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Mathematical theory of statistics, concerned with formal definitions and general results.

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Generalizing the relationship between cross-entropy and maximum loglikelihood

Let's say we are trying to learn a distribution $p(\cdot)$ by searching through a parametric family $p_\theta(\cdot)$. We can have access to $p(\cdot)$ either analytically or only through samples, and ...
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1answer
39 views

Can neural networks learn $g(x)$ from $\mathbb{E}[g(X_t)] = \int_{-\infty}^{\infty} g(x)p_t(x)dx$

Let $\mathbb{E}_x[g(X_t)]$ be the expected value of a random variable $X_t$ with known probability density $f_t(x)$ then for the continuous case $$\mathbb{E}[g(X_t)] = \int_{-\infty}^{\infty} g(x)...
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19 views

How to uniquely identify each Employee in an Organisation with a hash value between 0 and 511 [on hold]

let I be a set of random input values, with I = N . Then h meets this quality criterion if (∀1 ≤ i ≤ n)(|h(I) ∩ Pi| ≈ N/n ) if N >> n. Suppose you want to use Employee numbers to calculate a hash, ...
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14 views

Soccer Attacking And Defensive Strength Using Maher's Model

I have read the paper by Maher which talks about modelling football (soccer) score. He uses parameters like alpha, beta, gamma and delta for attacking strengths and defensive weaknesses (both home and ...
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1answer
28 views

Size of the Hypothesis Space

(I'm asking the same question as the linked one, I simply don't have enough reputation to comment yet, but hopefully, this one will more clearly explain what me and the other asker both mean) Let's ...
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1answer
29 views

Clarification on “intercept”?

I'm currently reading "Competition-Based Dynamic Pricing in Online Retailing: A Methodology Validated" by Fisher, Gallino, and Li. In the paper they mentioned that variables $\alpha_j$ and $\alpha_r$ ...
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0answers
12 views

Law of total covariance with variables conditioned on different variables

Suppose I have $X_1|\theta_1$ and $X_2|\theta_2$ such that $X_i \sim D(\theta_i)$ and $D$ is some known distribution with parameter $\theta$. $X_1|\theta_1$ and $X_2|\theta_2$ are assumed independent. ...
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27 views

Regression coefficient estimate bounded as a function of the error covariance

Consider the linear regression model with one non-stochastic predictor: $Y = x \beta + \varepsilon$, where $Y \in \mathbb R^n$, $x \in \mathbb R^n$, $\beta \in \mathbb R$, and $\varepsilon \sim \...
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0answers
20 views

How can I use equations of several averages of the same data derived by Excel cross-plots? [on hold]

I'm conducting a research in which a large set of data were used (picture 1). To enhance the correlation coefficient and learn about the trend, I grouped the initial large set into averages of fixed ...
2
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2answers
59 views

Difference between “Sampling” and “Subsampling”?

I just got this question in my mind, because I have seen so many times in the literature that these two words are being used alternatively, Sampling and ...
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0answers
5 views

Help with computing message on TrueSkill factor graph

I want to better understand the step for calculating the message from the game factor $h_{g}$ down to the difference variable $d_g$ on the TrueSkill factor. Such message is shown in the Rasmussen's ...
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3answers
49 views

What does a t-test tell us that just comparing two means doesn't?

I'm confused how comparing two mean values is different from doing a t-test. Can't I just see the two means and conclude if there's a difference? How does ttest makes sure if the 2 means are ...
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0answers
9 views

Is there any model that can detect and eliminate the fake boosting part of the data(data cleaning model?)

As far as I know, there usually were some fake part in some data For example, In many company's sale, there are some fake part in the data, it actually sale is 100000 dollars, but for some reason ...
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0answers
29 views

Is it guaranteed that a linear programming problem has a unique solution? [migrated]

Given a generic linear programming problem i.e. minimize $\hat C^T \hat X$ subject to $\hat A \hat X <= \hat B$ and $\hat X >= 0$ Is it guaranteed (mathematically speaking) that a solution ...
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1answer
22 views

In prediction, when should I use rolling windows vs. nonoverlapping ones?

