All Questions

0
votes
0answers
1 view

What is the added value of a multivariate Bernoulli distribution over a multinomial distribution?

I came across the multivariate Bernoulli distribution of Dai, Ding & Wahba (2013) that has the following form (in the bivariate case): $P(X_1,X_2)=p_{11}^{x_1 x_2} p_{10}^{x_1 (1-x_2)} p_{01}^{(1-...
0
votes
0answers
4 views

Chebyshev's inequality and Central Limit Theorem problem

With $Var(X) = 9$, find the $n$ sample size required so that with a probability less than 5% the mean of the sample differs from the expectation $µ = E(X)$ more than: a) 5% of the standard deviation ...
0
votes
0answers
7 views

How is the standard deviation in this coin tossing experiment calculated?

I'm reading Hypothesis Testing: The Basics, there is such an experiment: So, we have a coin. Our null hypothesis is that this coin is fair. We flip it 100 times and it comes up heads 51 times. Do ...
0
votes
0answers
5 views

Standard deviation of sum of samples from Bernoulli/Binomial

This should be simple I hope. In lecture notes from a physics course, the professor writes: $\text{Prob(success)}=\dfrac{k}{N}$. So query $q$ times, see some number $\mathcal{l}$ successes and ...
0
votes
0answers
8 views

How to split test and training dataset using 2 variables?

how to split training and test dataset using two variables x and y in python? sample coding: import sklearn from sklearn.model_selection import train_test_split train, test = train_test_split(data, ...
0
votes
0answers
8 views

Chi Square - alternative for three-way interaction

I am interested in the effect of predictability and expected value on the choice between two payment options. Basically, I have a 2(predictability of the payment option: predictable vs. unpredictable; ...
0
votes
0answers
6 views

Can a trained neural network recognize rotating characters?

Suppose I have a trained neural network that can recognize, for example numbers from 1 to 10, the size of the picture $28 \times 28$. I made the rotation of these pictures by 90 degrees. Does now ...
0
votes
0answers
6 views

how can i figure out my z statistic value is significant or not in two-step GMM?

topic: FOREIGN AID, CORRUPTION AND SUSTAINABLE DEVELOPMENT IN DEVELOPING ECONOMIES:A PANEL DATA ANALYSIS firstly i face higher value of z-statistics, my teacher told me it should be greater than 1.67 ...
0
votes
1answer
10 views

Symmetric probability density function proof

The problem is stated as: Let $f$ denote the density function of the random variable $X$. $X$ has a symmetric distribution around $a$, in other words, $f(a+h) = f(a-h)$. Prove that $E(X) = a$, ...
0
votes
0answers
5 views

Why with glmnet I obtain different coefficients for the different categories I want to classify?

I am performing a multinomial logistic regression using glmnet. I have 7 classes of trees to predict and different predictors. What I do not understand is why when I plot the coefficents vs. log ...
0
votes
0answers
9 views

How should I calculate mean CI - from raw data or mean values?

I have experimenatal data from medical industry. In the experiment 4 observations were weighted, each one 2 times for more precise measurement. As a final weight, a mean from each pair is reported. ...
0
votes
0answers
9 views

Defining custom Bayesian priors in R (BayesFactor package)

I'm performing some Bayesian analyses in R using the BayesFactor package, and was wondering whether it is possible to specify priors for the alternative not centered on zero (the current defaults ...
0
votes
0answers
6 views

Derivation of Formula for linear regression with data points forming a circle

Suppose we have one dimensional data with following conditions.1. The value of this single feature lies in the closed interval [-a,a].2. The associated target value with each data also lies in the ...
0
votes
1answer
10 views

Just want a quick confirmation on a simple normal distribution problem

Given mean = 167cm, standard deviation is 3cm, a) When four are randomly selected, all of their heights will be greater than 170? b) When four are randomly selected, two will have heights smaller ...
0
votes
1answer
7 views

Significantly different in categorical variables

I am working with a categorical variable with 4 mutually exclusive classifications (CC, CD, DC and DD). I had counted how many times each classification is repeated. (for example, 33 CC, 40 CD, 50 DC ...
0
votes
0answers
3 views

