Questions tagged [mathematical-statistics]
Mathematical theory of statistics, concerned with formal definitions and general results.
2
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0answers
16 views
Bias Variance Decomposition 2.7 in Elements of Statistical Inference
I try to derive 2.7 from the book. I expose my demonstration
$E_{\tau}[(y_{0}-\hat{y_{0}})^{2}]=E_{\tau}[y_{0}^{2}]-2E_{\tau}[y_{0}\hat{y_{0}}]+E_{\tau}[\hat{y_{0}}...
0
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0answers
8 views
Encoding quantitative outputs for regression
From Elements of Statistical Learning:
For a two-class G, one approach is to denote the binary coded target
as Y , and then treat it as a quantitative output. The predictions Yˆ will
typically ...
0
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0answers
14 views
How to denote token length in statistics
I have a vocabulary (V) that includes terms. (e.g., V = ['data mining', 'data', 'machine', 'machine learning'])
I also have a ...
1
vote
0answers
18 views
If $X$ is from (canonical) exponential family, do we always know the distribution of $T(X)$?
Assume $X$ are generated by a distribution from exponential family,
$$ f(X; \theta) = h(X)\exp\{\eta(\theta)T(X) - b(\theta)\}$$
After solving several exercises with various distribution functions, ...
0
votes
0answers
14 views
What statistical tool should we use in our study? [on hold]
The title of our study is "The Influence of Online Gaming to Interpersonal Relationships of College Students"
Our independent variable is Online Gaming (Time Spent & Type of Game) while our ...
2
votes
1answer
22 views
Asymptotic distribution of median estimator when density doesn't exist
We know that when density(say $f$) exists at the median(say $\theta$) then the median estimator(say $\hat{\theta_n}$) has the following property $$ \sqrt n(\hat{\theta_n}-\theta) \to^d N(0,1/\{4f(\...
1
vote
0answers
20 views
Why is degree of freedom so important? [duplicate]
As far as I'm concerned, the degree of freedom is simply the number of linear equations need to be satisfied. However, it seems closely related to the statistical deduction. For example
Dividing by ...
1
vote
0answers
28 views
How to derive a ranking function by analysing feature correlations
I am analysing some employee details to find the efficiency of the employees. Ideally I want some rankings to rank them based on these features.
My features include;
current salary
projects ...
0
votes
1answer
20 views
How do you confirm whether null hypothesis can be rejected in decision rule? [on hold]
I have been learning more about decision rule and found this example. One thing I don't get from this is the part where it says 'coefficient is not statistically different from zero'. What does this ...
0
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0answers
14 views
Hypothesis testing with matrix of measurements
I need to test if a treatment has taken effect in a certain group of patients for which I make a measurement of the relevant variables before doing the treatment and afterwards.
Usually, I would do a ...
0
votes
0answers
24 views
Proof without words (about statistics or probability)
Are there any well known proofs without words about statistical theorems like for example the CLT, LLN, or the Gauss-Markov theorem? There are many about mathematics in general (e.g. here, or here), ...
0
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0answers
11 views
(Existence part of) Neyman-Pearson via weak-* convergence
I would like a ask whether there is any statistical reference containing the following functional analytic argument for the existence part of Neyman-Pearson:
Let $(R, \mathcal{F}, \mu)$ be a measure ...
0
votes
1answer
18 views
Why Converting Regression to Ordinal Regression
Intro:
Ordinal Regression/Classification is a classification where the labels have orders (https://en.wikipedia.org/wiki/Ordinal_regression)
Question:
Can you comment what are pros and cons if ...
0
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0answers
20 views
Validity of T - test [on hold]
I have been ask to evaluate the validity of t-test resukts. I was wondering if anyone could help me.
1
vote
1answer
37 views
Regression on Auction Prices, Multiple Prices Randomness
I'm currently building a model to predict internet auction sale prices of products in a marketplace. There are a lot of instances where a product goes for multiple prices but it's basically the same ...
1
vote
1answer
46 views
What does the pmf of a discrete random variable look like if it can take on the value $\infty$?
What does the pmf of a discrete random variable look like if it can take on the value $\infty$?
Consider a stopping time $\tau$ of a Markov chain, which is a random variable that takes values in the ...
0
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0answers
20 views
Finding Sum of Squares in a multiple regression ANOVA table by hand?
