# Questions tagged [scale-invariance]

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### Are confidence intervals scale-invariant?

Suppose I estimate a mean and construct some sort of confidence intervals (e.g. based on normal approximation or bootstrapped) around the mean. I now wish to rescale my mean from, say, the mean number ...
0answers
10 views

### Scale invariant comparisons of two sets of vectors

I am dealing with the following problem. Let A and B represent two sets of real-valued vectors. The vectors are of the same dimension, yet the sets contain different number of vectors. I am looking ...
1answer
71 views

### scaling in time series

I would like to know if it is fine to use scaling(Time series * constant) before applying time series. Is it similar to data transformations( log , sqrt, Box-Cox) etc or is there any implication of ...
0answers
25 views

### Multi-group SEM: what steps in measurement invariance

Sorry for asking a stupid question but I had been struggling for quite a while now. I'm not sure what steps to talke to evaluate a moderating effect in a path analysis model. I now have a path ...
1answer
35 views

### Proving sufficiency by showing ratio of statistic pdf to sample pdf is independent of unknown parameter

Let $X_1,...,X_n$ be iid random variables with densities given by $$f_{x_i}(x|\theta)=e^{i\theta - x}\mathbb{I}_{(i\theta,\infty)}(x),$$ when $x>i\theta$ and $x=0$ otherwise. Let $T$ be the ...
2answers
59 views

### Why is invariance (in relation to neural networks) called invariance?

Why is the property of neural networks being robust to variances in the input referred to as invariance? Is it that the neural network's output is invariant, regardless of a variance in the input?
1answer
218 views

### Is there a “central distribution” for distributions for which the CLT doesn't apply?

The central limit theorems state roughly that under a certain set of properties of a sampling process, the distribution of a statistic from that sample will converge in distribution to the normal ...
1answer
2k views

### Why feature scaling only to training set?

I was following the book "Hands-On Machine Learning with Scikit-Learn & TensorFlow" by "Aurelien Geron". The following remark was made about feature scaling : - As with all the ...
0answers
767 views

### How do CNNs handle scale invariance?

Even after googling and reading fitting articles and answers to fitting questions here on StackExchange, I don't understand how CNNs handle scale invariance. I found logical sounding answers saying ...
1answer
109 views

### CFA vs Invariance of a test different CFI

I am currently learning how to implement CFA and invariance of constructs between two groups. My data below has two groups. So my steps are as follows Confirm the overall model works Check if both ...
1answer
795 views

### unequal group sizes in a multi-group CFA

I am testing measurement invariance across several demographic categories: age (will dichotomize), race, and BMI. The problem of unequal group sizes is most evident for racial categories: n White = ...
1answer
55 views

### Rescaling continuous scale to reduce (assumed) measurement invariance

I was wondering whether I could overcome (assumed) measurement invariance by rescaling continuous items. Example Let's say I have the following two questions (simplified for illustration): ...
2answers
570 views

### Difference between scale-space transform and wavelet transform

What is actual difference between scale-space and wavelet transform? It seems that wavelets require an orthonormal basis of kernels, whereas scale-space does not. Is it the only difference? Can scale-...
0answers
87 views

### Variance estimation for Levy process

Let $(X_t)$ be a Levy process. It then holds that $$E(X_{t+\Delta} - X_t) = \Delta \nu, \\ V(X_{t+\Delta} - X_t) = \Delta \mu,$$ under sufficient regularity conditions in terms of moments. For ...
0answers
25 views

### Intensity of fractional Gaussian noise

I try to understand the 2nd formula stated in the picture. It yields the intensity/volatility of an fGN process. It depends solely on H ?? Why is that? How is this volatility different from simply ...
2answers
164 views

### Is Shift and Scalar invariant same as independent under linear transforms?

I saw "shift and scale invariant" terms for the first time, and I'm wondering what's their meaning? in other word: Is Shift and Scalar invariant same as invariant under linear transforms? thanks.
0answers
88 views

### Conceptual help with scalar invariance testing

I'm having trouble understanding why scalar invariance is needed in testing a certain type of model. Let's say I have employee and supervisor ratings of deviance. I want to look at what happens when ...
1answer
139 views

### Parametrisation invariance/covariance of the Jeffreys prior

I've been trying to understand what exactly is meant by parametrisation invariance of the Jeffreys prior. Already I've read here that invariance is technically not the best term to use, and that it'...
1answer
3k views

0answers
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### Scaling of huge data and estimating the distribution

Suppose you have some sample of huge numbers and you want to fit some continuous distribution to these numbers. You will get some distribution that is loosely speaking highly "smeared", e.g. it has a ...
1answer
190 views

### Correlate heuristic metrics with future true performance

I am faced with a problem, that I'm pretty sure is a statistical one, but me taking 1 course in probability followed by 1 course in statistics back in university did not prepare me to adequately face ...
2answers
2k views

### Choice of weight function in Moran's I

I'm doing an autocorrelation analysis for a spatially distributed collection of observations. To perform my analysis, I am using Moran's I statistic. My questions are: (1) What are the implications ...
1answer
1k views

### Scale-invariant analysis of time series

When developing a general purpose time-series software, is it a good idea to make it scale invariant? How would one do that? I took a time series of around 40 points, and then multiplied by factors ...
3answers
356 views

### Why can scale invariance cause a loss of explanatory power?

Gary King made the following statement on Twitter: scale invariance sounds cool but is usually statisticians shirking responsibility & losing power by neglecting subject matter info What ...