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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8
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3answers
295 views

Why does increasing the sample size lower the variance?

Big picture: I'm trying to understand how increasing the sample size increases the power of an experiment. My lecturer's slides explain this with a picture of 2 normal distributions, one for the ...
0
votes
0answers
15 views

Overestimating variance with MCMC

I'm working with a very specific type of proposal distribution in MCMC algorithm. To validate it I use a simple multivariave Gaussian with $\mu=0$ and $\Sigma$ an identity matrix. The proposal ...
1
vote
1answer
16 views

Is this problem convex ? (regularization term on xTw)

Suppose we want to solve the following: $$ \min_{w} f(x^Tw, y) + \lambda g(x^Tw) $$ with $f$ a (logistic) loss and $g$ something like a variance. Is this a convex optimization problem ? What are ...
0
votes
0answers
8 views

How to add a fixed variance structure do a GAM

I am using GAM to fit a smooth line to represent the recovery of timber stocks following forest harvest. The data is heterogenous and I do not want to transform it. I understand that a nice way to ...
-1
votes
1answer
85 views

Variance of two correlated variables

Suppose X and Y are two correlated random variables, and var(X), cov(X,Y) are known. Is there a unique solution for var(Y) and can we determine var(Y) by only using var(X) and cov(X,Y)?
-1
votes
0answers
22 views

What should be the mean and variance of the bivariate normal distubution in the interval [closed]

Condition: Suppose I have standard normal distibution X~N(0,1). But now I have calculate the mean and variance of the data which lies between a$<$X$<$0. Also explain me the casse of the ...
0
votes
0answers
15 views

Bootstrapping - Variance of Time Series with Micro-level Data

I have micro-level (individuals) time series data and I am able to calculate some aggregate statistic for each time period. The data is not a panel, so each month is a different cross-section of ...
2
votes
0answers
7 views

Measure of variance between two populations

I have a set of genes, each of which composed of $10$ values, $5$ coming from population $a$ and $5$ coming from population $b$. I would like to define a measure of the variation between the two ...
0
votes
1answer
22 views

How exactly can I determine if customer ratings are based on (employee) vs. just random variation?

We have customer satisfaction surveys, and I can tell at least SOME portion of the variance is due to the employee that helped them. The surveys are all phrased -- how would you rate EMPLOYEE on ...
2
votes
1answer
46 views

Radial distance?

I'm looking at some code that calls $$\sqrt{(\sigma_x^2)^2+(\sigma_y^2)^2+(\sigma_z^2)^2}$$ the "radial distance", where $\sigma$ is the standard deviation. What is the significance of this measure?
0
votes
0answers
11 views

Genetic algorithm for factor selection

I'm planning to implement analysis of variance for different levels of factors, the problem is that I have 20 independent factors. Of course, the best model should include only significant factors. Is ...
1
vote
1answer
24 views

Relate $Var(y)$ with $Var(y)_{(i)}$

How can I relate $Var(y)$ with $Var(y)_{(i)}$ where $Var(y)_{(i)}$ is de variance of the data with the ith item removed. It is necesary first relate $\bar{y}$ with $\bar{y}_{(i)}$ and it complicates ...
3
votes
1answer
27 views

Residual variance for glmer

I am running a glmer model and I want to determine the total variance. My data is for survival and it is coded as 0 and 1, where 1 represents that the individual survived and 0 represents that the ...
5
votes
1answer
63 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 ...
0
votes
0answers
8 views

Random process variance estimation

I need to estimate a variance (ensemble average) of a stationary random process (Vp). My measuring device has "internal" white noise, with its own averaged variance(Vn, which is known by the device ...
0
votes
0answers
18 views

Squared uncertainties: what may it be used for?