Three Factor Multiple Comparison Post-Hoc Test for Levene's Test

My research question is to find out whether or not my samples are exhibiting any significant differences in their variance in response to three possible treatments. Here are my possible groups: ...
0
votes
0answers
5 views

gamboost (mboost) and estimating / controlling random effect variance (brandom learners)

I am experimenting with gamboost (package mboost) with the goal of combining a random effects model (random group intercepts) with a boosted tree model. For context, I have already built a standard ...
0
votes
0answers
3 views

Multivariate Adaptive Regression Splines interpreting hinge coefficients

I am learning MARS using the earth package in R. I read about MARS on page 321 of The Elements of Statistical Learning https://web.stanford.edu/~hastie/Papers/ESLII.pdf and the tutorial here http://...
0
votes
0answers
8 views

Is expectation maximization an approximation algorithm?

Is expectation maximization an approximation algorithm? Does it give the exact solution?
0
votes
0answers
5 views

Detect Negative Correlation

In the attached image, if I want to detect negative correlation between these two data sets using machine learning algorithms, which one do I choose? I have indicated the boundaries I first need to ...
0
votes
1answer
19 views

Continous random variable short proof

I am given the problem: If X is a continuous random variable with cumulative distribution function F and density function f, show that the random variable Y = X^2 is also continuous and express its ...
0
votes
2answers
17 views

How to analyze a small dataset?

I have this dataset and I'm not sure how to analyze it. I threw the classical regression methods such as OLS at it and haven't achieved much success. My response variables are ...
0
votes
0answers
7 views

Variance inflation factors for time series

R code: I got an error by using vif function. ...
1
vote
2answers
10 views

Why is the convolution of two box kernels a triangle kernel?

Can anyone show the mathematical steps proving $K_{box}*K_{box} = K_{triangle}$
1
vote
0answers
11 views

summarisng sequences in R?

I have a large data set comprising 45,000 days of a rainwater system switching between running on a tank or off the city water mains. The system switches between the two depending on the level in the ...
0
votes
1answer
12 views

Measuring class imbalance of a dataset

Is there a way to measure the balance of a dataset? A citation will also be useful.
0
votes
0answers
6 views

Arima forecasting on dataset with many 0s

I have a dataset which contains 30 0 values out of a total of 80 observations. Is there a good technique to fit an ARIMA model on the data without either removing the 0 values or performing a moving ...
0
votes
1answer
36 views

Proof of probabilities that may not be independent

I am given the problem: Given $P(A) = \frac{3}{4} $, $P(B) = \frac{3}{8} $, show that: a) $P(A or B) > \frac{3}{4} $. b) $\frac{1}{8} < P(A and B) < \frac{3}{8} $. The problem does not ...
0
votes
0answers
8 views

How do you derive a risk function from a loss function given a normal distribution?

Let X1....X25 be a random sample from a normal distribution N(p,1) such that the domain of p stretches from negative infinity to positive infinity. Let y = X-bar (I.e. the sample mean) Let loss ...
0
votes
0answers
10 views

Repeated measures ANOVA question

I'm new to statistics and looking for some guidance on choosing my variables for a repeated measures ANOVA. My data set consists of 4 dependent variables: 1. Gait speed 2. Balance test 3. Leg ...
0
votes
0answers
15 views

How do you select the best from a number of linear models?

I'm learning linear regression with the Carseats data set. I went through the data, cleaned it, encoded the dummy variables and checked for collinearity. The dataset has 400 observations on Carseat ...
1
vote
2answers
25 views

Maximum Likelihood Estimator (MLE) for $2 \theta^2 x^{-3}$

I'm having a bit of trouble solving this. $$ f(x_i; \theta) = 2 \theta^2 x_i^{-3}, 0 \le \theta \le x_i \lt \infty $$ I start by finding $f(\textbf{x}; \theta)$: $$ f(\textbf{x}; \theta) = \prod{f(...
0
votes
0answers
7 views

bayesian decision making - comparing expected loss

The problem is like this: Suppose that I am considering which country should I invest on, country A and country B, based on their GDP growth rate $\alpha$. There are two possible choices for each ...
1
vote
0answers
8 views

How do we perform residual analysis on binomial model with small counts?

