The expected squared deviation of a random variable from its mean; or, the average squared deviation of data about their mean.

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5
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2answers
47 views

How can increasing the dimension increase the variance without increasing the bias in kNN?

My question is about understanding Figure 2.8 in The Elements of Statistical Learning (2nd edition). The topic of the section is how increasing dimension influence the bias/variance. I can roughly ...
2
votes
1answer
20 views

variance in test accuracy will increase as we increase the number of test examples؟

I see this statement on 1 that say a True statement on Machine Learning Context. The variance in test accuracy will increase as we increase the number of test examples. my challenge is why ...
1
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0answers
11 views

Derivation of Variance for formula of Cohen's d statistic

Cohen’s d is one of the most common ways we measure the size of an effecthttp://en.wikiversity.org/wiki/Cohen%27s_d. Cohen’s d simply a measures the distance ...
4
votes
2answers
41 views

Variance of slope

I have a bunch of data that I fit a linear regression to, and now I need to find the variance of my slope. Is there an analytical way to get this? If an example is necessary, consider this my data in ...
1
vote
1answer
44 views

Limiting variance of normal mean

In Casella's Statistical Inference,in Example 10.1.8 on page 470, it says that the limiting variance of normal mean $\bar X_n$, is $\lim_{n\to\infty}\sqrt n\text{Var}\bar X_n=\sigma^2$. However, since ...
0
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0answers
20 views

When the null model performs better than more complex models

Consider a matrix $X \in R^ {n \times m}$ representing $n$ samples and $m$ features. Also consider a matrix $y \in R^{n \times k}$ representing $n$ samples and $k$ target values. $y$ has continuous ...
0
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0answers
18 views

Time-partitions of sample size

I am struggling with explain something I read in a Whitepaper. The essence is as follows. Let's begin with a random variable $X$ defined as number of events in an hours. Further, we assume that $X ...
0
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0answers
9 views

Bootstrap analysis for the estimation of Coefficient of variance of a subset

I wanted to estimate the precision estimated as CV= se/mean of a sampling effort (fishing effort=12 gill-nets) of the mean catches based on fish abundances(CPUEmean). I used in R the function: CV ...
0
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0answers
22 views

Interpretation of variance component

In a report, I came across the following table and unfortunately there is no description for it. I have very limited knowledge of statistics. Could someone kindly let me know what the interpretation ...
0
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1answer
9 views

I get a different result when I try and calculate the mean-variance formula of risky and riskless asset [closed]

I'm having trouble seeing how the expected return of a two asset portfolio, where the weight of the risk-free asset is positive, but the weight of the risky asset is negative, results in the final ...
1
vote
1answer
55 views

Relation between variance of eigenvalues and the effectiveness of PCA on the data

If the covariance matrix has eigenvalues $$\lambda_1 \ge \lambda_2 \ldots \ge \lambda_d > 0,$$ why is the variance of the eigenvalues, $$\sigma^2=\frac{1}{d}\sum_{i=1}^d (\lambda_i-\bar ...
1
vote
0answers
30 views

Item discrimination of poorly targeted items

In test theory, it appears to be widely recognized that very "easy" or "very difficult" items, relative to the ability of the sample of respondents, will have deflated correlations with the rest of ...
3
votes
1answer
22 views

Does it make sense to calculate the variance of a percentile measurement of a timeseries?

Developers often look at a percentile measurement of how long a task takes to complete as a measure of performance (e.g. 95th, 99th percentiles of page render time). However, in order to measure the ...
1
vote
0answers
32 views

calculate the variance of future value of a portfolio

I am trying (with no luck so far) to calculate the variance of future value of a portfolio. $E= \frac{(1+r)[(1+r)^{t}-1]}{r}$, $r$ is normally distributed random variable. How to calculate ...
0
votes
1answer
14 views

percentiles of deviation

Disclaimer - I am an amateur and self taught in stats so I apologize if the answer is painstakingly obvious. From what I've read, the average can sometimes hide data regarding extreme values and that ...
1
vote
1answer
22 views

How would you find the variance of an autocorrelated error?

Given the equation $e_t = pe_{t-1} + v_t$, and given the values of p and $Var(v_t)$, how would you calculate $Var(e_t)$?
1
vote
1answer
47 views

What is the demonstration of the variance of the difference of two dependent variables?