If the squared standard deviation of a set of values is the variance of this sample, then, what is the squared standard error of the mean of this sample ? and what may it be used for ? A quick search ...
0
votes
0answers
18 views

Variable bandwidth selection with Silverman's rule

In the formula for variable bandwidth selection, we end up with a standard deviation estimation. I have a hard time understanding what is exactly this standard deviation. Can you apply this method for ...
1
vote
1answer
25 views

Why is $E(u^2)=Var(y)$? (Binary Response Model)

I'm trying to show some results in binary response models, and a couple of the proofs use the "fact" that $E(u^2)=Var(y)$, but I can't see why this is. The setup is that $y$ takes on the value $0$ or ...
1
vote
1answer
21 views

Confidence interval for the variance when we know the mean of the population

We have $n$ random samples from a population which has normal distribution, and the mean of the population is known. How do we change the procedure of finding a confidence interval for the population ...
1
vote
1answer
50 views

Getting a meaningful metric for variation in this type of cyclical, panel data? WSS won't exactly cut it!

This is related to a previous question I have asked, but I am not after visualization but rather a meaningful summary statistic. Situation: I have many (150k) customers. Each generates his own ...
3
votes
3answers
57 views

What is the variance of an MLE for a trinomial distribution?

I am playing with the following trinomial (multinomial) distribution which can get values (a,b,c) with the probabilities: $(\theta^2, 2\theta(1-\theta), (1-\theta)^2)$. Say I have n observations from ...
0
votes
1answer
19 views

Variance of portfolio future values based on return distribution

I'm trying to estimate the distribution of future portfolio values based on the distribution of a portfolio's returns. First, to define some variables: Rt = simple return for period t rt = ...
0
votes
1answer
25 views

Compare two distributions of large sizes and unequal variances where one distribution is heavily skewed

My data is from cells that are treated under two different conditions and then their response to the condition is measured by one output variable. The cell populations in the two conditions are quite ...
0
votes
0answers
9 views

Combining several variances, obtained from weighted mean and moving average

I have three questions 1: Can variances for different mean calculations be combined to obtain the combined variance? \begin{equation} S = \sqrt{s_1^2 +s_2^2 + s_3^2} \end{equation} 2: When using ...
0
votes
0answers
25 views

DCC (Dynamic Conditional Correlation) in Stata - very low at beginning?

my question relates to posts found at the following links: Dynamic conditional correlation in Stata and Estimating correlation with DCC GARCH which provide great detail on calculating and graphing ...
0
votes
0answers
29 views

The effect of independent variables in linear regression

I have N numbers of dependent(X) and independent(Y) variables. X variables are log-normally distributed data so that I used linear regression on log-log scale to obtain expected values as E [lnX|Y=y] ...
1
vote
0answers
41 views

How can I verify that variance(factor)=1 from Exploratory factor analysis results?

I am reading upon Exploratory factor analysis. One of the assumptions of the Orthogonal factor model is that $$ \sigma^2(factor)=1 $$. Reference via "Applied Multivariate Statistical Analysis-by ...
3
votes
2answers
112 views

Unsure how to find the MLE for this model

The question I am trying to answer is confusing me as I don't know where to start to find a likelihood estimation The Question $y_i = μ + e_i $ where the $e_i$ are independent variables ...
0
votes
0answers
10 views

Variance of the second order stationary process's mean

So i have a second order stationary process with the following covariance function $r_X(t) = \alpha e^{- \beta |t|}, -\infty < t < \infty$ Now, $\bar{X} = \frac{1}{T} \int_{0}^{T} X(t) dt$ ...
4
votes
1answer
92 views

(Co)variance of product of a random scalar and a random vector

Given a random scalar $ x \in \mathbb{R} $ and a random vector $ Y \in \mathbb{R}^n $ that are independent, can it be said that: $$ {\rm cov}(xY) = {\rm var}(x){\rm cov}(Y) + {\rm var}(x)E[Y]E[Y]^T + ...
7
votes
2answers
183 views

How can you test homogeneity of variance of two groups with different sample sizes?

