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Questions about distributed lag non-linear models (DLNM)

I am new to DLNM, I have some confused questions: My research is about the environmental impact on health, and my data records are ordered as health cases as below: I want to use DLNM to analyze the ...
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1answer
7 views

Estimator when a coin is either fair or has two heads

Suppose that $X_1,\dots,X_n$ are independent and identically distibuted such that $X_1\sim\text{Bernoulli}(\theta)$. If $\theta\in\{1/2,1\}$, find the maximum likelihood estimator of $\theta$. Show ...
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0answers
4 views

In GLIM, how do I understand “the link maps mu to the entire real line, from −∞ to +∞”?

I always read in generalised linear model that the link function has to have a 1-1 correspondence from the range of mu to (-infinity, infinity). But, when we look at log link, for instance, it is not ...
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0answers
6 views

For alpha = 0.05, the critical mean is equal to____ [closed]

H0: Population mean equal to 100. H1: population mean greater than 100. Population standard deviation equal to 10. Sample size equal to 100. Answers are either A)95, B)98.355, C)101.645, or D)105....
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1answer
5 views

96% CIs for EDFs in GAMs using mgcv

I have been using the mgcv package in R to conduct Generalised Additive Models. I've been using Noam Ross's excellent free course to guide me (thank you Dr Ross). https://noamross.github.io/gams-in-r-...
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0answers
5 views

Can random effects be used in the spatial LGCP package (from JSS paper by Taylor et al. 2015)?

I am reading the excellent statistical software paper found here in this link. The paper is an R implementation of Log-Gaussian Cox processes for spatial point process applications. Whilst the ...
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0answers
6 views

Why doesn't the entropy decrease with an increasing number of observations?

I'm trying to think more about entropy. I have the following toy example: Consider a coin flip. Case 1: I think p_h = 0.5 The entropy of this is 0.5 ln(0.5) x 2 = ln(0.5) Case 2: I don't know what p_h ...
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0answers
10 views

Random Forests: How to extract the best model fitted by the rfcv function in R?

I am using the rfcv function in R rf_cv <- rfcv(data,data$y,cv.fold = 10) And one of the outputs given by the function is the Cross Validation error (w.r.t. ...
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0answers
8 views

Interpreting confidece interval qqPlot of a multiple regression

Hello I have a problem when trying to interpret a multiple linear regression graph and the qqPlot() function. I'm trying to do this with an example data of at least 28.000 obs. I used R to make the ...
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2answers
16 views

What if the P-Value is less than 0.05, but the test statistic is also less than the critical value?

Let's say you let the Null Hypothesis $H_0$ be that the mean volume of water in a bottle is some $\mu$, and the alternate hypothesis $H_1$ be that the mean volume is not $\mu$. Let's assume you pick a ...
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0answers
7 views

How to solve a system of non-linear equations under matrix form with two unknown quantities $a$ and $b$ (idealy scalars or matricial quantities)?

Firstly, I have already asked this question on another forum but couldn't get answers. So I try my chance here. I want to give you a maximum of informations and precisions about my issue. I have 2 ...
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0answers
7 views

Two True Positive for one ground truth in object detection

I am wondering is it possible to have two true positive predictions for one bounding box ground truth only. Following this section from Stanford. They define truth positive like this: We start with ...
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0answers
6 views

Custom Loss Function in Decision Tree for Ranking

I have built a Decision Tree and Adaboost model from scratch in Python and am now trying to customize the loss function being used. I am hoping to use a ranking loss function but am having troubles ...
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0answers
2 views

Is interval level of measurement the same as grouped data?

When data is grouped into intervals, will this be considered be as measuring data on the interval scale?
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1answer
15 views

Estimating the true nonlinear regression parameter with parameters from multiple specimens

I have collected data on the stress relaxation ($\sigma$) of 3 chicken tendons over time ($t$), and the following nonlinear regression model was fit through each individual tendon: $$\sigma = A + B e^{...
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0answers
4 views

error function hnp for residuals stan_glm

I am trying to diagnose the model for a dose-response assay under a Bayesian approach, however, I am not able to graph it to evaluate the residual components of the deviation using the stan_glm ...
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0answers
4 views

Method for predicting the probability of encountering variably-sized and distanced objects in a 2D random walk