Suppose I have daily time series data and I want to predict a month in advance using a set of features. I have lots of them so I'll be using regularized linear regression. To create the response I can ...
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3answers
1k views

Are all continuous random variables normally distributed?

All the time I see examples of the normal/Gaussian distribution with continuous random variables. So my question is do all continuous random variables have a Gaussian distribution?
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0answers
5 views

Lottery scenario with different odds for multiple outcomes

There are 21 chances to achieve six outcomes, ranging from most desirable to sixth most desirable. There are six players. Player 1 has 6 of 21 chances to attain the most desirable outcome. Player 2 ...
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0answers
18 views

How advanced are those models to someone with minimal Econometrics background? [closed]

How would you rank those models in term of difficulty, I'm required to understand those models and methods to some degree and need to set up my study plan to cover those models starting from the ...
2
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1answer
80 views

How can I predict logistic model? [closed]

The data is like this.(of course, I have a more data) ...
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0answers
21 views

how to train model with features have low variance in train set

Assume that I trained a nonlinear model , one feature of the training data has very low variance, because of this, the same feature of the test could be quite different, at least in scale, from the ...
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0answers
8 views

Binary Logistic Regression with varying zero inflations [closed]

I am investigating the effects of zero inflation on the logistic parameters. So i want to vary the percentages of zeros and ones on the response variable (y). for instance i need a code in R that can ...
2
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1answer
51 views

Covariance Zero Equals Independent?

We know that $cov(X,Y)=0$ does not warranty $X$ and $Y$ are independent. But if they are independent, their covariance must be $0$. My question is: what kind of distribution must $X$ and $Y$ be for ...
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1answer
15 views

Adjusting Nutrient Intake for Energy Intake OR Body Weight OR Both?

Introduction I am analyzing a data set which I am grouping in protein intake quartiles. Before using the protein intake data (in grams), I want to adjust it to avoid potential confounding. Problem ...
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1answer
32 views

Probability Distribution and Transformation

Let X have the following distribution function F(x)= 0 for x<0; x/3 for 0<=x<=2; 1 for x>2. Let Y=X^(2) To find P(Y<(X)) Do we simply substitute X^2 for Y and divide to get P(X<1) ...
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2answers
50 views

Confidence Intervals meaning [duplicate]

Lets say I know population std. deviation $\sigma=5$ and sample size $n=60$. Now lets say my sample mean is $\overline{X}=98$. I already know from central limit theorem that 95% of the time the sample ...
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0answers
21 views

Trends analysis: use the year when the data generation was concluded or the average of years when the data generation process took place

In my research, I want to determine time trends in a variable y, controlling for confounders a and b. My time variable x is the "year when the event y took place". In some cases, I have data for a ...
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1answer
33 views

how to solve this markov chain problem?

This is a problem in the book of "introduction to stochastic process ". Any help to solve this problem ??
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0answers
17 views

Generalizing on-policy distribution of states

The box on page 199 of Reinforcement Learning: An Introduction, Second Edition talks about distribution of states in on-policy episodic settings. I want to generalize it for continuing tasks as is ...
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0answers
20 views

Solving fraction value using Gamma function

How is Γ(3.3) = 2.68? I have tried using various formulas, but couldn't reach the exact value. Thanks for the help in advance!
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1answer
20 views

Attempting to find mean of Weibull function in R

I am using a Weibull distribution in R, and know that: E(X) = 1000 and Var(X) = 500,000 Knowing: E(X^r) = ($\Gamma$(1+ (r/$\gamma$))) * 1/c^(r/$\gamma$)) I ...
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0answers
17 views

the interrupt sequence

Player X throws a coin more than a thousand times. Player Y starts the game by betting on the basis of somersaults another perfect coin (if the symbols on the coins matched won X, if the symbols ...
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1answer
57 views

Conditional distribution of $(X_1,\cdots,X_n)\mid X_{(n)}$ where $X_i$'s are i.i.d $\mathcal U(0,\theta)$ variables

Let $(X_1,X_2,\cdots,X_n)$ be a random sample drawn from $\mathcal U(0,\theta)$ distribution. It is a common exercise to prove that the maximum order statistic $X_{(n)}$ is sufficient for $\theta$ as ...
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2answers
42 views

Should we identify outliers from population prior to taking sample?