I have two groups of data that have different sample sizes and in order to be able to analyze both sets they must have the same variance. I was told I should use Bartlett's to test the homogeneity of ...
0
votes
0answers
14 views

Assessing variability in a multiilevel model

This looks like a classical problem, but I couldn't find an answer, maybe because I use wrong keywords in my search. Let's assume you are tracking company monthly revenue values over a couple of ...
1
vote
0answers
33 views

Generalized linear model using quasi-likelihood

I am going to fit a model using quasi likelihood, (because the dispersion parameter > 1, y is a binary data). But when I ...
0
votes
0answers
47 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 ...
0
votes
0answers
5 views

Finding an area of low variance for (robust) linear regression

In order to determine a function for a Good-Turing approximation of the number $N_r$ of distinct words that occur $r$ times in a hypothetical language corpus, I'd like to run a (log-)linear regression ...
3
votes
0answers
33 views

Meta-analyses for variance rather than means

What are the main complications / differences when conducting a meta-analyses where the metric of focus is not effect size (i.e., means) per se, but instead estimates of variances from models? Nods ...
0
votes
0answers
9 views

Infer the variance of a sensor

Let's say that we have bag of marbles. We grab a random marble, and measure its weight. But because our sensor is noisy, we take $m$ different measurements. We do this $n$ times, getting $m*n$ ...
1
vote
1answer
30 views

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 ...
0
votes
0answers
15 views

Optimal length of observation window

I have a sample of N stocks, with time-series of daily returns. For each stock, I would like to compute the sample univariate variance of returns, using a rolling window. These variance will be used ...
1
vote
1answer
73 views

What is the probability that a girl is taller than a boy, with boys ~N(68, 4.5) and girls ~N(62, 3.2)?

"Given that boys' heights are distributed normally $\mathcal{N}(68$ inches, $4.5$ inches$)$ and girls are distributed $\mathcal{N}(62$ inches, $3.2$ inches$)$, what is the probability that a girl ...
2
votes
0answers
15 views

linearization of an estiamtor

Suppose we have two variables $x$ and $y$ defined in some population, with all values of $x$ known. A Poisson sample is drawn, with corresponding inclusion probabilities $\pi_k$ that are proportional ...
1
vote
1answer
24 views

Linear Regression Point Estimates

Suppose we construct the linear relation (using least squares) $$\text{Weight} = \text{Height}\cdot b + c$$ As I recall from school 30 years ago, Weight is normally distributed with the mean of ...
2
votes
1answer
28 views

Choosing Variance for Gaussian Prior

I'm relatively new to bayesian inference, and was trying to apply a bayesian model in a real-world scenario. Let me describe the model in brief: We have $N$ i.i.d. random variables $D =(X_1, X_2, ...
2
votes
0answers
23 views

Regression variable conversion

There is a question that I cannot solve. They may be solved by variance and covariance but I couldn't. So I thought there should be another way to solve. Question: A researcher has a sample of 43 ...
0
votes
0answers
12 views

Minimising variation in lines formed by categories

The background I have data that looks like this: This is basically a plot of a certain transformation on the concentration of some chemical elements. Each line represents a different sample. ...
1
vote
1answer
62 views

Conceptual questions: Variance of a process

Wikepedia, at Variance of Autoregressive model, mentions an expression of variance for an AR(1) process. I am learning signal processing (beginner level) and facing difficulty in understanding some ...
2
votes
1answer
57 views

Closed form for the variance of a sum of two estimates in logistic regression?

In logistic regression with an intercept term and with at least one dependent variable which is categorical, is there a closed form for the variance of the sum of the intercept and the coefficient of ...
2
votes
2answers
53 views

Derive the LLN for a certain sequence

I have a sequence of dependent random variables $X_1, X_2...X_n$. Each RV is correlated with two other RVs and uncorrelated with the others.The ones that are correlated satisfy the condition ...
1
vote
1answer
53 views

Variance of function of sample mean

Let's say $X_1, X_2, ..., X_n$ are iid $N(\mu,1)$. We can estimate $\mu$ with $\overline{X}_n$, which is distributed as $N(\mu, 1/n)$. We can estimate $P(X \leq k)$ with $\widehat{\theta}_n = ...
2
votes
1answer
55 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 ...