I know that the variance of the difference of two independent variables is the sum of variances, and I can prove it. I want to know where the covariance goes in the other case.
0
votes
1answer
30 views

Calculating variance [duplicate]

I am provided the following details (see picture) about a sample whereby $x$ is logarithm of income. How do I calculate the sample variance from this information?
0
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0answers
20 views

Equivalent to Welch's t-test in GLS framework

How can Welch's t-test be expressed as a generalized least squares model? A standard independent samples t-test (where it is assumed that the samples being compared are drawn from populations with ...
7
votes
1answer
133 views

What's the minimum of $\mu (1-\mu)/ \sigma^2$ over all continuous unimodal distributions on a bounded interval $[0,1]$?

All distributions on a bounded interval $[0,1]$ satisfy: $$\sigma^2 \le \mu (1-\mu)$$ where $\mu$ is the mean and $\sigma^2$ the variance. Now suppose that the distribution is unimodal, in the ...
5
votes
1answer
83 views

Does the uniform distribution have the greatest variance among all concave distributions on a bounded interval?

The uniform distribution on a bounded interval $[a,b]$ has variance $(b-a)^2/12$. Consider any concave distribution on the same interval (concave in the sense that the graph of the pdf lies above any ...
0
votes
1answer
12 views

How to say whether the variances of multiple groups are different?

I am building a hierarchical model for prediction purposes, and I am considering modeling the variances of each group in addition to the means. This is a graphical depiction of what I would like to ...
17
votes
4answers
916 views

Why shouldn't the denominator of the covariance estimator be n-2 rather than n-1?

The denominator of the (unbiased) variance estimator is $n-1$ as there are $n$ observations and only one parameter is being estimated. $$ ...
0
votes
0answers
14 views

Practical application of Cramer-Rao lower bound to calculate the variance of estimator

I would like to use the Cramer-Rao lower bound to help me estimate the variance of my maximum likelihood estimator, across a range of different samples of data. My question is, how do I do this ...
0
votes
0answers
17 views

Relation between raw and central moments

This question arose when reading Johansen's likelihood-based inference in cointegrated VAR models, the 2009 reprint, page 146. I will do my best to make my post self-contained. Let $Z_{0t}=\Delta ...
0
votes
0answers
61 views

How can the R-matrix in a mixed model be estimated?

In Henderson's Mixed Model equation: $y = X\beta + Zv + \epsilon$ where the joint variance of v and the error term is: $Var\begin{bmatrix} v \\ \epsilon \end{bmatrix} = \begin{bmatrix} G & ...
1
vote
1answer
21 views

How to Estimate the Error Term in a Heteroscedastic Model with Regression Through the Origin

Suppose we have a NO INTERCEPT model, $$y_i=\beta x_i+e_i$$ where $e_{i}$ follows a N(0,$\sigma^2 x_i^h$), so $e_i$ is equal in distribution to $e_{0i} x_i^{\frac{h}{2}}$, where $e_{0i}$ follows a ...
0
votes
0answers
6 views

Generating a random field from given power spectrum

How can I generate a random field in configuration space from a given power spectrum P(k)? I guess the variance of the distribution from which I extract the values of the field should be related in ...
0
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0answers
6 views

Variability of an attribute

In the biostatistics field, every subject has an attribute X that can be measured (blood test, etc..). There is a drug that some subjects need to take to treat some condition. This drug creates a side ...
0
votes
0answers
10 views

Anova Post Hoc Test

I am running an anova in SAS on the average hours worked for a country. With those countries grouped into 3 regions. When I run the anova I get a F value of 3.64 and P-value 0.0379. With these ...
2
votes
1answer
33 views

How does this expected value translate into a conditional variance?

I'm working with a simple local level model in a textbook \begin{align} y_t &= \alpha_t + \epsilon_t, \qquad \epsilon_t \sim N(0, \sigma_\epsilon^2) \\ \alpha_{t+1} &= \alpha_t + \eta_t, ...
2
votes
0answers
36 views

MLE estimate of normal distribution

I am quoting this from Greene's econometrics book: The occasional statement that the properties of the MLE are only optimal in large samples is not true, however. It can be shown that when ...
1
vote
0answers
27 views

Confidence interval for variances

I have a lot of variances $\sigma^2(x)$ as these: Now I have two task: remove the vertical outliers and compute the confidence intervals (for all cases, this is only one case). I think that their ...
2
votes
1answer
53 views