I am revising undergrad statistics course via this course, where i am learning technique to pull out sample from population. While ensuring that sample is decent representative of population, i am ...
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1answer
39 views

I have to answer the question R studio [closed]

Two computer factories assemblies notebooks from the same finished parts using different technologies. The measured assembly-times in factory A and B are the following ...
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0answers
34 views

Parameters in Autoregressive representation of an ARCH model

Suppose we have a $0$ mean time serie representing stock index returns about a title, $r$. I also know it follows an $ARCH(p)$ model with parameters $\omega$ and $\alpha$, specified in the following ...
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0answers
13 views

I'm trying to determine how a Mann Whitney U test was applied to this dataset in a paper.

http://aac.asm.org/content/51/9/3111.full In the text they say they used a Mann Whitney U test. In one section of the results they report this: Association of PBP 2 with antimicrobial ...
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0answers
42 views

Finding maximum likelihood estimator

Let $X_1, ...X_n$ be IID random variables with uniform$[ -\theta , \theta ]$ . I need to find the Maximum Likelihood estimator (MLE) of $\theta$. My work is as follows, The likelihood function is , ...
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0answers
54 views

What is the final goal of RobustPCA methods?

I have an ongoing research that is about clustering and for assigning each data point to a specific cluster, I'm using the Mahalanobis criterion that is gravely based on the covariance matrix of the ...
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1answer
26 views

List of machine learning classifiers that naturally assume data in normal distribution

I have searched about this question but no answer really made it comprehensive. To my knowledge, linear regression and most clustering algorithms naturally have the assumption that data need to be in ...
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1answer
87 views

Filtering out bursts with a consistent range from a time series

I have time series of bursts that look like this: … and zoomed in: Now, there are also spurious bursts (which I call noise) in the data, which look like this: … and zoomed in: As you can see, the ...
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1answer
45 views

Invert P-Value to get Confidence Interval

This is a weird problem, but please bear with me. I could use some insight. Imagine you have a black box that spits out p-values for $H_0: \theta = 0$. We'll call this black box $g(\cdot)$. Assume ...
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0answers
38 views

How do I get about this question?

I am not a student of statistics but I hope to get an answer of my questions with the help of the same. I run a business in which I manufacture certain types of products. These things are categorized ...
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1answer
21 views

What to do when the test data set has many “features” that are generated by dummfying a categorical variable that are not present in the training set

Say you have a variable (in this case industry) that you dummify (one hot encode) hence creating many new features in both the training and test sets for which you are getting ready to run a machine ...
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0answers
22 views

How to measure the strength of association between categorical variables and quantitative variables?

I used chi-squared test to measure the strength of association between to categorical variables and also I use Pearson Correlation Coeffiient to measure the association between two quantitative ...
5
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2answers
194 views

What is the distribution of min{0,X} when X follows some general normal distribution?

What is the distribution of $\min\{0, X\}$ when $X$ follows some general normal distribution?
5
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2answers
206 views

Notation in statistics (parameter/estimator/estimate)

In statistics, it is very important to differentiate between the following three concepts which are often confused and mixed by students. Usually, books denote by $\theta$ an unknown parameter. Then ...
2
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1answer
76 views

Does applying standard normalisation lead to normal distribution?

Does applying standard normalisation to data variables mean changing the distribution of data variables to normal distribution having mean=0 and variance=1?
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0answers
20 views

What does Diagonal Rescaling of the gradients mean in ADAM paper?

I was reading the paper on ADAM, which it mentions "invariant to diagonal rescaling of the gradients," - what does it mean? Also, another paper called "NORMALIZED DIRECTION-PRESERVING ADAM" - mentions ...
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11 views

FHS: Filtered Historical Simulation of VaR

If I wish to run a FHS for VaR model, first I estimate the GARCH model on the historical returns $r_{t}$, then I obtain the historical innovation time series as $z_{t}=\frac{r_{t}}{\sigma_{t}}$, where ...