I am working on an archaeological research problem (how people discover new resources on a landscape) and need some assistance on where to look or terms to research for a particular simulation I'm ...
2
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0answers
6 views

Test for parallel trends in difference-in-differenes models with staggered treatment

Following a comment from a previous thread (below), I would appreciate if you may advise me on how to test for parallel trends in Stata for a DiD model with multiple groups and staggered treatment (i....
0
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1answer
11 views

Variable Selection : Removing Linear Dependency by SVD using the Condition number and then eliminating the variable causing multicollinearity

I am trying to perform regression with over 5000 feature variables(X) and I would like to eliminate multicollinearity. Incremental VIF computation is expensive. Incremental PCA works but I might lose ...
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0answers
2 views

How to compute cohort study sample size for proportion metric and continuous metric?

I'm trying to design an retrospective cohort study to investigate the effect of smoking on lung cancer, and I've built an propensity score matching model that can match users, shown as follows. $$ P(...
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0answers
4 views

Interpretation of the alpha parameter in the Rational Quadratic Kernel

I've been working on Gaussian processes and a problem that keeps bugging me is the alpha parameter on the rational quadratic kernel I know that the rational quadratic is an infinite sum of squared ...
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0answers
11 views

asymptotic normality of z-estimator

I'm working on Problem 5.4.1 in Bickel and Docksum's Mathematical Statistics Let $X_1, \dots, X_n$ be i.i.d. random variables distributed according to $P\in\mathcal{P}$. Suppose $\psi:\mathbb{R}\to\...
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0answers
24 views

Can the null hypothesis be **more** true than the alternative hypothesis or vice versa? [duplicate]

As the title says, my question is can the null hypothesis ($H_0$) be more true than the alternative hypothesis ($H_1$) or vice versa? For example, if the statistical power is really high (extremely ...
1
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1answer
15 views

Can Granger causality be two ways?

If $X$ causes $Y$,$X \rightarrow Y$, as defined in Granger causality, is it possible that $Y \rightarrow X $? How can we prove if it is not possible? That is the relationship is one-directional.
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0answers
11 views

Testing for differences between pooled biological samples

I am trying to test for differences in absorbance between a control and treatment group. Due to cost, each measurement is derived from the mixture of 5 independent samples. Overall there are 5 ...
3
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0answers
20 views

Estimating standard deviation of underlying distribution

I need to estimate the standard deviation of an underlying normal distribution. I have the following statistics of one sample: mean, min and max, standard deviation, and sample size; however, I do not ...
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0answers
5 views

BIC for mixed continuous and discrete paramameters

I am interested in doing a BIC analysis for models which have mixed continuous and discrete variables. To give a minimalistic example which captures the relevant structure, let $\theta\in\mathbb{R}^2$ ...
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0answers
3 views

How does this mglearn library function works?

I am using a linear regression example where I load the dataset from mglearn library implemented as the following: ...
0
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1answer
20 views

How to model binomial data when the dependent variable is LITERALLY dependent on the independent variable

I am designing an experiment where a subject makes a choice between two options ("low value" (LV) and "high value" (HV)). The subject will experience both options during a trial ...
7
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2answers
41 views

Is this possible that $Cor(X, Y)=0.99$, $Cor(Y, Z)=0.99$ but $Cor(X, Z)=0$?

Let $X$, $Y$, and $Z$ are three random variables. Intuitively, I think that it is impossible to have $Cor(X, Y)=0.99$, $Cor(Y, Z)=0.99$ but $Cor(X, Z)=0$. My intuitive thought is that $X$ and $Z$ are ...
2
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0answers
11 views

How do I scale a dichotomous variable for a prior in brms?

Lets say that I am predicting reaction time. Every subject responds to 100 trials of different flashes of light. I have two predictors: one is continuous (e.g., brightness of the light) and one is ...
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0answers
10 views

NN and Output in two case, how this solution is reached? [closed]

I read my notes and get into stuck here. is there any idea how $5$ and $3$ is calculated here for option $1$ and option $2$?
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1answer
27 views

Statistical modelling

I am pretty new to R. I have 2 general questions when it comes to modeling. What statistical model would be best to test whether there is a difference in weight between male and female (sexual ...
1
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1answer
25 views

Unpooling standard deviation from a combined set and a subset

I do not have access to the original data set. AB: Overall mean: 149.41 sd: 89.13 N: 2284 B: ...
2
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0answers
12 views

Covariances between two different multinomial distributions

Let's say we have two random vectors $X$ and $Y$ of the same length with different one-trial multinomial distributions: $X_1, X_2, ... , X_k \sim$ Multinomial$(n=1;p_1, p_2, ... ,p_k)$ and $Y_1, Y_2, ....
1
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0answers
22 views

Central Limit Theorem - does the number of times the samples are taken matter in terms of the CLT?

