Questions tagged [mathematical-statistics]
Mathematical theory of statistics, concerned with formal definitions and general results.
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9 views
Dependence between bernoulli random variables
Suppose I have $X$ such that $P(X=1)=\pi$ and $P(X=0)=1-\pi = q$, and $Y$ such that $$P(Y=1|X=1) = 1-q(1-\rho)$$
$$ P(Y=0 | X=0) = 1-\pi(1-\rho),$$
then I can simulate $X,Y$ such that their ...
1
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1answer
112 views
How to write diff() mathematically?
I am using R/Python diff() operation. e.g., https://docs.scipy.org/doc/numpy-1.14.0/reference/generated/numpy.diff.html
I would like to know if there is a ...
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0answers
2 views
Pointwise Mutual Information using spacy or just detailed explaination
So, I have been trying to play around with NLP recently and decided to work on a project involving Emotional Analysis. I have been following this particular research, http://www.cse.yorku.ca/~aan/...
1
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0answers
17 views
How can we call likelihood function a joint PDF when the individual terms do not represent Probabilty
My understanding of the Probabilty Density Function is that they evaluate to 0 at a particular point . So if we have some i.i.d points $x_{n}$ from a Normal distribution and we write :
\begin{equation}...
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0answers
15 views
Minimal Sufficiency for Two Parameters
Let $X_1, ..., X_n$ be iid $f(x; \theta, \lambda) = \dfrac{\lambda e^{-\lambda x}}{1-e^{-\lambda \theta}}$ for x $\in [0, \theta]$.
I am asked to find
I want to find
A minimally sufficient ...
0
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1answer
27 views
Rao-Blackwellize Bernoulli
Let $X_1, .. X_n$ be iid Bernoulli($\theta$).
I want to estimate $\lambda = \theta(1-\theta)$, usin $\delta$ (unbiased estimator for $\lambda$) where
$\begin{cases}
\delta = 1 & X_1 =1 \...
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1answer
35 views
What's the probability of the alternative hypothesis being true given that we rejected the null?
Suppose that
$$ H_O: \mu = \mu_O$$
$$ H_A: \mu = \mu_A$$
$$ p_O = proportion \ of \ situations \ \mu = \mu_O \ $$
$$ p_A = proportion \ of \ situations \ \mu = \mu_A \ $$
$$ p_A + p_O = 1 \text{ (...
4
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4answers
215 views
Understanding p-Values using an example
I know there might already be tons of questions around understanding the interpretation of p-Values, however I would ask the question in a very limited form and with the use of a specific example
...
1
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1answer
25 views
can you help me to do a difference of CDF?
I have 2 CDF's with equal number of points that I want to compare. These are from:
Temperature of 1 month from 2012
Mean temperature across months
What can I do to obtain this difference, this is ...
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0answers
20 views
cumulative distribution functions (CDFs) [on hold]
i want to know why is important use CDF for this analysis of TMY (typical meteorological year) because i have the data of the month for compare with the long term mean
This the example of the manual
...
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1answer
7 views
Creating a custom metric based on diverse feature scalse
I would like to create a custom metric that takes into account multiple features and produces a certain score.
However, the issue is that I have data that has many different data types, such as ...
2
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0answers
34 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}}^{2}]$
$= y_{...
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0answers
13 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 ...
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0answers
15 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
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0answers
21 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)\}$$
After solving several exercises with various distribution functions, ...
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0answers
14 views
What statistical tool should we use in our study? [on hold]
The title of our study is "The Influence of Online Gaming to Interpersonal Relationships of College Students"
Our independent variable is Online Gaming (Time Spent & Type of Game) while our ...
2
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1answer
26 views
Asymptotic distribution of median estimator when density doesn't exist
We know that when density(say $f$) exists at the median(say $\theta$) then the median estimator(say $\hat{\theta_n}$) has the following property $$ \sqrt n(\hat{\theta_n}-\theta) \to^d N(0,1/\{4f(\...
1
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0answers
22 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
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0answers
29 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
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1answer
26 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 ...
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0answers
15 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
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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), ...
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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
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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 ...
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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
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1answer
43 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
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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 ...
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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
22 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}^...
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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
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0answers
15 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 ...
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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
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2answers
78 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?
...
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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, ...
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0answers
20 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
18 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 ...
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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
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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 [closed]
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 ...
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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
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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 ...
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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
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2answers
39 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
$c_h$ : ...