I seem to be having quite a bit of trouble with this problem in an old stats exam. Its basically asking me to fill out an analysis of variance table by hand. My data is given as follows:
and we are ...
0
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0answers
8 views
covariance for measuring linear relationship, how about the non-linear relationship
I once heard the statement that
Covariance is a measure of the linear relationship between two variables, such as X and Y
If X and Y has non-linear relationship,...
0
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0answers
20 views
Proof that the mean is a complete sufficient statistic and the sample variance is an ancillary statistic
I have $X_1, X_2, ..., X_n $ that are random samples from the single variate $N(\mu,\sigma^2) $. I want to prove that the mean $\bar{X}$ and the sample variance $s_x ^2 = \frac{1}{(n- 1)} \sum_{i=1}^...
0
votes
1answer
18 views
Interpreting the Chi Square for a 2x2 contingency table
Here is my problem. I need to implement an algorithm to find if there is a dependency between 2 categorical variables. My population can vary a lot as it is an input I don't have control over. My ...
0
votes
0answers
14 views
AICc value How to derive?
initially let me introduce a concept widely used in ARIMA in the following. $AICc = AIC + \frac {2k^2+2k} {n-k-1}$ where n denotes the sample size and k denotes the number of parameters. Thus, AICc is ...
0
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0answers
11 views
What statistical test for multiple groups of paired data
I'm a student performing a research on seeds and their coagulation effectiveness. I have five groups (seeds) and I measured the clarity of water before and after (5 groups, 3 trials total). So as I ...
0
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0answers
11 views
Confidence vs. Count in association rule mining: which one is better?
I am writing a program that mines association rules from a large data set. I have an array of association rules, and I have to decide which ones are more representative of the patterns I am studying.
...
5
votes
2answers
77 views
If $F_X(z) > F_Y (z)$ for all $z\in \mathbb{R}$ then $P(X < Y ) > 0$?
I came across this question in a review of an old exam I took. I didn't get the answer correctly then, and I'm struggling to figure the answer out now. Can anyone help me reason through this?
...
0
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1answer
30 views
How can I prove the following relation between the probabiloity of X and its expectation using Cauchy-Schwarz inequality?
For a random variable $ X \geq 0 $ and $E[X^2] < \infty $, I'm asked to prove the following:
$ P(X> 0) \geq \frac{(E[X])^2}{E[X^2]}$
It makes intuitive sense to me that it must be the case, ...
1
vote
0answers
19 views
Quantile Regression loss function/ check function proof
Can anyone help me to show that this statement is true. I have looked in Koenker's Quantile Regression (2000) and a load of other sources but I cannot find a solution. There seems to be a trick ...
1
vote
0answers
17 views
How do I know which GLM family to use?
I have the following question:
I need to specify the distribution, link function and linear predictor. I know how to do find the link function and linear predictor if I know the first but don't know ...
0
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0answers
16 views
Infer statistical model prediction confidence coefficient based on the past predicted and actual results
Currently, I encountered such as a problem: For example, when I built a statistical model based on the past 3 month data and using the model to predict for the next month. But I found that the ...
5
votes
4answers
2k views
If I can make up priors, why can't I make up posteriors?
My question is not meant to be a criticism of Bayesian methods; I am simply trying to understand the Bayesian view. Why is it reasonable to believe we know the distribution of our parameters, but not ...
0
votes
0answers
20 views
Bernstein’s inequality and trimmed mean (truncated mean)
Give that
and
for <0
How can we calculate upper bound for
My best guess is that we can use Bernstein’s inequality but I'm not sure whether this is right way or not... if so, what will be ...
1
vote
2answers
31 views
What is the use of knowing the underlying data distribution?
I am trying to understand few basic concepts of data mining, machine learning, etc. and I am new to this field
Say that I have a data sample and I have done maximum likelihood estimation or some ...
2
votes
1answer
48 views
Best Course of Study for Data-Science/Statistician Interviews [on hold]
This is my first question here, so please pardon my gaffes.
I am currently working as a Data-Scientist, a position which I worked up from Junior Analyst position.My bachelors is in Computer Science ...
0
votes
1answer
25 views
Expectation of matrix X multiply by indicator matrix
Let X1, . . . , Xn, X be i.i.d. R-valued random variables
Suppose an indicator matrix I{A} be 1 if A is true and 0 otherwise. Then for τ > 0,
and
How this could be true....? Can anyone walk ...
