}
\hat a
\\
\hat b
\end{pmatrix}$$
under which circumstances is the following statement true
$$ \hat X^T \hat X = var(X) = \begin{pmatrix}
var(\...

I am working on this problem where I have 20 odd features (input variables) and two dependent variables. The objective is to find the variance structure of one of the dependent variables. More ...

I understand that to calculate the standard error of a pearsons r correlation converted to a z score you follow -
1 / (āNā3)
But how do you calculate the variance from the standard error please? I ...

From Wikipedia: https://en.wikipedia.org/wiki/Residual_sum_of_squares, the RSS is the average squared error between true value $y$, and the predicted value $\hat y$.
Then according to: https://en....

I've been reading about asymptotic variances, and wondered if there exists something like a conditional asymptotic variance. For example, if $\hat{\beta}$ is the OLS estimator then
$$Avar(\hat{\beta})=...

Note: while I asked if is ok or not to add a constant to the log response ratio here, with this question I focus specifically on the formula of the variance of the log response ratio when adding a ...

I know that we can calculate the standard error for the AUC for all estimators, assuming that the conditional density is fixed. What I'd like to do, however, is additionally account for the randomness ...

I have data for 300 devices and each device has been tested a different number of times so some devices have 2 data points and some have 8. For example, one device scored 5, 6.5, 6.5, 6, 6, 6 whilst ...

Does applying standard normalisation to data variables mean changing the distribution of data variables to normal distribution having mean=0 and variance=1?

Why are so many efforts spent on estimation and comparison of mean, but not variance?
For example, t-tests are used to comparing the population mean.
When reporting the data, we usually describe ...

Let $A$ and $B$ be two constant matrices and let $x$ and $ y$ be two random vectors, what is the general formula for $Var(Ax+By)$? I know the formula for when $x$ and $y$ are scalar random variables ...

I have a set of data which are responses to ten questions.
I have done some text analysis which gave me 10 similarity matrices (one for each question) between all responses for each question.
I ...

How can I express the following analysis of deviance in an ANOVA table , by hand not with R..

I am trying to prove, under the assumption $E[u_t^2x_t^Tx_t]=\underbrace{E[u_t^2]}_{\sigma^2}E[x_t^Tx_t]$, that the
$$AVar[\beta_{POLS}]=\sigma^2 E[x_t^Tx_t]^{-1}$$
My result:
$$\begin{eqnarray}AVar[...

My interest is to develop a relation of the correlation coefficient when the data (both the dependent and independent variables) have measurement errors.
Intro
The measured values are related to the ...

Will someone please explain what the difference is between standard error and margin of error and when to use which? I have not had luck finding a simple explanation on the differences anywhere on the ...

How does one estimate the standard error of the leave-one-out cross-validation estimate of the prediction error?
For each fold (leave out the $i^{th}$ observation), the LOOCV estimate of the ...

I read from Elements of Statistical Learning that the leave-one-out cross validation estimator has high variance, and I read the related stackexchange posts as to why this is the case 1. But I'm ...

In a simple regression, that is clear from the formula of the standard error of the estimator $ \hat{\beta} $:
$${\displaystyle s_{\hat {\beta }}={\sqrt {\frac {{\frac {1}{n-2}}\sum _{i=1}^{n}{\hat {\...

A predictive model that I currently use relies on PCA with varimax rotation to reduce the dimensionality of the data (whether this is appropriate is a separate question).
The dataset consists of ...

I am building a predictor for $y = f(x)$ using training samples ${(x_i, y_i)}$ (assume) drawn i.i.d from some distribution $p(x,y)$, by optimising the empirical L2-loss:
$f(x) = argmin_f \; \sum_i ||...

Sorry that this might be a very simple question, but I got confused: say we have a Binomial distribution $Bin(n, p)$, and two random variables, $X$ and $Y$, drawn from it.
Is the covariance between $...

I found this term on the Keras blog website, quoted below
Your main focus for fighting overfitting should be the entropic capacity of your model --how much information your model is allowed to ...

There is an example given on the Scikit-Learn site that compares the bias-variance decomposition of the rmse of a single SVR model against a bagging ensemble. Unfortunately, the data is being ...

I have a data set that has been divided into $n$ data subsets.
I am sampling from each of these subsets and getting a tuple consisting of mean, variance, confidence and number of sampled points used.
...

I have a simple model in INLA (the regressor is a single model=iid term), which reports the precision of the hyperparameter. How ...

I have data that I am attempting to model with negative binomial regression. However, I am aware that this data has a high degree of variation (I am looking at patent count data - a significant number ...

How is the var/cov error matrix calculated by statistical analysis packages in practice?
This idea is clear to me in theory. But not in practice. I mean, if I have a vector of random variables $\...

TL,DR: It appears that, contrary to oft-repeated advice, leave-one-out cross validation (LOO-CV) -- that is, $K$-fold CV with $K$ (the number of folds) equal to $N$ (the number of training ...

I am measuring the proportion of a sample that gets all successes in 10 different questions of a survey. For example, one question is "Do you smoke?" and a success for me is "No". Another question ...

How do different cross-validation methods compare in terms of model variance and bias?
My question is partly motivated by this thread: Optimal number of folds in $K$-fold cross-validation: is leave-...

- regression
- self-study
- mean
- mathematical-statistics
- standard-deviation
- r
- covariance
- normal-distribution
- expected-value
- distributions
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- anova
- probability
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- estimation
- random-variable
- hypothesis-testing
- correlation
- heteroscedasticity
- machine-learning
- sampling
- pca
- sample
- confidence-interval
- mixed-model

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