All Questions
4,885 questions
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Monte Carlo simulation with Importance Sampling - variance of estimator vs weighted variance
I am using Monte Carlo simulations associated with Importance Sampling and I have some difficulties interpretating the variance estimator:
Using a dummy example extracted from here, I use Monte Carlo ...
- 1
1
vote
1
answer
77
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If the errors are homogenous but non-normal, can the linear estimator be BLUE?
Under the Gauss-Markov assumptions, the requirements for OLS to be BLUE are:
Linearity: The estimator must be a linear function of the data
Unbiasedness: The expected value of the estimator should ...
0
votes
0
answers
42
views
Modeling time-varying variance of a signal
I have a signal whose variance varies in time
It turns out, by observation, that these fluctuations of the variance arise when some other variables (let's call them input features) transition sharply ...
- 262
1
vote
2
answers
215
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Are intraclass correlation (ICC) and the correlation within groups related concepts? How so?
I'm attempting to re-learn linear mixed-effects models with lmer via some tutorials online, but I'm struggling with the concept of intraclass correlation (ICC). I'm ...
- 2,071
1
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0
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26
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Bishop Gaussian Basis
In Pattern Recognition and Machine Learning by Christopher Bishop he says in Section 3.3.2 titled Predictive distribution
If we used localised basis functions such as Gaussians, then in regions away
...
- 11
4
votes
2
answers
393
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Can standard deviations from multiple studies be averaged to use for a sample size calculation?
Imagine you are planning a clinical trial to evaluate the effectiveness of a new treatment for improving VO2peak in patients with chronic stroke. Based on an initial study by Jin et al., you estimate ...
- 43
4
votes
2
answers
181
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Deriving MSE($\hat{\beta}$) under Linear regression
I was able to derive the MSE, but there's a part of the derivation which I don't really get. Here's what I got:
Facts:
$\mathbb{E}(\hat{\beta})=\hat{\beta}\space$ (unbiased estimator)
$\text{Cov}(\...
- 389
1
vote
0
answers
13
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Spatial effects competing for variance with error term?
I am simulating a dataset from a spatial model. Each data point is distributed as follows:
$$
y_i \sim \mathcal{N}(\mu + \phi_i, \sigma^2)
$$
Here $\mu$ is a fixed value, estimated as an intercept. ...
- 43
1
vote
0
answers
37
views
How can I measure Monte Carlo convergence in distribution with heavy tails?
I'm performing a Monte Carlo study on a simple agent based simulation, and I'm trying to formulate a heuristic for the number of MC samples to use. I'm able to measure convergence of statistics like ...
1
vote
1
answer
41
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Question About Approximating the Variance of the Sample Mean for an AR(1) Process
$
\newcommand{\on}[1]{\operatorname{#1}}
\newcommand{\ol}[1]{\bar{#1}}
\newcommand{\Cov}{\on{Cov}}
\newcommand{\Var}{\on{Var}}
$
Problem Statement: Suppose that the time series data $\{x_i:i=1,\dots,N\...
- 6,039
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36
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Fitting a regression line which passes through the anchor point
In our setting, we have data $X_1, \ldots, X_n$, which can be ordered as $X_{1,n}\leq X_{2,n}\leq \ldots \leq X_{n,n}$ and we have the points $(-\log (1-\frac{i}{n+1}), X_{i,n})$ for $i=1,\ldots,n$.
...
- 656
0
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0
answers
39
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How to check the Variances between 2 estimators are same or not
Let say I have 2 batches of electric bulb from some manufacturing processes
First batch was run from 10 am to 2 pm (just assume). In this batch total $N_1$ number of bulbs are produced and among them $...
- 415
5
votes
1
answer
114
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How to report the between study variance through tau2 for vaccine effectiveness using R's metafor?
My colleague and I have been performing a meta analysis using R's metafor package and the rma.uni function to estimate pooled ...
4
votes
1
answer
95
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Is this equation of the GARCH(1,1) model correct?
I am new to the GRACH model and have read many papers, but I am confused about the equation provided below. Is the equation (15) correct? If the $z_{t}$ is the error, why does the author define them ...
- 292
1
vote
1
answer
58
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Identify maximum in quadratic regression
I am looking for a way to find the maximum in a quadratic regression.
Specifically, I have two variables X and Y. Y is a discrete and commonly used scale representing the severity of a disease, ...
- 433
0
votes
1
answer
36
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Independence of regression coefficients
Possibly a basic question but am doubting myself.
I have iid samples $(Y_i,X_i,W_i,Z_i)$. I am interested in performing the two following regressions:
$Y = \alpha_0+\alpha_1 X+\alpha_2 Z$
$Z = \beta_0+...
