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Questions tagged [variance]

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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Two Approaches to Calculate the Variance of a Sum

I came across a problem today in which it indicated the weight of a baseball $X$ has mean 5 and variance $4\over25$. It then indicated a carton contains 144 baseballs, and we are to obtain $T$ the ...
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Understanding Conditional Variance Decomposition for Sensitivity Analysis (Sobol Indices)

I am trying to understand both terms of a formula that describe the variance of a model output, Y, in terms of its conditional variance, as below: $E_{X_i}\left(V_{X_{--i}}\left(Y\middle| X_i\right)\...
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How does model accuracy compare across the folds in cross validation

If we have two cross validation from KNN and linear regression like this: KNN: ...
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Best confidence interval for sample mean of any variable in L2

I was thinking about a very basic matter, and arrived at the conclusion I know a lot less about it than I thought. When people have data $ X_1^N $ sampled i.i.d. from a distribution: $ X_1^N \sim X $,...
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is coefficient of variation better measure of highly variable features?

I am trying find highly variable features (genes in my data) for downward consensus clustering analysis. I have used variation, median absolute deviation and coefficient of variation (CV) for finding ...
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Pooled Covariance Matrix with very different amount of samples per class

I have a dataset with 10 classes, and want to estimate the covariance. It turns out that due to numerical stabilitiy, it is much better to use a pooled covariance matrix. Suppose I have $N$ samples ...
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Relation between pairwise distance sum and sum of distance to mean (gap statistic)

I'm trying to understand the gap statistic used for optimal choice of $k$ in k-means clustering. I'm trying to understand part of the explanation which includes this equality: $D_k=\sum_{ij}\Vert x_i-...
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Total Variation Distance Uniform Distribution

Hello I am trying to solve the following but the answer is wrong and I cant seem to see my mistake. Question : Find the total variation distance between P = Unif([0,s]) and Q = Unif([0,t]) where 0 ...
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ACF plot shaded blue region

Please see ACF plot attached (Python). I would like to understand why the shaded region of my plot takes a curved shape? My understanding so far is that the confidence band changes because the ...
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41 views

How to estimate the mean and variance of a Gaussian distribution variable? [on hold]

I have two variables 2X and 0.5Y, both are independent and follows Gaussian distribution. How to estimate their mean and variance analytically? I want to know their individual mean and variance, then ...
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Summation of two Gaussian distributed data with different coefficient of mean and variance

I need some help on Gaussian distribution. i have two dataset, both are identical and independent distributed, but having mean as 2μ_1 and μ_2, same scenario for the variance. How can I add them? ...
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estimating the mean of constant + noise

(This is almost certainly covered in Statistics 101, but I missed that class..) I have a real-world sampled signal $S[t]$ that is a constant $\hat{S}$ plus some noise $\epsilon[t]$. My goal is to ...
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Differences in means of raster files

I am analysing long-term data on a raster. I group this data in three parts depending on a factor value. Now, I am taking means in each group pixel by pixel and would like to detect pixels on the map ...
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56 views

Var(XY), if X and Y are independent random variables [duplicate]

if X and Y are independent Random variable then what is the variance of XY?
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What happens with my variance if I multiply observations by 5?

Suppose a dataset with observation values: 2 3 4 4 2 Variance of this observation, assuming this is the entire population, would be: Where the average is: 3. ...
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99 views

Are i.i.d. random variables always associated with a distribution function? [closed]

It is known that independent and identically distributed (i.i.d.) random variables are mutually independent and each random variable has the same probability distribution as the others. However, is ...
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Combined Variance of two groups with different sample sizes [duplicate]

I have the mean and standard deviation for Male and Female groups in a study, I'm trying to get the combined mean and standard deviation. The two groups have different N's. I can get the weighted ...
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Variance of fitted level of a variable constructed from the fitted difference

I estimated an error correction model for $y_{t}$: \begin{align*} dy_{t+1} & =c(0)+c(1)*dy_{t}+c(2)*(y_{t}-c(3)-c(4)z_{t})\ + u_{t+1} \end{align*} where $y$ and $z$ are cointegrated. Let $\hat{dy}...
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Is there a mistake in the expression of this variance?

I'm busy reading through an econometrics textbook (page 147), and I don't understand the step $$\mathrm {Var}\left(n^{\frac 12}\left(\hat\beta - \beta\right)\right) = \boldsymbol{A^{-1}}\sigma^2\...
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60 views

Moving average process - stationarity

If we consider a moving average process of order 1, is that stationary? Because, although, the mean will remain the same for Yt and Yt+k, the variance and co-variance will change if you calculate ...
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Does the peak of a Normal Distribution mean anything? [closed]

What does the peak of a Normal distribution show? Let's say if I have a flat peak, does this mean I have a larger variance? What if I have a sharp peak? For example, Does the "blue distribution" ...
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38 views

Calculating the probability that the standard deviation is above or below a certain value

I'm given $n$ samples from a random number generator that produces normally distributed values. Can I calculate the probability that the standard deviation that the RNG uses is $\sigma > \sigma_{...
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How bias arises in using maximum likelihood to determine the variance of a Gaussian?

While reading Christopher M. Bishop Pattern Recognition and Machine Learning, I ran into the following explanation for why there is an error in estimating the variance of Gaussian distribution using ...
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Binomial distribution intituition for N

I am unable to convince myself intuitively as to why the variance of a binomial distribution increases with increase in n (number of trials). In general, I expect that as n increases, the distribution ...
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Is $s_0^2$ an unbiased variance estimator for a distribution that is symmetric around zero?

Let $X_i$ be a random variable, and define the following statistic $$ s^2_? = \frac{1}{n} \sum _i X_i ^2$$ Suppose that the $X_i$ comes from a symmetric distribution, is $s^2_?$ an unbiased ...
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What is the variance of the least of several series?

