# Questions tagged [mathematical-statistics]

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

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### regression to the mean and its formula in R

In this book, the estimate of the regression to the mean phenomenon is said to be: $Prm=100(1-r)$. Where $Prm$ is the percent of regression to the mean, and $r$ is the correlation between the two ...
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### Independence of the sample mean and sample variance

For $X_i \stackrel{indep}{\sim} N(\mu_i, 1)$, I have to show that the sample mean $\bar{X}=n^{-1}\sum_i X_i$ and $S_{XX}=\sum_i (X_i-\bar{X})^2$ are independent the theory of random projections onto ...
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### 2 x 2 x 2 design

I'm doing a 2 x 2 x 2 design. To be specific, it's a 2 (BETWEEN-subjects variable) X 2 (WITHIN-subjects) X 2 (WITHIN-subjects) factorial design. And three Dependent Variables I know MANOVA is the one ...
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### how to estimate the precipitation value from other relative data

I have climate data but the precipitation values are missing, I would like to know if there is any formula used to estimate the precipitation value from the other recorded climate data: temperature, ...
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### How to analyze the data set

I have a data set with all the zip codes in a city Texas, and the number of stores each zip code has. So on excel, it looks like following: Column A (list of all the zip codes) 22160 etc; Column B (...
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### Question on method for analysis

First of all, I have begun researching as a masters student and I am forcing myself on more statistical validation and significance testing - this is not my strong suit. As such, I am applying ...
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### Why not use % change in regression instead of log diff?

Given that log difference = percent change why not make the series stationary by just using percent change as the regresor. a. It's not an approximation and we can interpret an coefficient as a ...
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### Equation for weighted mean of percentages

I am trying to get the equation for a weighted average of percentages to be normalized between 0 and 1. Am I doing it correctly? Thank you so much!
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### Likelihood function when there is no common dominating measure?

When we have a statistical model $\{ P_\theta, \theta\in\Theta\}$ on some common probability space, usually we define "the" likelihood function $L(\theta)$ via a Radon-Nikodym derivative ...
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### annualized probability of default for loan including time component

i am struggling with this. say i am given an annual probabilty of default for a company going insolvent as 0.02. so 2%. say this client then takes out a 100k , 150 day loan on jan 1st 2018, what is ...
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### Can use Factorization criterion for proving given estimator is not Sufficient?

I was learning about the Sufficiency of Estimators and Factorization criteria. Now, I noticed that whenever we prove a given estimator is not sufficient, we use a counterexample with concrete values. ...
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### Expectation of Gaussian random vector over a subspace

Suppose $\boldsymbol{x} \in \mathbb{R}^d$ is a Gaussian random vector, distributed as $\boldsymbol{x} \sim \mathcal{N}(\boldsymbol{\mu}, \sigma^2 \boldsymbol{I}_d)$, where $\boldsymbol{I}_d$ is an ...
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### What are the interpretations of these different types of stochastic convergences?

Thanks for passing by! I am studying an introduction to stocastic processes and I found 4 types of stocastic convergences with their definitions as follows: Let $(X_n)_{n\geq0}$ be a sequence of $r.v.$...
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### Mathematics foundation under choice of varying size input problem

I am reading this paper Taxi Destination Prediction, in which trying to predict the destination of the taxi. The dataset is composed of many complete taxi trajectories. In the dataset, the input is ...
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### Sources for learning (not just running) statistics/math through Python

I am interested in examples of sources (Python code, Python packages, books, book chapters, articles, links etc) for learning statistical and mathematical concepts through Python (it could also be ...
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### proof of Cramer-Rao lower bound

I am trying to understand the proof for this theorem from the book Casella and Berger (2nd ed.) page 336. $W(X)$ if any estimator for samples $X_1,\ldots,X_n$ on distribution $f(X|\theta)$. I notice ...
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### Does wealth index created in stata (command: pca and predict) considers all the components whoese eigen value more than 1 or just first component?

I am trying to calculate the wealth index of a rural community of Nepal. For this, I used 10 household assets variables after conducting a descriptive analysis. I used the principal component analysis....
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### What's the definition of $O_{p}(\cdot)$ in the vector case?

For a scalar random sequence $X_n$, we write $X_n=O_p(a_n)$ if for every $\epsilon$ there exists $M_{\epsilon}$ such that $\limsup_{n}\Pr(|X_n/a_n|>M_{\epsilon})<\epsilon$. What's the extension ...
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### Finding the mode of multiple sample modes

I'm running an experiment where I'm collecting samples of different size (numeric data only) and computing the mean, median and mode of each sample. I'm interested in finding out the mode across all ...
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### Predict daily count of delivered packages

I have a historical information for delivered packages (send time and receive time). Also I have an information for packages in transit (send time only). For example, all of the packages in transit ...
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### Test time series performance across subjects against chance

I'm wondering if anyone had any advice on testing where (if at all) the average of several time series deviates against chance. That is, I have an output from an SVM, computed at several time points, ...
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### Is it possible to produce two [random] graphs that always pass each other

My question is whether it is possible to create two graphs that go up one point or fall one point at a time [e.g. every minute] in a random walk, and they will pass over each other for sure all the ...
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### Suitable statistical test for multiple categories data?

I am compiling my research result which ended up like a table below: ...
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### Advantages and disadvantages of windsorizing, truncation and logistic transformation of explanatory variables in a logistic regression contect

I am using a logistic regression model to develop a ranking function; e.g. customer A has a higher chance of not paying the invoice than customer B. My data contains many explanatory variables with ...
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### Sample size to test a three-way interaction

I'm want to run a study with 2 categorical IVs and 1 continuous IV. The DV is continuous. It's my understanding I will need to run a multiple regression to test the effects. How do I determine the ...
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### Condition numbers, invertibility and multicollinearity

The following is an excerpt from Greene's Regression Analysis (Seventh Edition): a) What does it mean to be "difficult" to invert a matrix accurately? Shouldn't all matrixes be either ...
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### Doubt in independence of 2 random variables

If 2 random variables are independent, then $f(x,y) = f(x)f(y)$. Is converse true? $F(x,y)=F(x)F(y)$. Is converse true? $E(x,y)=E(x)E(y)$. Is converse true? where $F$ is cdf and $f$ is pdf I recently ...
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### How do I find the MLE of the APE distribution in R?

The random variable $Y$ is said to have a two-parameter APE distribution, denoted by $\text{APE}(\alpha, \lambda)$, with the shape parameter $\alpha>0$ and scale parameter $\lambda>0$ if the ...
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### How to convert Incidence rate ratio into probability?

I understand that converting odds ratio into probability one can divide the odds by the odds plus one. Is it the same formula to convert Incidence rate ratio into probability? I'm trying to interpret ...
I am referring to a simple multiplayer perceptron (e.g. only one hidden layer and one output layer). Notation: Assume we have $K$ dimensional output. The number of samples we have is $N$. And we ...