Questions tagged [mathematical-statistics]

Mathematical theory of statistics, concerned with formal definitions and general results.

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Should I convert the number after log transformation back to the original for calculating RMSE?

When I built the model, I applied the log transformation to all variables including the dependent variables. Now, I'm calculating the RMSE for the evaluation, and the result is in the log format, ...
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17 views

What does “density” really mean in probability density function in statistics? [duplicate]

I am familiar with the concept, but I simply can’t get my head over the intuition behind it. While being a derivative, it describes the rate of change for one unit. Simply put, we can say that it ...
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10 views

What are the ways to generate multivariate data? [on hold]

I am trying to teach myself statistics and I was curious how to generate multivariate data. Say, given 1000 multivariate observations I want to generate 10,000 observations. If I randomly sample these ...
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4 views

Finding the CRD factorial on a experiment data

I am about to finish my thesis . But i am stuck in a problem. I have researched on two varieties of strawberry one is chandler and the other is camarosa. I have found the phenol content of both the ...
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27 views

How to avoid division by zero [on hold]

I have a formula as follows. y = (x1 - x2) / (x3) I observed that sometimes x3 becomes zero, which results in division by ...
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1answer
17 views

Odds of an event happening over a long period of time

If there is a fluctuating chance of rain throughout the day how do you calculate the chance that it will rain at some point throughout the day? For example, tomorrow there is a six hour period with ...
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1answer
20 views

If the VIF is 2 then what is the value of correlation coefficient $R^2$

If variance inflation factor is 2 what is the value of correlation coefficient $R^2$? $$VIF = \frac{1}{1-R^2}$$ Given $VIF =2$, then is this calculation correct? $$\begin{align} 2 &= \frac{1}{1-...
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10 views

How to make sense of prediction risk of the estimated regression function?

I have some trouble of understanding the following definition for "conditional prediction risk" and "prediction risk" of estimated regression function as provided in the picture. I understand that ...
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21 views

Changing a conditional probability to a deterministic function

Suppose that we have a conditional density function $p(y|x;\theta^*)$, where $\theta^*$ represents distribution parameters and are assumed to be deterministic. Is it possible that we write this ...
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1answer
13 views

How to represent numerically the diversity of groups of datapoints with a single value?

I work for a performing arts organization, and am trying to create a numerical figure to represent the amount of genre-diversity in each of our seasons. So let's say that we have a Spring Season and a ...
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1answer
25 views

Definition of exponential family with dispersion parameter

I was recently reading a discussion of generalized linear models that considered the response to come from an exponential family with a dispersion parameter so $$ f(y|\theta,\phi) = \exp\left(\frac{y\...
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0answers
20 views

Statistical Significance of a 3D Volume

I have two 3D volumes of a single patient. One 3D volume before surgery and one 3D volume after surgery. The 3D volumes are MRI images (Mangetic resonance imaging). Each 3D volume has dimensions [100, ...
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1answer
41 views

Why does the No Free Lunch theorem imply that we must design algorithms to perform well on specific tasks?

I'm currently studying deep learning using the textbook Deep Learning (Goodfellow, Bengio, & Courville - 2015) and had a question regarding a concept of machine learning provided in the book. ...
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2answers
18 views

Coefficients in Cox model

The output of coxph has coefficients vector as follows: ...
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0answers
11 views

How to calculate confidence intervals in R using earth package? [closed]

I want to calculate the confidence interval using varmod.earth function as shown in the example of R packages. I run the code and it is showing that: !is.null(leverages) is not TRUE. I could not ...
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22 views

Test differences between rates

I ran a digital advertising test with 4 different groups of demographic. 4 different segments visited the website > goal : purchase Segment A - 1000 visitors - 10 purchases > 1,0% purchase rate ...
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0answers
22 views

Multiple state transition probabilities in Markov model

I have a problem where, in a multi-state Markov model with monthly timesteps, I have a state X where, in an average of 1 year, individuals exit from the state in this proportion: 56% of individuals ...
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2answers
41 views

How to modify a linear regression model when the variance is not constant?

