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What is the covariance of a sum and a double sum?

can someone please explain what the covariance of the following is? $ \text{Cov}\big(\sum_{i}^{m}{X_{i,k}},\sum_{k}^{o}\sum_{i}^{m}{X_{i,k}}\big) $ In Wolfram it says $ \text{Cov}\big(\sum_{i}^{m}{...
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1answer
9 views

Find $\alpha$ and $\beta$ so that $f_X(x)$ can be a density function

\begin{equation*} f_X(x) = \begin{cases} \frac{4x^2}{5} & \text{ , if } 0 < x \leq 1\\ \alpha(5-2x) & \text{ , if } 1 \leq x < 2\\ \beta x^2 & \text{...
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0answers
7 views

Expressing a hazard function with a Cox proportional hazards model

I'm trying to wrap my head around Cox models as well as how to express them in the form of hazard functions when you have both categorical AND numeric covariates. I need some assistance with this ...
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0answers
4 views

Can I complete a Moderation Analysis with transformed data?

I am completing a moderation analysis (model 1) in SPSS with the Hayes PROCESS macro, however I had previously applied a logarithmic transformation to my outcome and moderator variables for them to ...
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0answers
4 views

Two-Way Anova Help?

Suppose I want to find out if there is a relationship between salary bracket and gender, where $M$ represents male, $F$ represents female and $A,B$ and $C$ are three different salary brackets. ...
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0answers
13 views

Interval width for truncated confidence intervals

I'm conducting a simulation study to compare different methods of constructing CIs for a single proportion. The traditional (Wald/Asymptotic) CI can estimate the upper and lower bounds above 1 and ...
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0answers
9 views

Gaussian Process Regression - Draw from posterior

I recently came across Gaussian Process Regressions and started exploring it a bit further since it grabbed my attention. In Rasmussen's book Gaussian Process Regressions for Machine Learning I found ...
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0answers
3 views

Class reversal during model training

In my model training of an XGBoost model in spark, I noticed that higher probabilities are labelled as negative class, and lower probabilities are named positive class. This is odd since usually we ...
0
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1answer
9 views

Error Propagation of standard devi

I have following problem: I do measurements with technical triplicates and biological dublicates. So I prepare the same sample two times and measure each one three times. This gives me an average ...
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0answers
4 views

constrained GAM using bspline

I have presence/absence data for an animal as well as associated environmental covariates, temp, salinity, and oxygen. I'm using a GAM to find the relationship of the response over each covariate. I ...
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0answers
4 views

Reporting F-statistic from Prism

I'm a grad student trying to prep an abstract for a poster submission. I've run the data in Prism (2 factor RMANOVA, treatment x time), but I always struggle with how to properly report my stats. ...
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0answers
12 views

Interpretation of higher coefficient for group with smaller mean

I am running a fixed effects poisson model with robust standard errors in STATA (xtpqml). The model I run it on has my count data as dependent variable and then as my independent variable I have a ...
-1
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0answers
8 views

a sequence of i.i.d random variable property [on hold]

Let $X_1,\dots, X_n$ be i.i.d random variables taking values in $\mathbb R$ with the fact that expectation of $X_1<0$, and variance is finite. Suppose that $\{\eta_n\ge 0\}$ is a sequence such that ...
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0answers
11 views

Probability getting lost [on hold]

What is the probability that it is lost in Toronto? In Calgary? In Vancouver?
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0answers
5 views

Simulate cointegrated prices and VAR model

I am trying to simulate cointegrated stock prices and use a VAR Model to make forecasts. This is the code I wrote so far: ...
2
votes
1answer
24 views

Is appropriate to use empirical Bayes (EB) in this way?