Let's say that in R, we generate $n$ random variables $Y_1, \dots, Y_n$ which all follow an exponential distribution. We then construct the mean $\bar{Y_n}$. The process is repeated $m$ times, so we ...
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0answers
5 views

Strict Sense Cyclostationary and Shifting the X with $\theta$

Fellow stackexchangers, I did my best to put a topic that describes the question that I am going to ask. I am reading Probability, Random Variables, and Stochastic Processes by Papoulis and I am ...
1
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0answers
11 views

Interpreting Pooled OLS and FE different results

I know there are many similar questions like this one, which I have consulted (e.g Panel Data: Pooled OLS vs. RE vs. FE Effects ; Pooled OLS vs RE and FE ; Difference between OLS and FE) . Yet I haven'...
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0answers
13 views

Prediction interval for linear regression with autoregressive error

Suppose that ${y_{t}}$ and ${x_{t}}$ are time series variables. A simple linear regression model with autoregressive errors of order ${p}$, say AR(P), can be written as \begin{equation} y_{t}= \...
0
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0answers
4 views

Distance between two clusters vis-a-vis distribution of data

This was a question asked to me in an interview for graduation. I am interested to pursue in side of probability, statistics and machine learning. Professor asked me how would you calculate distance ...
1
vote
1answer
23 views

The expectation of the inverse of a negative binomial random variable?

Suppose $X \tilde{} NB(n,p)$ and $\mathbb{P}(X=x) = \binom{x-1}{n-1}p^n(1-p)^{x-n}$. Then what is $\mathbb{E}(\frac{1}{X}) = \sum_{x=n}^\infty \frac{1}{x}\binom{x-1}{n-1}p^n(1-p)^{x-n}$? Many thanks
1
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1answer
22 views

Question about interpretting an interaction term in a regression

If I run the regression: $y = \beta_o + \beta_1 * Black + \beta_2 Black*X + \eta$ where Black = 1 if the individual is black, and x is a continuous variable, and I am omitting x separately as a ...
1
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0answers
4 views

High-variance residuals in event group in CoxPH

I am using R and coxph() to fit a Cox proportional hazard model. When I plot the deviance residuals using ...
0
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0answers
9 views

Finding expected value of operating units

Given $N \cdot k$ operating units, every unit consist $k$ elements. If one element is missing from one operating unit, it stops working. Choosing $m$ element randomly, what will be the expected value ...
1
vote
2answers
23 views

Overfitting or under-fitting. which one is the most common error that happens in classification tasks?

I have read many blogpost and articles about overfitting and underfitting, and I have, to some extent, understood what they exactly are, and different ways to overcome these two problems. However, I ...
0
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0answers
11 views

What is a good way to find research with statistics data? [closed]

I'm searching for some researches for a study project , I'm looking for some researches that contains data bases or statistics data so i can apply my project on those researches , any practical way to ...
1
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0answers
5 views

r quantreg - quantile regression with clustered standard errors

I fit a quantile regression using quantreg:::rq on clustered data. I use the Huber sandwich estimator to obtain cluster-corrected standard errors, which is ...
1
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1answer
22 views

Building a score with logistic regression coefficients

I built an interest score for each individual in my database and wanted to have a second opinion on my methodology. We consider that an individual is considered as ‘interested’ when he has an open ...
0
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0answers
21 views

simultaneous independent time series forecasting

I have a number of independent time series. With the term independent I mean that they are not multivariate time series. There is not direct relationship between them (there is not any variable or lag ...
2
votes
1answer
25 views

Is it a good idea to use a linear model (like logistic regression) to generate new features for a non linear model (like random forest)? [duplicate]

The setting is a 2-class classification problem. We have too many features, some of them not very informative and with many zeros. We are thinking in ways of selecting the best features, and PCA (in ...

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