I have a very basic question. I have a model that has residuals that don't follow a constant variance pattern, but rather it has a clustered pattern (see the figure attached). Any idea of how to deal ...
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1answer
32 views

Mean and variance of a variable (inside a function) without known its distribution, but known mean & variance of the function

Let $$Z_k = A\, e^{i(2\pi B+\phi_k)}, \qquad k =1,2,3\dots$$ be a complex function with dependent on $\phi_k$ and others are real constants. Assume that the mean $\mathbb{E}[Z_k] = \mu_{z_k}$ and ...
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3answers
4k views

Why does independence imply zero correlation?

First of all, I'm not asking this: Why does zero correlation not imply independence? This is addressed (rather nicely) here: https://math.stackexchange.com/questions/444408/why-does-zero-correlation-...
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36 views

Getting sets of random correlated variables

For the training of a machine learning model I need to add additional features, and these features are correlated. I need to run the model N times adding these features with random values, and for ...
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0answers
27 views

Which statistical methods to be used?

I am analyzing data in order to show the reasonings of interindividual variabilities of the results of a laboratory data that was measured repeatedly over 100 hours in a single group. But the timings ...
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1answer
25 views

class grade and weigh [closed]

A statistics class has the following activities and weights for determining a grade in the course: test 1 worth 15% of the grade, test 2 worth 15% of the grade, test 3 worth 15% of the grade, homework ...
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0answers
9 views

How to use parcel route data to calculate a threshold [closed]

I have a parcel delivery business and I want to calculate a threshold for each route. I need this to compensate more when a driver delivers above a threshold. This will encourage drivers to help their ...
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1answer
35 views

Home-brewing GARCH implementation

Motivation I want to wrap up my own GARCH implementation to make sure I have understood the underlying model/assumption. to leverage forecast::auto.arima to ...
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1answer
97 views

Central Limit Theorem only needs sample size, N?

I think explaining the central limit theorem needs two elements: the sample size and the number of samples drawn. But nobody seems to talk about the number of samples drawn when they are making some ...
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1answer
49 views

Proof $E[Z'TZ]^2=\operatorname{tr}^2(T)+\operatorname{tr}(T^2)$ [duplicate]

How to prove second moment of a quadratic form where $Z$ has normal distribution with mean zero and covariance matrix identical?
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1answer
45 views

Variance comparison of $XY$ and $\min(X,Y)$

There are two independent random variables and each is Gaussian with $\mathrm{E}(X)=mx, \mathrm{E}(Y)=my$, variance of X, i.e. $\mathrm{Var}(X)=vx, \mathrm{Var}(Y)=vy$, respectively. I would like to ...
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1answer
60 views

How to find the relationship between two variables using regression? [closed]

I have a Raspberry Pi hooked up to a sensor, which will send a data to the device every second. As you may have guessed, what I want is to find a relation between this independent variable time and ...
2
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0answers
31 views

Switching $H_0$ and $H_1$ by replacing $p$ with $1 - p$

I was reading the source code of tseries::adf.test, and it writes ...
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0answers
16 views

Leave-One-Out Property (LOOP)

I was reading this paper, and I was looking at the leave-one-out property that they mention in Appendix B. The property is as follows: For $x\in \mathbb{R}^n$, define $x_i$ to be the $i$th element ...
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0answers
10 views

Analyzing Data for multiple treatment groups

I'm currently designing a research proposal to analyse the effect of varying the amount of cash transfered in a conditional cash transfer program on raising school attendance rates. The cash ...
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1answer
35 views

How to make a model to distinguish positions using data from sensors?

What I would like to do I need ideas about how to analyze data and make a model to distinguish positions where an object locates using data from receivers. I don't know of a similar case like my ...
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0answers
9 views

Where is the single-crossing point between a distribution and its single mean-preserving spread?