Calculating effect size (lnR) variances for studies with different study designs for use in meta-analysis

My question concerns the calculation of effect size variance for studies that are going to be included in a meta-analysis. I want to calculate variance so that I can weight each study by the inverse ...
1
vote
0answers
11 views

Varaince decomposition without stochastic variance

I am working on an analysis that doesn’t feel natural until now. I am trying to analyze a dataset that consists of the prediction results of forest growth simulators, so actually I’m trying to make a ...
1
vote
0answers
25 views

Getting a combined variance, given two variances

I'm getting two error variance values from two third-party sensors, and need to multiply these variances with the position state estimates of the target they're tracking. Once that's done, the ...
0
votes
0answers
32 views

Variance of random walk

A discrete random walk $X_t$ starts today. We are asked what to prepare for the next years. Is this correct: $ var(X_{2 years}) = 2 \: \: \int_{2\pi f}^{\pi} \:\: \phi(w) dw $ i.e. summing the ...
0
votes
0answers
9 views

Distribution-specific variance component to use with R-squared for ordinal logistic GLMM

I think this should be straightforward, though I cannot find an answer after digging around a lot within work by Nakagawa et al. on $R^2$ values for GLMMs. My question is similar to that posed before ...
3
votes
1answer
100 views

What's the difference between the variance and the mean squared error?

I'm surprised this hasn't been asked before, but I cannot find the question on stats.stackexchange. This is the formula to calculate the variance of a normally distributed sample: $$\frac{\sum(X - ...
0
votes
0answers
17 views

Power spectrum of unlogged AR(1) process

Our variable of interest $X$ is nonnegative. We model $ \log(X) $ as AR(1) process. $ \log(X) $ power spectrum: $ S_{xx}(w) = \frac{\sigma^2}{1-\varphi^2} \frac{\gamma}{\omega^2 + \gamma^2} $ What ...
0
votes
0answers
7 views

Reference for explained variance situation

I have a data set with 5 parameters and 1 output. I am working on a regression problem and I've build different models by first using 1 input parameters, then 2, then 3, ..., untill the model uses 5 ...
-1
votes
1answer
33 views

Binomial distribution [closed]

folks! The problems is Suppose you can make free throws at a 70% rate. Let X be the number of free throws you make in 20 tries. Model this with a binomial distribution: 1)?= E[X] 2)?=Var[X] ...
1
vote
2answers
52 views

The meaning of scale and location in the Pearson correlation context

According to wikipedia, pearson correlation is scale and location invariant. Does scale refer to "variance" and location refer to "mean" ? Thanks.
0
votes
1answer
64 views

Generating data from Probit regression, cut off 0 and variance 1 necessary?

I am trying to create a dataset using a Probit regression model in R, where I have an intercept and three covariates. I first fix a set of coefficients for the three covariates, generate these ...
1
vote
1answer
23 views

Relationships of two regressional coefficients

I have two one dimensional dataset $X$ and $Y$. I run regression and obtained $A$ from $Y = AX$. And another regression and obtain $B$ from $X = BY$. What's the relationship between $A$ and $B$? Is ...
2
votes
0answers
44 views

Why is normality assumption so important (even for large N) for Chi-square test for the Variance

In my textbook i found the note that for a Chi-square test ($\chi = \frac{(n-1) \cdot s'^2}{\sigma^2}$) the assumption of a normal distribution in the population is very important - and much more ...
3
votes
1answer
75 views

One sample test of uniformity in R

I have a dataset of two columns: one with IDs and one with a column of single digits (0-9) (see below). I would like a statistical significance test for whether the data is uniform. Ideally, I would ...
0
votes
0answers
13 views

variance of data of correlated poisson means?

I want to find the mean and standard deviation for the data for the following question. We have 10 houses of known different sizes. The number of people living per square meter has a poisson ...
2
votes
1answer
29 views

Why is the variance of a moving average process calculated this way?

I have a moving average process that looks like: $$ Y_{t}=\frac{e_{t}+e_{t-1}}{2} $$ And I can see that the variance has been calculated as follows: $$ {Var}\left ( Y_{t} \right )={Var}\left \{ ...
0
votes
0answers
40 views

Wrong variance of mean

I'm told that the $Var(\overline{x}) \approx Var(X)/N$, where $\overline{x}$ is the mean of $N$ elements from $X$. However, I have a data set where these variances seem to differ by a factor of about ...