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0 answers
8 views

Asymptotic distribution of t-test with two coefficients

I have the following CEF: $$ y_{i}=\beta_{1} d_{i}+\beta_{2}\left(1-d_{i}\right)+e_{i} $$ And the following assumptions: $$ d_{i} \perp\left(y_{i}(0), y_{i}(1)\right) $$ $$ \mathrm{E}\left[e_{i} \mid ...
5 votes
1 answer
59 views
+100

Finding the MVUE of the center of a circle of unknown location

Is there a known analytic solution for finding the minimum variance unbiased estimator of a disk of an unknown location given that a sample of $n$ points was drawn uniformly and randomly from the disk ...
0 votes
0 answers
9 views

what is the probability of this event?

given this outcome of the dice {2, 3, 4, 6, 6}. You decide to re-roll both sixes. What is the probability that you roll either a small straight (four dice are in a row) or a large straight (all five ...
0 votes
1 answer
12 views

How do endogenous variables relate with the error term?

Are endogenous variables stochastic or non-stochastic? If they are stochastic,can we say they are uncorrelated or correlated with the error term? I read this in Basic Econometrics by Gujarati (5th ...
2 votes
2 answers
119 views
+100

Bounds on the conditional variance of a truncated binomial

I have a binomial variable $R$ drawn from $binom(N, p)$, and I'm interested in the variance of $R$, given $R \ge Q$. The pmf of this variable $R^*$ is $$ \phi_{R^*}(l) = \frac{\phi(l, N, p)}{P} $$ ...
0 votes
0 answers
21 views

How can generate 95%CI for GAM model in Stata?

I am analyzing a dataset with generalised additive models(GAM) in Stata. I want to obtain 95% confidence interval(95%CI) for my result. I have read the documentation in Stata ("Help gam") ...
1 vote
1 answer
20 views

After using inverse probability weight, two groups are still significant

I used the inverse probability weight to eliminate the bias of demographics. After creating the propensity weight, I conducted series chi-square tests to compare demographic variables among treatment ...
3 votes
1 answer
64 views

Joint distribution of longest run and number of runs in a sequence of $n$ coin tosses?

A coin with probability of heads $p \in (0, 1) $ is tossed $n$ times. What is the joint probability distribution of the number of runs and the longest run? Schilling (1990) discusses the distribution ...
0 votes
1 answer
11 views

Why not perform weight decay on layernorm/embedding?

I am learning the code of minGPT. In the function, the author excluded layernorm and embedding layer from experiencing weight decay and I want to know the reasons. Besides, what about batchnorm?
0 votes
0 answers
15 views

Imputed binary response outcome

I am currently working on a group project with COVID data. The response variable is a binary outcome (positive/negative) from swab test; and let's only consider age groups (0-18, 18-60, 60+) for ...
3 votes
1 answer
301 views

Maximum Likeilhood estimate of shape parameter of GPD is negative, even though exceedances are positively skewed

I am looking at fitting a Generalized Pareto Distribution (GPD) to extreme events which exceed a certain value threshold for Bilbao waves data. Selecting threshold at c=7.5, resulting in 154 ...
0 votes
1 answer
10 views

Lightgbm, time-series and spikes repeated on a yearly basis

I have a data set (time-series) with the shape {$2190$x$63$}. There are 63 variables, 2 products ($A$ and $B$) worth of 3 years of daily data, thus I have $1095$ observations per product and total of $...
5 votes
2 answers
210 views

Objective criteria for assumption violations that do not utilize p-values?

Suppose we have a standard regression model and want to identify whether we have violated the assumptions of the model. Traditionally, we might utilize a significance test to determine whether (for ...
0 votes
0 answers
2 views

Degrees of freedom when comparing models applied in a secondary (test) dataset

Two models in R: mod_a = lm(height ~ age) mod_b = lm(height ~ age + sex) Those models have different degrees of freedom. Once they are applied in a separate set, ...
1 vote
2 answers
10 views

How to properly explain a delta between 0.10 to 0.05 in proportions

Assuming I have proportions for clicks to impressions of 0.10 for p1 and 0.05 for p2. This is equivalent to 10% and 5% click through rate. One way is to say that p1 is 5% higher but can we even say ...
8 votes
2 answers
357 views

Sum of sample given a priori knowledge of its maximum

Given a sample of discrete random variables $X_1, X_2, \ldots, X_n \sim F$, I am looking to calculate the distribution given by the probability mass function: $$P\left(\sum_{i=1}^n X_i = x~\middle|~\...
2 votes
1 answer
78 views
+100