Given a number of series (or images) that are independent and have a Poisson distribution with the same mean, what is the variance of the series generated from taking the point-by-point minimum? i.e. ...
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How to find confidence interval for variance?

Well, I'm taking a statistics class online, and the problem goes like this: Drug concentrations​ (measured as a​ percentage) for 25 randomly selected tablets are shown in the accompanying table. For ...
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Variance of a Sum of Random Variable [duplicate]

Unsure about my teachers solution as she was not very convincing when she presented the solution and was quite confused herself. $$Y = a+bX+cZ \\ X \sim \mathcal{N}(4,\,\sigma^{2}_x)\\ Z \sim \...
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How can i make constant variance for ARIMA model?

I want to fit ARIMA model to univariate time series. For this i took log then difference twice but the variance of the series is not constant. i also try with box.cox transformation but variance is ...
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20 views

Average and Variance of the Rate of Change in a Continuous Variance

I have a continuous variable, $P_t$ whose evolution is unknown. However, I obtain a history of it i.e. $P_0, P_{dt}, P_{2dt}, ...... , P_T$. For a continuous process variable, I know that the rate of ...
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23 views

Correct approach to testing for homogeneity of variance across ~2000 conditional distributions?

I'm not well-versed in statistics so apologies in advance for struggling to ask this question the right way. Essentially, I have 1836 timeseries of stock prices. For each of these timeseries, I am ...
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Intuition for why the “interaction variance” in an ANOVA is an estimate for the population variance

As I understand it, the general idea of the F-test is to exploit two different ways of estimating the variance in the population if all values actually come from a single population (see my reply here:...
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Estimate for the error of an error?

Searching through Wikipedia and StackExchange I managed to understand that, for a set of $N$ normally distributed values, the unbiased variance $Var[s^2]$ of the unbiased variance $s^2$ of the ...
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How to detect and quantify a structural break in time-series (R)

Background So first some background to gauge the level of understanding I might have. Currently completing MSc thesis, statistics has been a negligible part of this although I do have a basic ...
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combining gridsearch with regression : how to estimate variance of residuals

I'm trying to do measurements based on image processing : first I do some image processing to find detect the pixels that changed between the background and my image, and then I perform a linear ...
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How robust is the normality assumption for two sample independent t-tests?

I'm working with a dataset where the distributions are non-normal. They are independent samples where the variances are roughly equal. Can I still run a two sample independent t-test? If not, is ...
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How are R2 and adjusted R2 mathematically related to the idea of explained variance?

I am trying to understand in what sense, $R^2$ and $R_{adj}^2$ represent the "explained variance." I can't find any similar question that explores the connection in mathematical detail. My current ...
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How can one variable show difference between samples, when the previous didn't? ( according to t-test)

I don't have Statistics background, and I'm trying to learn and perform some tests. I work in oligonucleotide purification, and I have two machines for that purpose. They should release the exact same ...
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Variance of Normal Order Statistics

Suppose we have $X_1, \cdots, X_n \overset{\textrm{i.i.d.}}{\sim} \mathcal{N}(0, 1)$ with $n > 50$, and let $X_{(1)}, \cdots, X_{(n)}$ be the associated order statistics. Are there any references ...
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proportion of total dataset variance explained by prior grouping in DAPC

I have read several treads but it still unclear to me how to estimate the proportion of variance that can be explained by a prior grouping when "Discriminant Component Analysis" (DAPC) is performed. ...
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Variance Of Betting Strategy

I have a Python model for football matches, and I backtested it against some data. I have a dataset of hypothetical profits / losses from the model, which I've standardised by dividing by the stake. I'...
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80 views

can I work out *the* standard deviation from a value given as “+/- 1 standard deviation”

I'm confronted by a table of values: 17.1 (16.6) 18.0 (9.5) 38.1 (22.5) 30.6 (16.7) In the left-hand column we have some mean values. I’m told that the values ...
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How to show that the error variance of the best linear predictor is inferior to the proportional predictor?

Let's consider the 1D case. How do we prove that the error variance of the Best Linear Predictor (BLP) is inferior than the Proportional Predictor (i.e. the Linear Predictor without the intercept)? ...
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Describing the spread of outcomes from simulations

In general, what is the term to describe the 5th and 95th percentiles of outcomes coming from a simulation study? Say we obtain a vector of outcomes y. In R we can ...
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22 views

How to test correlation of variances?

Assume I ask several people two walk 100 steps several times. After each of their walks, I keep track of how far apart their footsteps were and the total distance they traveled. Assuming these people ...
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Calculating variance of process with time-varying variance

This is a question stemming off a previous post I had regarding calculating portfolio volatility. For a portfolio consisting of multiple assets, I understand that there are multiple ways to calculate ...
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Maximum Possible Variation Ratio

When calculating the maximum possible variation ratio for a variable, what does k represent? Bachman and Paternoster (2017, p. 107) define the variation ratio as: ...
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How to use past attendance data to predict results of a change in time

My church has 3 services (830am, 10am, 1130am) on Sunday. I have attendance numbers for the past 9 months for each of those 3 services. The 10am service has become impacted, and the church is ...
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What is the marginal variance of the mean of $y$ if I only know the variance of the conditional mean of $y$?

Suppose an estimate for the conditional mean of $y$ given $x$ is $\hat{E}(y|x)$. Suppose the variance (or the variance estimate) of $\hat{E}(y|x)$ is known to be $V(\hat{E}(y|x))$ for all $x$. The ...
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Interpretation of Mean Square Error formula

This is a very basic question. I'm looking at a physical problem where one wants to estimate a parameter $\lambda$ of a system. Suppose I perform a measurement on the system. I call the (stochastic) ...