Background. I have data from a study where participants make a series of judgments (a series of decisions with a binomial outcome, either $y=1$ or $y=0$). I have a model of the underlying decision-...
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0answers
7 views

K-Means Unable to Detect Small Clusters

I am just wondering about this issue brought up by our teacher about a drawback of K-means being unable to detect small clusters. It's homework that we should come up with ideas about why this is so ...
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0answers
16 views

Orthogonal matrix and inner product

Assume that $A$ and $B$ are both orthogonal matrix. The question comes from a proof I read which I attached in the following. $\begin{align}&\arccos(\max\{|\langle Ax,By\rangle| : \|Ax\|=\|By\|=1\...
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0answers
6 views

Bayesian liability threshold model

Let $\bf{y}$ denote a vector of binary data, such as whether a group of individuals suffer from a particular disease, and let $\bf{X}$ denote a matrix of potential predictors, including an intercept ...
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0answers
5 views

Identifying anomalies multiple time series using statistical methods

I am trying to detect anomalies from a Time Series sequence, that is calculated as an aggregate count of multiple unique Time Series'. For example, in the graph below: We have aggregate counts shown ...
0
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0answers
14 views

Example of random process with negative variation

I study about random processes. Let us have $\{X_1, X_2, \dots X_n\}$ observations. I learned, that in stationary time series the sample autocovariance function is defined as $$ \widehat{γ}(h)= \...
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0answers
17 views

Why is PCA (using sklearn library) increasing the size of my dataset?

I used PCA on the Fashion MNIST dataset, with the intention of reducing the size of the dataset. ...
0
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0answers
10 views

how to use categorical variable with continuous variables in a EM mixture model

I'm trying to use the mclust and flexmix packages in R to do unsupervised clustering of my data which has both continuous variables and categorical variables. I'm having a hard time understanding how ...
-2
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0answers
15 views

Confidence Intervals 111110 [on hold]

If a sample of 30 wheels has a mean of 60 cm, give a 95% Confidence Interval for the mean diameter of the wheels from the factory. Enter your answer as an interval [ a, b ] where a, b should be ...
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0answers
10 views

How can I combine multiple variables of different scales [on hold]

I have several factors that I want to combine into one. But each factor is of a different scale. Factor A goes from 0-1, factor B goes from 1-10, factor C goes from 20-40, etc. I don't want the ...
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0answers
23 views

Finding the MGF, distribution, and parameter of a random variable

I am currently working on the following problem from my textbook Introduction to Probability by Blitzstein and Hwang: Judit plays in a total of $N\sim Geom(s)$ chess tournaments in her career. ...
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1answer
20 views

Are Python classes in Spark notebooks beneficial or common in the data scientist community? [on hold]

Being a software developer, I am coming from an object-oriented programming background, and I think in terms of classes and objects. I am currently working on a ...
0
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0answers
8 views

Applying settlement and Regional fixed effects

I'm reading a paper by Gyöngyösi and Verner (2019), and noticed that the authors have included fixed effects at the settlement (seems to be akin to village/town) and at the region level, in a number ...
0
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0answers
9 views

Too large standard errors of parameters from the covariance matrix when fitting data using curve_fit

I have some troubles when try to fit my data using curve_fit. I don't really know where I am wrong: in code or in math. First, I have too large variances which I get from the covariance matrix: ...
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0answers
8 views

Using text and images for training, but only images for inference

I am working on a problem with data like: $\{X, T, y\}$, where $X$ are images, $T$ is useful information about those images, and $y$ are image labels. I would like to build an image classifier that ...
0
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0answers
12 views

Neural Network unable to learn [on hold]

I am following trask's article to build a bare bone neural network in Python. Though he builds 1 layer Network (that maps 3 inputs to a single output) and a 2 layer network (that has 3 inputs, 4 ...
0
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0answers
6 views

AutoEncoder Reconstruction error for Anomaly Detection

I'm building a convolutional autoencoder as a means of Anomaly Detection for semiconductor machine sensor data - so every wafer processed is treated like an image (rows are time series values, columns ...
0
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1answer
38 views

How to carry out the score bootstrap?

