Questions tagged [mathematical-statistics]
Mathematical theory of statistics, concerned with formal definitions and general results.
6,950
questions
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11 views
Feasible to uncover the missing link in data using ML approach
Currently I have deal data and order data like as shown below.
the project background is that we would like to check whether the customer has booked the required orders (against their deal). For ex: ...
1
vote
0answers
7 views
How can I calculate the sample size of self-control study design for a two-arm meta-analysis
I recently encounter with a question is that I want to perform a traditional two-arm meta-analysis, however, some of the included studies are self-controlled study design.
The natural way to deal this ...
0
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0answers
7 views
arriving at demand from weekly sales projection and historical sales data [closed]
I have weekly sales amount projection for the year 2022, and I have historical sales amount data from the year 2018. How can I arrive at an expected customer demand at an hourly level from the weekly ...
0
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0answers
5 views
The impact of autocorrelation on variances of coefficients in random-effects model
What is the impact of autocorrelation on variances of coefficients in random-effects model?
Let's say the model takes this form: $y_{it}=\beta _{0} + \beta _{1}x_{it} + \epsilon _{it}$ where $\epsilon ...
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0answers
10 views
Can someone help me to understand this? [closed]
During morning hours, employees arrive randomly at an office drink’s dispenser at a rate of 2 every 10 minutes. During a 30-minute period one morning, the probability that n employees arrive at the ...
0
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0answers
20 views
Econometrics problem with regression [closed]
Suppose we estimate the regression $Y=\beta_0+\beta_1X$, where $Y$ is a firm’s stock price and $X$ is its debt-to-equity ratio. We find $\hat\beta_1= −130$. XYZ Corporation’s current equity is \$8.4 ...
1
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0answers
9 views
preference between completely randomized or stratified/paired randomized design under covariate not predicting outcomes?
Consider potential outcome of $i-$th unit $Y_i=(Y_i(0),Y_i(1))$ with $0$ as control and $1$ as treatment and say $X_i$ is the only covariate associated to $i-$th unit. Assume $X_i$ does not predict $...
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0answers
18 views
VIFs in Fixed-Effects-model
I know that R is providing some Warnings messages when you try to get your VIFs to test for multicollinearity.
But why is that?
Does someone know a good paper or the answer itself?
CODE:
...
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1answer
21 views
Two proportions, many locations & 3 way proportions?
I have results and I'm not sure how to test for significance. I am a new student with not a lot of stats experience, so please be kind.
I have whale that makes two calls - X and Y. I measured the ...
4
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0answers
30 views
The use of a pseudo variance $\int_{-\infty}^\infty \text{sign}(x) (x-\mu)^2 f(x) dx$ in place of $\int_{-\infty}^\infty (x-\mu)^2 f(x) dx$
Difference between odd central moments and even central moments
When we compute $n$-th central moments
$$\mu_n = \int_{-\infty}^\infty (x-\mu)^nf(x) dx$$
then there is a difference in interpretation ...
1
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0answers
29 views
How to insert a constraint on coefficients of logistic regression model?
I want to build a logistic regression model on my data, which contains three continuous predictors and a logical response. I need to constrain the regression coefficients to be not less than 0 and sum ...
0
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1answer
29 views
Probability distribution & Interpretation
If my distribution looks similar to Poisson but not an actual Poisson distribution which is verified using a QQ plot, is there any way to convert such distribution to a proper Poisson distribution ...
0
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2answers
90 views
Why Student's t-test doesn't require normality of population?
this PSU master's degree course says t-test can be used if either of the conditions is true:
population is normal.
sample size n>30.
However, I read that t test is applicable when $X_{i}\stackrel{...
0
votes
2answers
36 views
Can one perform Bernoulli trial by restarting trial if everyone is assigned control or treatment?
Suppose I have $n$ patient. I want to give an assignment of treatment such that probability of patients receiving treatment is $0.5$. Say I have $n$ unbiased coins to determine treatment or control ...
0
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1answer
18 views
Why do we call an assignment mechanism unconfounded assignment mechanism?
Consider some experiment with $n$ units along outcomes $Y=(Y_1,\dots, Y_n)$, covariates $X=(X_1,\dots, X_n)$ and treatment vector $W=(W_1,\dots, W_n)$ where $Y_i=(Y_i^1,Y_i^0)$ for treatment and ...
2
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0answers
11 views
Can we recover joint distribution from a continuous range of convolutions?
Given a correct model of the joint distribution of a random vector $(X,Y)$, we can derive (though not necessarily in closed form) the correct distribution model for $pX+(1-p)Y$ for any $p\in[0,1]$.
...
