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

learn more… | top users | synonyms

2
votes
0answers
26 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
8 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
25 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
10 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
57 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
14 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
21 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
27 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
10 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
42 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
50 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
51 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 = ...
0
votes
0answers
12 views

Combining two estimates of variance

I have a sample of N stocks, and a sample period of length T. At each time $t$, I have the following information: For each stock i, I have an estimate of variance (of returns) ...
2
votes
1answer
51 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 ...
2
votes
1answer
28 views

What is the variance of a Polya Gamma distribution?

I have a simple application that needs the variance of a Polya Gamma distribution (I know the mean since I found it here- http://arxiv.org/abs/1205.0310). This paper says that there is a closed form ...
0
votes
0answers
19 views

Separating variance due to treatment from variance due to sampling units

Consider a dancing competition where dancers are given a score between 1 and 100. Several teams participate in the competition, and each team gives several different performances. For each team, the ...
4
votes
1answer
58 views

ANOVA-type test but with known population variance of each group

I have a set of $N$ samples $s_{i}$, each one sampled from a normal distribution with standard deviations $\sigma_i$, which are known. I would like to know if the distributions have the same mean. I ...
1
vote
0answers
33 views

Unbiased estimator of the variance [duplicate]

I am going through the book The Elements of Statistical Learning and I'm finding it extremely terse. I have a background in probability but not statistics so perhaps that is why. Anyway, in Chapter 3, ...
0
votes
0answers
11 views

statistically analyse pass rate of test in different locations

I'm looking to analyse some data and as it's been a long time since my statistics days I'd like to know which area of statistics my problem lies. Lets say I have a number of different driving ...
10
votes
4answers
188 views

Is there a measure of 'evenness' of spread?

I looked up on the web, but couldn't find anything helpful. I'm basically looking for a way to measure how 'evenly' a value is distributed. As in, an 'evenly' distributed distribution like X: and ...
1
vote
0answers
35 views

What is the mean and variance of this probability distribution?

I don't know if this distribution has a name or not so the best I can do is describe how it is obtained. You start with two arrays of n uniform random variables U(0,1) where n>2. I will provide a ...
2
votes
1answer
74 views

How can I quantify the difference between two categorizations/distributions?

I have a sample of survey data comparing two populations, non-addicts (sample size about 50000) and addicts (sample size about 500). The differences between mental health evaluations of the two ...
0
votes
0answers
27 views

Solution to a problem

I came across a question in a book titled "An introduction to Generalized Linear Models" which is given below By adding $-\mu$ and + $\mu$, I found the solution to (b) as $S^2 = \frac{1}{n-1}[ ...
0
votes
0answers
22 views

What is variance and co variance related to time series?

I'm trying to understand the Mahalanobis distance method which makes use of a covariance matrix. However i am not clear about the idea of variance and covariance with respect to time series. And also ...
1
vote
1answer
29 views

Variance of Mean of Samples from Unknown Distribution

I have a bunch of IID samples from a random variable with unknown mean and unknown variance. I now need to know the variance of the average of these samples. I found some references. In decreasing ...
2
votes
0answers
32 views

Mean and variance of Cox process

Consider the (doubly-stochastic) Poisson point process with rate $ \lambda(t) = \rho e^{-t/\tau} $ where $\rho\sim\Gamma(\alpha,\beta)$ is a Gamma-distributed random variable. I require the mean ...
0
votes
0answers
6 views

Why high variance noise change the direction of eigen vector? [duplicate]

Why eigen vector turns towards direction of maximum variance?.I have observed that classical PCA fails in presence of outliers.Can u explain
2
votes
0answers
39 views

Sum of Bernoulli random variables

I need some help with a homework assignment. The question I'm given is: "Suppose that $X_1, X_2,..., X_n, W$ are independent random variables such that $X_i\sim Bin(1,0.4)$ and $P(W=i)=1/n$ for $i=1, ...
0
votes
0answers
20 views

sample size to estimate variance

I am trying to follow a thread Calculating required sample size, precision of variance estimate? and am facing difficulty understanding a step in the answer, specifically the step given below $ (n-1) ...
0
votes
0answers
12 views

Calculate variance of subpopulation given variance of overall population and its complement

I'd like to be able to calculate the sample variance for a subpopulation [B] given the sample mean and variance for its complement [A] and the overall population [A+B]. I have the sample mean and ...
1
vote
2answers
60 views

Motive behind preserving variance

Dimensionality reduction techniques preserve some properties of the data. I was wondering how preserving variance (as PCA does) can be helpful? Precisely speaking, PCA takes the covariance matrix and ...
2
votes
1answer
22 views

“Under the ANOVA null, within group and between group sample variance are both estimates of the pop. variance” — why only under the null?

