# Questions tagged [mathematical-statistics]

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

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56 views

### Probability Mass Functions [closed]

I have asked a related question Probability Mass Function making the Truncated Normal Discrete I am trying to understand the difference between 2 answers (the difference between 2 PMFs given). What is ...
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### Bayes error and nearest neighbor classification

Upon studying for my midterm using Pattern Classification by Richard O. Duda, David G. Stork, Peter E.Hart (2001), I stumbled upon the following exercise: Using the solutions manual written by David ...
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### What kind of regression to use in predictive model for a positive-only value

I'm trying to use regression in Excel to predict the % of bin contamination (dependant variable), based on my independent variables that are generally relating to demographics such as age/household ...
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### Relationship among exponential family, natural exponential family and exponential dispersion model

I have read the wikipedia of these three notions: (1)exponential family (2)natural exponential family (3)exponential dispersion model I have known the following relationship among them: (1)The natural ...
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### Linear regression residuals and OLS method

Assuming a simple linear regression framework, $y_i=\beta_{0}+\beta_{1}.x_{i} + \epsilon_{i}$, why can't I estimate $\beta_{0}$ and $\beta_{1}$ by optimizing the sum of residuals such that the sum is ...
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### Why does regression to the mean work?

According to Wikipedia, regression towards the mean is "the phenomenon that arises if a sample point of a random variable is extreme (nearly an outlier), in which case a future point is likely to ...
38 views

### Comparing performance of Quasi-binomial model and Beta-binomial model

I read some books in biostatistics about fitting binary date with Beta-Binomial regression model and Quasi-Binomial regression model. It proposes a setting: Setting: Assuming we have a sequence of ...
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### Why duality of confidence interval and hypothesis testing fails in random effect test for presence random effect?

I am reading Faraway's Extending the linear model with R chapter 10 section 2. "In this case, the lower bound is zero. This is not surprising given our earlier uncertainty over whether there ...
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### Confidence interval of a sample of a survey

I am having trouble framing my question and identifying variables because of sub-populations. If I have a survey of 10,000 people from a population of 100,000 people and within that survey 2,500 leave ...
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### model output without correlation to input variable

let's assume that a,b,c,d,t,u,v,w,x,y,z and o are all correlated to one another. I want to make a prediction for outcome variable "o". However, I don't want my prediction to be to ...
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### Global minimum of prediction intervals for multiple linear regression

I'm trying to solve the following problem: Prove that the width of the prediction interval for $\hat{y}$, given the vector $x_0 = (1, x_1,...,x_{p-1})$ of explanatory variables, reaches a global ...
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### High value for SD for data in range -100 to +250?

I Have a 1D data . I am trying to approximate this data to a gaussian distribution. I want to use MLE to estimate the parameters. ...
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### Are the position indices (quartiles, median, mean) of distribution in classes always different from those of the unit distribution?

Are the position indices (quartiles, median, mean) of distribution in classes always different from those of the unit distribution? If so, for what reason? In theory, since the class distribution is a ...
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### Asymptotic distribution of a method of moment estimator via the delta method

Let $X_1,...,X_n$ be a random sample from X with a Beta distribution $B(\theta; 2)$, with $\theta > 0$, i.e. : \begin{align*} f(x,\theta) = \theta(\theta+1)x^{\theta-1}(1-x) \mathbb{I}_{0<x&...
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### How to implement the contribution analysis using PCA?

I have been looking into implementing the Q-Residual and Hotelling's T statistics calculation to the PCA components which is similar to the following article and website: Structural Health Monitoring ...
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### Order statistics is minimal sufficient statistics for unknow density function

I'm trying to prove the problem, but there is a problem on definition of term. The theorem that I use to prove it is However, what exact meaning of "family of densities ~ all have common support&...
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### Simplifying the expected loss integral

I'm currently taking a class on machine learning and we discussed loss functions and minimizing the expected loss to get decision boundaries. The Profressor gave this integral for calculating the ...
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### Estimate assignment probabilities of a multi-class classification problem

I a dataset of $N$ observations $x_1, \ldots, x_N$. We know that to each observation $x_i\in\mathbb{R}^k$ one of $m$ possible class labels has been assigned to it $y_i\in\{1, \ldots, m\}$. For each ...
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### Estimate the square of the response variable for the in-sample observations

experts, I already have an ML/DL model to predict E[Y|X] and now I want to estimate E[Y^2|X]. I am not sure if I need to run a new model whose feature vector is X and response is Y^2. Let E[Y|X] = f(X)...
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### Statistical modeling vs data mining [duplicate]

What is the difference between "statistical modeling" and "data mining"? I have searched the internet, but I can't see it clearly. Is there any overlap? Can they be considered ...
61 views

### Steps in CLT proof unclear

In john rice Mathematical Statistics and Data Analysis we find a proof about the central limit theorem. Let $X_1, X_2,\ldots$ be a sequence of independent random variables having variance $\sigma^2$ ...
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### How can I simply the following Bayes probability?

I know $p(x_2|y)$, and I can calculate $p(x_1|y)$ How can I simplify $p(y|x)=\frac{p(x|y)}{p(x)}\cdot p(y)$ in terms of the above? Where $x \in \{x_1,x_2\}$
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### Does the margin of a classifier scale with the dimension of the problem?

Consider a binary classification problem on $\mathcal Z=\mathcal X \times \mathcal Y$, where $\mathcal X$ is some subset of $\mathbb R^d$ and $\mathcal Y = \{-1;1\}$. You have a dataset of $n$ ...
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### Confirmatory Factor Analysis identifying

I have been explained this technique in class. However, I did not understand some stuff. The professor said that a model to be estimated needs to be at least identified. Identified meaning to be when ...
In trying to predict the binary class label $y∈\{0,1\}$ given the input $x$, how can I avoid making assumptions about the data, what are the forms of the distributions and how many parameters do I ...
### Why is the p-value given by p-value${}=P(\chi^2>\Delta D)$ rather than p-value${}=2P(\chi^2>\Delta D)$ as $(*)$?
In the Binomial Regression Models for Binary Data, we have the general Wald statistics result for the Hypothesis $H_0: \beta_j=0, \, H_a: \beta_j \neq 0$ that the p-value is given by \text{p-value}=...