Consider two random variables, $Z_A$ and $Z_B$, with the same expected value $\mu$, having distribution functions $F_A$ and $F_B$, respectively. Let $Z_B$ be obtained by a single mean-preserving ...
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0answers
22 views

Gauss's Original Gaussian Distribution Proof Help

I am refering to the proof of the guassian from the famous document: https://www.maa.org/sites/default/files/pdf/upload_library/22/Allendoerfer/stahl96.pdf I have attached the pictures below of the ...
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0answers
28 views

Pupils - Correlation between exam mark and answer from 1 to 5 of a test

100 pupils have their exam mark from 1 t0 50 and separately they have reposed a questionary with 10 questions. The variable that represents the answers for the questions of the questionary are ...
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0answers
34 views

Prove that the Pitman estimator is itself complete sufficient

It's a homework question, but I just have no idea about it ... Let be random variables according to a distribution having joint density ,where is a location parameter. Assume that there exists a ...
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0answers
10 views

Deriving Multiplicative Update Rules for Regularized NMF

After reading the following CrossValidated post, I cannot derived the correct multiplicative rules for regularized NMF from this paper. They obtain the coefficients $|I_u|$ and $|U_i|$ in the ...
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2answers
28 views

Evaluate methods across datasets based on distance metrics

I want to evaluate $n$ methods, says $M_1,\cdots,M_n$ on $m$ datasets $D_1, \ldots, D_m$. For each method $M$, I have a score function $f(M,D) \in [0, \infty)$ for dataset $D$. A perfect method will ...
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1answer
41 views

Have a question about bivariate random vector [closed]

When X follows beta (2,2) and X = x, the conditional distribution of Y is the binomial distribution B (15, x). The probability mass function P (Y = y) of E (X), Var (X), E (Y), and Var (Y) obtained by ...
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0answers
18 views

All different size groups to create m groups from n samples

Suppose we have $n$ samples that we want to divide in $m$ groups. How can we get the total number of groups and their sizes (if possible)? Examples: For $n = 6$ and $m = 3$ we would have $3$ groups as ...
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0answers
32 views

Prove the relevance of the Pearson correlation distribution for hypothesis testing?

The statistic used in testing $H_0: \rho=0$ versus $H_A: \rho \ne 0$ is: $t_r=\frac{r\sqrt{n-2}}{\sqrt{1-r^2}} \sim t_{n-2}$ in which $r$ is the sample Pearson correlation of two variables, say $X$ ...
3
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1answer
35 views

solve an exercise of two samples using Kolmogorov-smirnov

I'm looking for books and information like crazy and I can not find what I need. Well the example proposed is about methods that have been used in literature students and these are the data collected: ...
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0answers
57 views

What is the correct way to write the elastic net?

I am confused about the correct way to write the elastic net. After reading some research papers there seems to be three forms 1) $\exp\{-\lambda_1|\beta_k|-\lambda_2\beta_k^2\}$ 2) $\exp\{-\frac{(\...
2
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2answers
39 views

Understanding simplification of constants in derivation of variance of regression coefficient

In looking over TooTone's answer in Derive Variance of regression coefficient in simple linear regression, there's a step in line 3 below where $(\beta_0 + \beta_1x_i + u_i )$ is simplified to $u_i$ ...
3
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0answers
23 views

Reconstruction from statistics

imagine to have data like the following $\begin{matrix}X1 & X2 & X3 \\\ 1 & 2 & 3\\\ 4 & 5 & 6\\\ 7 & 8 & 9\\\ \dots\end{matrix}$ where each row is a multivariate ...
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0answers
33 views

For p>>n, where p is number of predictors and n is number of observations, is n P or P+N?

For p$\gg$n, where p is number of predictors and n is number of observations, is n P or P+N? For example, if I am building a binary classifier, and I have 165 positive and 165 negative observations, ...
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1answer
26 views

proof for distribtion of proportions of a binomial variable

Is it true that the proportions of a binomial variable: $$ {\displaystyle f(k,n,p)=\Pr(k;n,p)=\Pr(X=k)={\binom {n}{k}}p^{k}(1-p)^{n-k}} $$ follows a normal distribtion when n approaches infinity ...
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0answers
25 views