Optimize classification rule in multinomial logistic regression

We know that in the case of logistic regression, a classification threshold p=0.5 is generally not an optimal choice when seeking to optimise sensitivity and specificity. This is generally due to the ...
0 votes
0 answers
4 views

SUR regression gets error "LU computationally singular: ratio of extreme...": can work around but still concerned about error margins

I originally posted this to stackoverflow, and was advised by I_O that the question would be appreciated more here. I am not sure how to reformat this to be appropriate here, so I am copying it over ...
0 votes
0 answers
6 views

How can the power of a clinical trial be estimated mid-recruitment?

For my PhD I started a three-arm, clinical trial which due to the pandemic I have to stop after having recruited 69 participants instead of 150 originally calculated to give a power of 80%. The trial ...
0 votes
0 answers
9 views

Adding independent variables to mixed effects model and controlling for interaction

I have formed 2 separate mixed effects models to see how these variables affect "chance" (this is risk taking behavior): ...
0 votes
0 answers
4 views

Why do permutation importances for my model all zeros?

I really am at a loss here. I have several tree-based binary classification models trained on a balanced dataset of ~300 samples and ~15000 features. The models have AUROC around 0.8. I want to ...
1 vote
0 answers
27 views

Arithmetic with normally-distributed variables

Suppose $x \sim \mathcal N(\mu_x,\sigma_x^2)$ and $y \sim \mathcal N(\mu_y,\sigma_y^2)$ are random variables, and suppose $\mu_y$ is large compared to $\sigma_y$. I want to know about $$ z=\frac{x}{y^...
0 votes
1 answer
22 views

SE Interpretation

Can you help me to interpret the following standard deviation? It is a linear regression problem, I need to predict Rent which depends on the size of an Apartment. Rent=23.411+13.806. The question is ...
1 vote
1 answer
758 views

What is meant by subgroup?

I am learning about control charts but I am unable to wrap my head around the concept of subgroups. What are subgroups? I understand that they are group of homogeneous data, but why do we need to ...
4 votes
2 answers
756 views

Multi-label classification with neural networks: Are correlations between class labels taken into account?

I am solving multi-label classification problem (assigning each image 1 to N labels) and want to use neural network (like in this post). Does this approach take correlations between class labels into ...
1 vote
1 answer
19 views

Permutation test for adonis under NA model?

I am having issues understanding why the permanova computed with adonis2() in vegan is returning a ...
3 votes
2 answers
21 views

Using weather forecasts as exogenous data for timeseries forecasting

I'm using Facebook Prophet as a forecasting model and I want to use weather data (temp for example) as additional regressor (exogenous data or external variable). Additional regressors are integrated ...
0 votes
0 answers
7 views

How to incorporate offset variable in coxphf()?

...
0 votes
0 answers
7 views

ANOVA interaction effect

https://i.stack.imgur.com/wdXwB.jpg If I'm performing ANOVA using the formula in R: aov(Ileibacterium ~ diet*cage, data) Context - there are 3 cages per diet with 3 ...
-1 votes
0 answers
19 views

Error while sending the email in marketo [closed]

Hope you are doing well! These are some errors I was facing while sending the email: 1- 550 [internal] [oob] The message was blocked by the receiver. 2- 550 5.4.1 Recipient address rejected: Access ...
0 votes
1 answer
8 views

Three-level Meta-Analyses: correlation comparisons and correction for publication bias?

I'm conducting a three-level meta-analysis on correlations using the {metafor} package on R. I'm quite a newbie when it comes to three-level meta-analyses, so I have two doubts. 1) From each study, I ...
2 votes
0 answers
9 views

Heavy tailed residuals in linear mixed model

I'm a new user of linear mixed models and I'm experiencing some troubles with that. I have a dataset with 680000 measures of milk production from 2017 to 2020, from a population of almost 37000 cows ...
2 votes
1 answer
76 views

Why do fixed effects in a logistic regression model differ depending on the presence of a random slope?

If I have two linear regression models, one with a random slope and one without (but otherwise identical), the fixed effects in the two models are identical. My understanding is that this stems from ...
1 vote
1 answer
172 views

3-way interaction not signficant; how to interpret subsequent 2-way interactions.