In Statistical Methods by Snedecor and Cochran, it states something to the effect of "the within-group variance is an estimate of overall variance given the null hypothesis" and this point is used to ...
1
vote
0answers
42 views

variance of the variance for finite population for normal distribution

I am interested in calculating the variance of the sample variance for a finite population...of course in the limit of sampling the entire population, this will be zero. There seems to be one author ...
3
votes
1answer
61 views

You will randomly select 10 balls from the box with replacement what is $E(\bar X)$

A box contains 100 numbered balls - 21 with the number 1, 36 with the number 2 and 43 with the number 3. You will randomly select 10 balls from the box with replacement and you take the mean of the ...
1
vote
0answers
38 views

Minimum variance for sum of three random variables

I have been working on the following problem: Given you have VarX = 1, VarY = 4, and VarZ = 25, what is the minimum possible variance for the random variable W = X + Y + Z, or min Var(X+Y+Z)? My ...
1
vote
1answer
52 views

Is there a name or reference in a published journal/book for the following variance formula?

Variance can be combined as $$v=\frac{1}{n-1}\left(\sum_{i = 1}^{numGroups}n_{i}(m_{i}-m)^2+ \sum_{i = 1}^{numGroups}(n_{i}-1)v_{i}\right)$$ where $v$ is the combined variance, $n$ is the total ...
2
votes
0answers
28 views

Variance of difference of $x_{i,t}$ and $x_{i,t+1}$

We have $n$ observations of human performance before and after a training program. We have a random sample of $n$ individuals and assume population distributions are normal. We thus have: $x_{1,t},\ ...
5
votes
1answer
139 views

Are normally distributed residuals not necessarily homoskedastic?

Let's say I've ran a linear regression and I'm checking the model diagnostics. I made a histogram of the residuals and they appear more or less normally distributed as below. I thought for a long ...
0
votes
0answers
8 views

Scaling Specificity to larger data set

Suppose I have the following 2x2 table ...
0
votes
1answer
45 views

Variance of product of two random variables

I’m trying to calculate the variance of a function of two discrete independent functions. The first function, “f(x)”, returns a value of 0 with probability 0.243, a value of 1 with probability 0.306, ...
1
vote
0answers
72 views

Why is permutation test wrong with variance but correct with standard deviation?

I am trying to understand the limits of permutation testing. I wrote up a small permutation test example in R, and found that permutation testing seems to fail when using absolute difference in ...
1
vote
1answer
42 views

Asymptotic consistency with non-zero asymptotic variance -what does it represent?

The issue has come up before, but I want to ask a specific question that will attempt to elicit an answer that will clarify (and classify) it: In Poor Man's Asymptotics, one keeps a clear distinction ...
2
votes
1answer
39 views

Calculating the expected value and variance of an estimator of a normal quantile

I don't quite understand how to use the estimator function and the variance function and plug in the sample mean. I expected that we would plug in the value $\bar X - 1.645s$ into $E(s)$ and $V(s)$. ...
2
votes
1answer
62 views

Almost sure convergence and limiting variance goes to zero

Say an estimator converges with probability one and at the same time its variance goes to zero in the limit. How is it different than an estimator that converges with probability one but its variance ...
0
votes
0answers
31 views

Convergence of an estimator with infinite variance

Is it true that an estimator with infinite variance can converge both in probability and with probability one?
0
votes
0answers
33 views

Inter-cluster variance

Can you please help me understand how is inter-cluster (between clusters) variance defined? As opposed to intra-cluster variance which is pretty straightforward, I have not managed to found a clear ...
0
votes
0answers
29 views

Finite variance of harmonic mean estimator when samples are bounded

Harmonic mean estimator is notorious for the possibility of having infinite variance. Now I want to show that it has finite variance when samples are bounded. I am wondering whether my following ...
1
vote
0answers
23 views

Variance of weighted importance sampling when random variables are bounded

I am trying to find out whether the variance of weighted importance sampling can be shown to be bounded when the original samples are bounded. More specifically, say $Y_1, \cdots, Y_n\in\mathbb{R}$ ...