All Questions

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-...

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 ...

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 ...

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 ...

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, ...

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; ...

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 ...

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 ...

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 $E(X) = a$, ...

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 ...

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. ...

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 ...

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 ...

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 ...

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 ...

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: ...

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 ...

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://...

Is expectation maximization an approximation algorithm? Does it give the exact solution?

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 ...

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 ...

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 ...

R code: I got an error by using vif function. ...

Can anyone show the mathematical steps proving $K_{box}*K_{box} = K_{triangle}$

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 ...

Is there a way to measure the balance of a dataset? A citation will also be useful.

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 ...

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 ...

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 ...

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 ...

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 ...

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(...

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 ...

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 ...

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 ...

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 ...

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 ...

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. ...

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 ...

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 ...

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 ...

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-...

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 ...

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 ...

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 ...

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 ...

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 ...

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 ...

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 + \...

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 ...