- 122
0
votes
1
answer
44
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clarification on Variance formula [duplicate]
It is possible to calculate the variance using two formulas. one is dividing by n and the other is dividing by n-1. Thus, my question is that
is the result we get by dividing (n) and (n-1) the same?
...
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2
votes
1
answer
40
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Why sum of squares to calculate dispersion [duplicate]
The variance gives an idea of the dispersion of a distribution. To calculate the variance the sum of the difference of each value with the mean, each of these differences squared, is required. The ...
- 21
0
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0
answers
45
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Asymptotic Variance of the 'naive' estimator in measurement error model
Consider the classical measurement error model:
$$Y= \beta_0 + \beta_1 X_1 + \beta_2 X_2 + \varepsilon$$
where $W=X+U$ is observed. X is the 'true' quantity and U is the measurement error. Var$(X) = \...
0
votes
1
answer
120
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How to estimate the variance of the regression coefficients via Variance-Covariance Matrix?
everyone
I am not used to the matrix algebra. I know the maximum likelihood method to get the point estimation of the regression coefficients well. However, I don't understand the mathematical method ...
- 41
0
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0
answers
29
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Per-Item inter rater reliability with multiple values and raters
I am trying to find the best statistical calculation to measure the agreement between 72 different raters on one item. My goal is to convey in a statistic how spread the raters are on their rating and ...
- 101
5
votes
2
answers
346
views
What is the median of the minimum or maximum of multiple samples?
Suppose I have a variable with a known distribution, and suppose I sample that variable k times and record the minimum. If I repeat this many times, will the median of the minimum converge to a ...
- 55
3
votes
1
answer
96
views
Variance of the estimator of unconditional mean of AR(1) process
AR(1) process is defined as: $y_t=c+\phi y_{t-1}+\varepsilon_t$ where $\varepsilon_t$ is IID with mean zero and variance $\sigma^2<\infty$. For a stationary process, i.e. $\phi\ne 0$, the ...
- 62.3k
1
vote
0
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32
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Conditional variance of random walk with given start points and ending points
If I have a random walk with 0 drift and I observe that $X_1 = x_1$ and $X_k = x_k$, bu I don't have all the points from $X_i$ for $i \in \{2, ..., k-1 \}$, how do I estimate them and given an CI? I ...
- 235
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0
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12
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Covariance of multivariate negative binomial with random effects
I am fitting a negative binomial-2 regression model where there is a multivariate normal random effects term. I would like to find an equation for the covariance of two outcomes. In "the ...
- 53
2
votes
0
answers
48
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Understanding Volatility Clustering: Conditional or Unconditional Variance?
A stylized fact observed in financial time series is volatility clustering. Volatility clustering is commonly described as the fact that large changes in asset prices are followed by large changes, ...
- 1,465
2
votes
1
answer
39
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analytical asymptotic approximation of the expected maximum, mean, and minimum distance of nearest neighbours in unit ball
Say I uniformly at random distribute $x = n^3$ (independent identically distributed) points in a ball of radius $r=1$ in $\mathbb{R}^3$.
What can be said about the expected maximum, minimum, and mean ...
- 277
4
votes
1
answer
281
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Can I include a variable related to the outcome variable into statistical analysis?
My research question is about the contact patterns during the pandemic and what characteristics of people who contacted more person during the national lock down.
The outcome variable is a variable ...
- 301
1
vote
1
answer
48
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Is the variance of the mean of a set of possibly dependent random variables less than the average of their respective variances? [closed]
Is the variance of the mean of a set of possibly dependent random variables less than or equal to the average of their respective variances?
Mathematically, given random variables $X_1, X_2, ..., X_n$ ...
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5
votes
1
answer
216
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In a sum of high-variance lognormals, what fraction comes from the first term?
If $X_i \overset{\textrm{iid}}{\sim} \text{Lognormal}(0, \sigma^2)$ for $i=1,\ldots,n$ and $Y_1 = X_1 / \sum_{j=1}^n X_j$, then I would expect that a particular* limiting distribution of $Y_1$, ...
- 195
2
votes
1
answer
52
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Why can the standard error of the weighted mean be smaller than the standard errors of the individual measurements?
I am combining two independent measurements with their respective standard errors using a weighted mean. The measurements are:
It seems counterintuitive to me that the standard error of the weighted ...
- 63
13
votes
3
answers
999
views
What does it mean for observations to be uncorrelated and have constant variance?
I am learning about linear regression from the textbook Elements of Statistical Learning by Friedman, Tibshirani, and Hastie. In this section they suppose we have a set of training data $(x_1, y_1), \...