2
votes
0answers
16 views
High dimensional linear regression inference
I am reading through high-dimensional literature currently but I got confused. Especially about statistical inference with LASSO, anyone can clarify me the main difference among
Van De Geer(2014)ON ...
1
vote
0answers
13 views
setup time optimization using statistics [closed]
I work at a manufacturer with numerous products. The diversity if variants is very high. For almost every product the machines have to be converted. There are essentially 3 characteristics, which ...
0
votes
1answer
19 views
How do I estimate probability of success with no successes? [duplicate]
My $6$ friends and I tried buying tickets to a popular event. Everyone who wanted a ticket got a random number and if your number is less than or equal the number of tickets available, you can buy a ...
-1
votes
0answers
13 views
Help with this question please [closed]
I would really appreciate step by step solution on how to answer this. Very confused.
1
vote
1answer
29 views
Probability integral transforms - Cauchy distribution of 1/x and X
When revising for exams, I recently came across the following question:
Suppose that $X$ is Cauchy distributed, ie has a density function
$$f_X(x) = \frac{1}{\pi(1+x^2)}$$ Show that $1/X$ is ...
1
vote
2answers
38 views
In k-means clustering, why sum of squared errors (SSE) always decrease per iteration?
In k-means clustering, why sum of squared errors (SSE) always decrease per iteration?
How can prove it by mathematical derivation of formulas?
k : number of clusters
m : number of examples
$c_h$ : ...
0
votes
0answers
27 views
Statistical inference [closed]
An example for which one or both of the sufficient condition of consistency is not satisfied but the statistics is consistent for the unknown parameter?
0
votes
1answer
35 views
Can I have some help for Statistics/probability theory
Let
$\Omega = \{0,1\}^{\mathbb{N}} = \{\alpha=(\alpha_1,\alpha_2,...):\alpha_i \in \{0,1\}\}$
Fact. There exists a $\sigma$-algebra $\mathcal{F}$ such that for every $\beta = (\beta_1,...,\beta_n)\in\...
0
votes
0answers
8 views
Estimate weight parameter between two levels and make profile likelihood in R [on hold]
I have to estimate the weight parameter between two levels in a feature (men and women) in a Gamma function with an identity linkfunction. Though I have not tried this before and therefore not very ...
0
votes
0answers
2 views
Mixed Models of this designs
How will I state the Mixed Model of the following designs:
1. Randomized Block Design
2. Split Plot Design
Any help will be appreciated, thanks .
0
votes
0answers
19 views
Why sigma-finite measure?
I am learning measure theory and the concept $\sigma$-finite measure makes me a bit confused. Why do we need the $\sigma$-finite assumption in many important theorems?
0
votes
1answer
29 views
About Mean absolute error and standard deviation
I've calculate the "Mean absolute error" for my predicted data and I want to calculate the standard deviation of an error to find the +- range from mean absolute error. The question is do i need to ...
2
votes
2answers
39 views
How to calculate error when $\sigma=0$ in a test sample? [duplicate]
A test has probability $P_f$ of failure where it is expected that $.0001 <P_f < .01$.
Given $N$ test samples where all tests succeed and there were no failures (thus $\sigma=0$), what is the ...
0
votes
0answers
26 views
How do we prove this identity related to expectation and variance?
Prove that if $\textbf{a}$ is a vector of constants with the same dimension as the random vector $\textbf{X}$, then
\begin{align*}
\textbf{E}[(\textbf{X} - \textbf{a})(\textbf{X} - \textbf{a})^{\prime}...
0
votes
1answer
25 views
What Statistical Method is Useful for Comparing Two Different Groups?
I'm working on a project and I want to know what statistical method would be useful to see if my hypothesis is true.
The project I'm working on is Calculus Rentention.
My hypothesis is: do students, ...
0
votes
0answers
20 views
Variance Calculation Issue
I want to calculate variance for the given problem , i am confused when to use n or n-1 , if nothing is mentioned.
also, what should i use in this case. please explain
0
votes
0answers
11 views
Given two related ratios within a population, derive a third ratio (eg. redheads, non-redheads, and skin cancer)
Example (the numbers are just for illustration).
If
A redhead is 3 times more likely to get skin cancer than a non-redhead.
Redheads are 7% of the population.
Then
What percentage of skin cancer ...