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0answers
13 views
Log Naive Bayes NLP dropping the denominator [duplicate]
I'm learning about the the Naive Bayes classification and I don't get what the squiggly alpha sign means and what it means that "Denominator remains constant for given input." Is it because ...
0
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0answers
27 views
Check that a function is valid pdf [closed]
How can I check that an empirical-function $f(x)$ is a valid pdf? In particular I would like to know how to check (in R) the condition $\int_0^\infty f(x)dx = 1$, where I know the values of $f(x)$ but ...
0
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0answers
12 views
Is the ordering of a sufficient statistic meaningful (soft question, maybe)?
Suppose we have distribution with a vector of parameters, and a random sample of size n from said distribution. Is the writing order of a sufficient statistic meaningful?
For a normal distribution, we ...
1
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0answers
37 views
Information theory: Understanding the original proof of the Entropy Power Inequality (Stam, 1959)
I am trying to understand the proof for the Entropy Power Inequality (EPI), pulished by A.J. Stam (1959; pages 108-109) in Some Inequalities Satisfied by the Quantities of Information of Fisher and ...
2
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2answers
87 views
Why did meta-learning (or model stacking) underperform the individual base learners?
I want to use meta-learning, specifically, stacking to combine the results of two algorithms, denoted here A and B. The results of A and B correspond to the first and second columns in the dataset '...
1
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1answer
56 views
Can a subset of the indexing set of a RV, given rise to a non-stationary time series, be considered weakly stationary or vice versa? [closed]
Given a non-stationary time series $X_t$, is it possible that a subset $[t_1, t_2]$ of the indexing set is considered weakly stationary? And also, given a weakly stationary time-series, can a subset ...
2
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2answers
32 views
What's the drawbacks of choosing a high statistical power and low significance level?
I want to perform an AB test for two products (a control and a variant). I want to detect a 20% uplift with a very high certainty i.e., statistical power and a very low probability of a type I error (...
0
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1answer
33 views
please help me with this question of probability [closed]
If A and B are events in a sample space S (with associated probabilities P(A) and P(B)), and
P(A) + P(B) > 1, then if any other event C occurs, either A or B must also occur.
1
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0answers
70 views
Monte Carlo integration for a random integrand (or a set of integrand)
I understand that the Monte Carlo integration works for a fixed function, say $$\int f(x)p(x)\mathrm{d}x\approx\frac{1}{N}\sum_{i=1}^Nf(X_i),$$ where $p$ is a probability density function on sample ...
0
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0answers
31 views
Prove sum of T(Xi) also belong to exponential family
In mathematical statistics, suppose we have an independent and identically distributed sample X = ($X_1$, $X_2$, …, $X_n$) from a distribution that belongs to the exponential family. Say we can write ...
0
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0answers
19 views
How to describe this expression? [closed]
I need to present the following mathematical expression (Monge's problem) in a talk. I'm not sure how to do it correctly/accurately.
$$\underset{G}{\text{argmin}} \int \| x - G(x) \|^2 d\mu(x)$$
Is it ...
0
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0answers
20 views
Deducing $L^1$ Boundary from Mahalanobis Boundary
Assume maximum likelihood estimators $a,b$ of size $p$, with corresponding estimated covariance matrices $V^a,V^b$. In fact $a,b$ are two regression coefficient vectors.
Denote $q=a-b$ the vector of ...
0
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0answers
7 views
Jensen-Shannon Divergence for ranking distance of two or more pairs of distributions
let's say I calculate JSD between two distributions A and B as: JSD(A, B)= x and JSD(C, D)=y and JSD(K,L)= z. If x>y>z, can I say K and L are closer to each other than D and C and A and B? My ...
1
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0answers
57 views
Non-parametric test for two sample quantiles
I would like to know if there is a non-parametric test on quantiles.
EDIT: My focus is on continuous distributions (e.g. Weibull distribution).
In a general setting we define quantiles as $Q_X(p) = ...
0
votes
1answer
14 views
Whether can stacked generalization (stacking) further improve the performance if learner A significantly outperform B?
We know that stacking is the most popular meta-learning technique. It learns from the predictions of the base learners that learn from the training dataset. Now assuming there are two base learners, ...
0
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0answers
14 views
Convergence theorems for Kernel Perceptron and Kernel SVM
Context
Some time ago I asked whether SVMs could work on arbitrary Hilbert spaces, my motivation for asking it was due to my discomfort towards the kernelized version of SVM, which, in my mind, ...
1
vote
1answer
33 views
Can I say X causes Y if all confounding factors are accounted for?
Say I wish to understand the causal relationship between some set of covariates X and an outcome of interest y given some treatment T. For example, this may be as simple as modelling the relationship ...