- 343
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0
answers
17
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Declustering impact, stationarity and discretization
I have a seasonal time series, and I am considering declustering (before any other preprocessing steps) it using runs declustering. If I observe an extremal index of 1, can I claim that my data is i.i....
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1
vote
0
answers
20
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central moments of random variable from _estimates_ of draws from the distribution function
I am trying to estimate the first two central moments of random variable $r$. The information I have about $r$ is a set of estimates $\hat{r}_i$ for $i \in \mathcal{I}$, each with corresponding ...
0
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0
answers
18
views
Measurement error R in Kalman Filter [duplicate]
I want to calculate the measurement error R for Kalman filter if I have such data:
True value of the golden bar is 18 g. A tool was used to measure the weight of the bar: 17.7, 17.8, 18.1, 17.8.
How ...
0
votes
1
answer
47
views
Variance around true value, not mean
The water temperature is 19 C, which is true value.
I have measured the temperature of the water and I received such results: 18.7, 18.8, 19.1, 18.8. Can I calculate variance here around true value (...
1
vote
1
answer
26
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Estimate sample variance of return-on-ad-spend (ROAS)?
I'm trying to make sense of the correct method to calculate the variance of ad-revenue for my marketing company. During an a/b test we need to estimate the sample variance to compute our confidence ...
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1
vote
2
answers
44
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Calculating variance between paired samples, where one sample is constrained to always be the lower bound?
I'm sure this is a solved question, but I haven't been able to hit on the right search terms.
Suppose I have paired samples A and B. A represents a derived variable (say distance "as-the-crow-...
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votes
1
answer
27
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Unbiased and consistent estimator with positive sampling variance as n approaches infinity? (Aronow & Miller) [duplicate]
In Aronow & Miller, "Foundations of Agnostic Statistics", the authors write on p105:
[A]lthough unbiased estimators are not necessarily consistent, any unbiased estimator $\widehat{\...
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2
votes
1
answer
205
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Expected Value Chi Square distribution
I'm trying to simulate the distribution from the sample variance $s^2$ and compare it with the theoretical distribution.
Therefore, I perform a fairly simple simulation (upfront, I'm not a ...
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5
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1
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59
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In Regression Through the Origin, why do the CIs of the slope depend on datapoints with zero x value?
I'm working with a Regression Through the Origin model as described in this reference.
The model is $Y_i = \beta X_i + \epsilon$ and the least squares estimate of $\beta$ is $\hat\beta = \frac{\sum ...
- 151
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1
answer
91
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Emtrends pairwise comparisons all have same standard errors. 3 way interaction
I have created a linear mixed model and am using emtrends to determine the impact of a dichotomous variable on the effect of a continuous variable, across levels of a categorical variable. Is it ...
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0
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29
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Expected value of a decreasing function of two random variables
My question is exactly equal to the question posted at Expected value of decreasing function of random variable versus expected value of random variable with just one extra assumption: the two random ...
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0
answers
55
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Does the mean of the maxima of a set of distributions converge?
This question is related to a recent one I posted. In that question I ask what statistic might best represent the central tendency of the true discrete distribution of a property for a sample for ...
- 165
3
votes
2
answers
82
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What is the variance of a regression after t generations?
Suppose we have a regression:
$$x_{t+1} = b x_t + e_t.$$
Taking the variance of each side we get
$$\operatorname{Var}(x_{t+1}) = b^2 \operatorname{Var}(x_t) + \operatorname{Var}(e_t). $$
Now suppose ...
- 133
3
votes
3
answers
125
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What statistic best estimates the sample mean in case of missing data in a distribution?
I have samples of particles and am interested in the particle lengths. The problem is that the samples are assessed using image analysis. As the particles overlap, the measurements are incomplete and ...
- 165
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0
answers
23
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Variance Component Estimation of Weighted Total Least Squares
Note: I'd like to make the cited document accessible to everyone but I am unsure how to do this.
I am a bit confused by this 2014 article "Variance components in errors-in-variables models: ...
- 425
1
vote
1
answer
43
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How to analyze between-group differences in within-group variances over time in a 3-level model?
The data I am using is collected within the physical fitness surveillance program in schools. In these schools, either no intervention, healthy lifestyle intervention, healthy schools network ...
0
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0
answers
28
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Constrained Cholesky Decomposition
Suppose that I have an $(n\times 1)$ vector of random variables, $\varepsilon$. However, I know that $k$ linear combinations of $\varepsilon$ are 0. Specifically, I know that for a $(k\times n)$ ...
- 1
2
votes
1
answer
32
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Time series and separating variance by time scale
There is a single-variable time series wich can be thought as being stationary in the long run. The observations are taken at irregular time intervals. The values of observations can be assumed to ...
- 152