I know there are similar questions on this topic but I have checked all of them and haven't found the specific answer to my (simplistic) questions. There are 3 explanatory variables: A(3 levels, ...
0 votes
0 answers
8 views

Poisson family GLM with 1 categorical independent variable error missing value where TRUE/FALSE needed

I want to test if a few test subjects show improvement over days in a test. I have 2 groups, 1 that did some training before the test and 1 that did not. My test lasted three days, with 10 trials a ...
0 votes
0 answers
2 views

Coefficient of correlation between differently spaced time series

I have a timeseries with input flow values in a water plant (measured every 5 minutes) and the meteorological data containing the precipitation in the last 1,3,6,12 and 24 hours (each displayed every ...
1 vote
1 answer
79 views

Probability that a Random Variable is Greater Than Another

Say I have two independent random variables - one is drawn from a uniform distribution on [0, 50] while the other is drawn from a uniform distribution on [0, 100]. How would I calculate the ...
0 votes
0 answers
9 views

The multivariate Inverse-Gamma

On wikipedia they give a multivariate form, which to my understanding is used when V is known up until the scaling factor for a Normal-InverseGamma conjugacy. I tried to find a source of the ...
0 votes
0 answers
32 views

ANOVA: significant interaction but not significant post-hoc

I am running an ANOVA (in R, using the afex package and aov_car function), with two inter-subject variable (Group, which can have two modalities and Sex, which can also have to modalities) and one ...
0 votes
0 answers
8 views

Normal distribution of ratio [closed]

Given the following variable: Actual returns / Expected Returns I will assume a normal distribution N(1,S^2). Do you think is it correct?
2 votes
1 answer
1k views

Deriving step size/learning rate in the hinge loss passive-aggressive/perceptron algorithm

Recall the perceptron algorithm: cycle through all points until convergence $\text{if }\, y^{(t)} \neq \theta^{T}x^{(t)} + \theta_0\,\{\\ \quad \theta^{(k+1)} = \theta^{k} + y^{(t)}x^{(t)}\\ \}$ ...
0 votes
1 answer
171 views

Machine Learning Models for Classification with Categorical Variables

To start, I'd like to say I have very little experience in machine learning, or statistics/computer science in general. What I am interested in is a list of models I can use to classify a binary ...
1 vote
1 answer
19 views

Using ML model and decision tree to create a new risk classification

The idea of this project was to use a Machine Learning model to find the best variables to include in a decision tree algorithm. After evaluating with caret a number of different models I found the ...
0 votes
0 answers
12 views

Negative multinomial distribution

The pmf of negative multinomial distribution is \begin{align*} P(\boldsymbol{\rm{X}}=\boldsymbol{\rm{x}})=\frac{\Gamma\left(x_0+\sum_{i=1}^{m}x_{i}\right)}{\Gamma\left(x_0\right)}p_0^{x_0} \prod_{i=1}...
2 votes
0 answers
79 views

(Generalised) Negative Multinomial Distribution

Fix some probability vector $( p_1, \ldots, p_N)$, and let $X$ be a categorical random variable with these probabilities, i.e. $$P ( X = x ) = p_x \quad \text{for } x \in \{ 1, \ldots, N \}.$$ ...
1 vote
0 answers
9 views

Selecting a test to prove that the observed changes in the performance of two machine learning models are statistically significant

I have developed two machine learning models which I evaluated with two different datasets. My initial hypothesis was that their performance would be higher in dataset 2 as compared to dataset 1. ...
-1 votes
0 answers
12 views

Autocorrelation of residuals

I am working with R and I got the following residuals in time series. But I have problem determine if the are autocorrelated or not. Any help?
2 votes
2 answers
2k views

How to do likelihood ratio test to compare two panel models (plm) in R

I have a problem to run a likelihood ratio test to compare two panel regression models in order to find whether one model is significantly better than the another one. However, neither lrtest nor ...
0 votes
0 answers
9 views

Learning Algorithm Time & Sample Complexity

Let $X=R^{2}$. Let $u=\left(\frac{\sqrt{3}}{2},-\frac{1}{2}\right),\ w=\left(-\frac{\sqrt{3}}{2},-\frac{1}{2}\right),\ v=\left(0,1\right)$ and $C=H=\left\{h\left(r\right)=\left\{\left(x_{1},x_{2\ }\...
0 votes
0 answers
19 views

Without encoding, how can we solve high cardinality issue?

I already referred the posts here but this question is different. I don't wish to use categorical encoding. details given below I have a dataset of 3000 unique customers purchase data. The dataset ...

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