2
votes
1answer
30 views
Clopper Pearson Confidence Interval for 100%
I was using the following site: https://www.medcalc.org/calc/diagnostic_test.php to generate confidence intervals for some data I collected. One of the data-subsets had 81 true positives and 0 false ...
1
vote
2answers
41 views
Confusion about independent and identically distributed?
Say that I wish to measure the height of male within the population (so gender=Male is the only factor I am accounting for). Say I collect 100 observations of male height from an elderly population. ...
11
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4answers
2k views
Is the CDF of the Mean always 0.5 for all kind of distributions?
Can we say that the value of the cumulative distribution function at the mean F(X< Mean) is always 0.5 for all kind of distributions (even ones that are not symmetric)?
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27 views
Bounding The Brier Skill Score
Consider models $M^f,M^r$ (focus and reference), which obtain Brier scores $BS^f,BS^r$ over some testing dataset. The Brier skill score is defined as $BSS=1-\frac{BS^f}{BS^r}$. Generally speaking, BSS ...
3
votes
0answers
56 views
Proof that the MLE of logistic regression doesn't have a closed-form solution [duplicate]
It is well known that the maximum likelihood estimator of logistic regression does not admit a closed form solution. Whereas, ordinary least squares regression does have a closed form solution, at ...
0
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0answers
18 views
Name for bandit model with observations
I would like to know if there is in the literature a bandit model in which the observation model is of the type
$$
o_t = \mu_{a_t} + \eta_t,
$$
where $a_t$ is the action selected at time $t$, and $\...
0
votes
0answers
13 views
Matrix Values to Probabilities with Logistic Regression
I have a Non Negative Matrix Factorization algorithm and I'm calculating the A-hat matrix from it.
Rows of the matrix are customers, columns are my products and values are the occurrences of product ...
0
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0answers
6 views
Building a probabilistic model to predict the amount of liquid funds to keep on hand based on historical deposits/withdrawals
Fractional reserve banking allows a bank to keep only a certain proportion of total funds as liquid funds while lending out the rest.
I am trying to build a model that will output the probability ...
1
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0answers
11 views
Invertibility step in proof of asymptotic normality of M-estimators
I am looking at a certain proof of asymptotic normality of M-estimators and there is a matrix $V$ which is known to be invertible anda random variable $X_n = V + o_p(1)$ (that is, the difference ...
-1
votes
1answer
46 views
MLE - CDF vs PDF as the likelihood-function?
Would maximum-likelihood estimation: with the cumulative-distribution function as the likelihood-function and the probability-density function as the likelihood-function, yield the same/equal ...
0
votes
1answer
65 views
How to prove the following properties about $\chi_1^2$?
Given two independent r.v. $X\sim N(\mu_1, 1)$ and $Y\sim N(\mu_2, 1)$. What is
$$
f(x)=P(\min\{X^2, Y^2\}>c).
$$
0
votes
1answer
69 views
Hypothesis testing MLE for $H_{0}: R\mu=r$ [duplicate]
As in Multivariate normal distribution - hypothesis testing MLE.
Suppose $X_{1}, X_{2},\ldots,X_{n}\in R^{p\times 1}$ are i.i.d. observations from a multivariate normal distribution $N(\mu,\Sigma)$ ...
0
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0answers
39 views
Bootstrap confidence interval for mean
Take an iid sample $X_1,\dots,X_n$ from a distribution with (unknown) mean $\mu$ and variance $\sigma^2$. Let $\bar{X}_n^b$ be the bootstrap sample mean, and choose $R_n=R_n(X_1,\dots,X_n)$ s.t. $$C_n=...
5
votes
1answer
106 views
Hypothesis Test for mean vector of Multivariate Normal Distribution
Given two independently $X_1$ and $X_2$ and that these are bivariately normally distributed with mean vector components $\mu_1$ and $\mu_2$ and variance-covariance matrix shown below:
If we want to ...
1
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1answer
53 views
Why does $V(\bar x_1 - \bar x_2) = \frac {\sigma_1^2}{n_1} + \frac {\sigma_2^2}{n_2}$? (Samples are independent)
I don't quite understand why this is the case. I'm new to stats and when I think variance, my mind immediately goes to $S^2 = \frac {\sum(x_i - \bar x)^2}{n - 1}$. Is there a rule that I'm ignorant of ...
1
vote
1answer
27 views
Proof of Gauss-Markov Theorem: Unaccountable Line
I'm trying to follow Faraway's proof of the Gauss-Markov model in his book Linear Models with R, 2nd Ed., on pages 22-23, but I have been having numerous difficulties. The latest difficulty is thick ...
0
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0answers
10 views
Predicting number of views of a video based on previous uploads
I am working on a project to predict number of views we are expecting a YouTube video will get. Suppose for a specific YouTube channel we have number of views for 100 videos uploaded previously. We ...