I want to translate the "score bootstrap" that Kline and Santos (2011) propose into R code. The method is described on page 6 as follows. STEP 1: Obtain the full sample OLS estimate $\hat\beta$ and ...
0
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0answers
8 views

Explaining Profitability in Banks Using Panel Data Dynamic/Fixed Effects Model

I am currently looking to study the profitability of banks. My 4 independent variables, which are taken from banks balance sheet, are just financial ratios. My time is 13 Years, and I have 21 banks. ...
0
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0answers
15 views

How to compare a model with my data [on hold]

using R I have to compare a model, that is the Fitt's law, with my data. In particular the Fitt's law states that MT = a + b × log2(2D/W), with MT is the time needed to perform a task, a and b being ...
0
votes
1answer
20 views

How to tell if difference in f-score is significant?

I have $N$ data points, each of which has an associated label that is either $0$ or $1$. For which data point I know the true label. Say I put all true labels in a vector $t$. Next I ask Alice to ...
0
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1answer
26 views

Uncertainty Quantification in Time Series Analysis

The stock market value of the data point connected by the red line is predicted by linear regression using market values as well as Twitter sentiment data and more in a certain period of time (red ...
0
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0answers
7 views

How to estimate conditional CDF using python StatsModels

I am using statsmodels '0.10.1' to obtain conditional CDF of a 2 variable problem. ...
0
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0answers
9 views

How to compute RSquare from GLS regression in a Fama Macbeth procedure

I am trying to compute the RSquared from the Fama Macbeth procedure using GLS regression, but for some reason I get negative values, so I was wondering what the problem might be. The Fama Macbeth ...
0
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0answers
10 views

Using garchFit to fit an ARCH(1) process

I tried using the garchFit function FinTs library. This is what I am trying to run: garchFit(formula=~arma(0,1,2)+garch(0,1), data$`1 YR`) However I get the ...
2
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1answer
80 views

Why is Elastic Net called Elastic Net?

What is the etymology of "Elastic Net"? Does it have anything to do with a "lasso"?
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0answers
4 views

plot fuzzy_partitions in R [on hold]

I am trying to fuzzify a distance measure of a point using only fuzzy_partitions. I do not need a full fuzzy inference engine as all what I do need to aobtain is the corresponding fuzzy membership ...
0
votes
0answers
14 views

Bayes classifier and unavoidable error

Consider the following two-class classi cation problem, where $Y = 0 \text{ or } 1$. Suppose $Y$ is a random variable satisfying$ P(Y = 0) = \frac{1}{3}$ and $P(Y = 1) = \frac{2}{3}$: Moreover, we ...
0
votes
1answer
12 views

How to simulate data for ordinal cumulative probit/logit model with random effect?

I am currently working on a project to improve the knowledge score on certain disease. The outcome variable is ordinal with 8 levels. In order to estimate the sample size, I need to run a simulation. ...
2
votes
1answer
22 views

Conditional independence problem for poisson random variables

I have this problem: Let $X = V + W$ and $Y = V + Z$ where $V, W, Z$ are independent Pois($\lambda$) random variables. I found that $Cov(X, Y) = Var(V) = \lambda$ It now asks to find whether $X$ ...
0
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0answers
8 views

German credit dataset : interpretation of checking_status feature

I am struggling to understand the meaning of some features of the german credit dataset (https://archive.ics.uci.edu/ml/datasets/statlog+(german+credit+data)). I am particularly interested in, the ...
0
votes
1answer
22 views

How can I generate a completely balanced combination

Attaching a code that generates unique combinations of 8 letters but, it still lacks a condition wherein all letters should have equal counts per column. For my code, basically, letter a to h should ...
4
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0answers
45 views

How does random variable nesting in GAMs work (mgcv)?

Consider me very new to the world of GAMs, I am actually using it out of necessity rather than by choice but I thought it could be a chance to learn something new anyway. Originally I had hoped to ...
0
votes
0answers
13 views

Optimal grid for Nadaraya-Watson CV bandwidth selection

Is there any rule of thumb or optimization technique for number of grid points for Kernel Regression? I am doing Nadaraya-Watson on 10 years data (2500 daily observations) of Swap rate. While ...
0
votes
1answer
26 views

Neural network (or deep learning) or gradient boosting for large data with a few features?

I'm dealing with a supervised regression problem, a financial data set with 5m observations and a few features (about 5 to 10). All the features are continuous numeric values, without any missing ...

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