I know that both Pearson and Deviance residuals tend to be approximately normal for Poisson and Binomial model with large counts when standardized, so we can exploit that to perform the residual ...
0
votes
0answers
16 views

Strange rugarch error: $ operator invalid for atomic vectors? [on hold]

So, I am trying to make a huge nested for loop (optimizations be left for later) to fit all of the GARCH models available from rugarch. This is my MLE that ...
1
vote
0answers
4 views

Calculating the margin of error on an estimated total number of class instances in population

I have a completely random sample of size 10 from a population of objects (population size 1000, if that helps) which can belong to either one of two classes, A or B. Based on a guess from superficial ...
0
votes
0answers
11 views

Rules of thumb for partial residual (component + residual) plots as diagnostics for linearity?

Here are the standard diagnostic plots of a multiple linear regression model that includes an autoregressive term at lag-1 (i.e. AR(1)). I have logged & z-scored my input data. Ben Bolker says ...
1
vote
1answer
12 views

Help in understanding how we arrive at 'reduced form equations'

Referring to equations 1 and 2 above, I understand that the object is to estimate the endogenous variables (consumption (c) and income(y)) as a function of the exogenous or predetermined variables. ...
0
votes
1answer
14 views

How to estimate the probability distribution of two parameters given a discrete output?

I'm currently facing a new type of problem, and i have no idea how to solve it, so any suggestion will be really appreciated ! The problem is the following: I have a matrix of temperatures, depending ...
2
votes
0answers
10 views

How to choose between additive and multiplicative decomposition in time series

I have a time series which is the number of weekly flu cases from 2010 to early 2018 in one county. I want to remove seasonality from my data so I can have a clearer data to infer the relationship ...
3
votes
2answers
32 views

The counterfactual model for causation

My professional training took place in the late 1990's and I don't recall hearing some of the terminology that seems nigh-universal nowadays. I believe the accepted name is "counterfactual model for ...
0
votes
0answers
9 views

Corelation between two dichotomous variables

I have a data from a research with responses (yes/no) about three questions (A,B,C) and I would to see if the variables are correlated. First of all i compared the proportion of agreement(yes-yes, no-...
0
votes
1answer
28 views

R: What's the right way to add an interaction term in lm()? [on hold]

I'm working with the Carseats data. I'm making a model to predict the sales of Carseats and I'd like to make an interaction term with Price and Competitor Price. Is it as simple as ...
1
vote
2answers
27 views

Proof expression for the autocovariance function of AR(1)

The representation for the model AR(1) is the following: $Y_t=c+ϕY_{t-1}+ε_t$ where $c=(1-ϕ)μ$ ($c$ is a constant). I want to understand the calculations that there are behind the general formula ...
0
votes
0answers
9 views

Cannot seem to converge beyond a loss of 3 on an object detector being trained on YOLO

Data I have scoured the internet for resources on how to tackle this problem, but there seems to be a lot of resources that point me in the wrong direction. I am looking for a methodical guide, or ...
0
votes
1answer
14 views

Minimal sufficient statistic for location exponential family

Let $X_1,\dots,X_n$ iid with pdf $$f(x|\theta)=e^{-(x-\theta)},\,\,\,\theta<x<\infty,\,\,\,-\infty<\theta<\infty.$$ Part (b) of Problem 6.9 in Casella and Berger asks to find a minimal ...
0
votes
0answers
11 views

Bayesian posterior pdf for weighted dice with uniform prior

We want to find posterior pdf for dice tossing with uniform prior. We are interested in rolling of weighted dice. The outcome is 1,2,...,6. We assume that prior pdf is uniform. Assume that we ...
1
vote
0answers
10 views

Using PCA in domain adaptation

In literature, I see people using (Kernelized) Principle Component Analysis, not for feature extraction, but for domain adaptation. In other words, I have data from a source domain and I would like to ...
1
vote
1answer
11 views

Why would you introduce a constant in a moving average model, when you already have the option of differencing?

In the online forecasting book of Hyndman (https://otexts.com/fpp2/MA.html) firstly the use of differencing is explained. After that he shows the formula for a moving average model: $$y_t = c + \...
0
votes
0answers
7 views

A generalized LASSO constraint

I want to use LASSO in R but shrinking towards some fixed vector $A$, instead of shrinking towards 0. The desired L1 constraint, given coefficient vector $\beta$, is $||\beta-A||_{1} \leq k$, rather ...

15 30 50 per page