Questions tagged [mathematical-statistics]
Mathematical theory of statistics, concerned with formal definitions and general results.
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10 views
Back-Transformation for Ln(X+1) of zero rich data
I have seen and read several similar questions, but mine pertains specifically to zero rich data.
I will be back transforming my data based on a first order Taylor series approximation. As outlined ...
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0answers
13 views
Approximate distribution for sum of squares of standardized Poisson random variables
Suppose that $X_1, ..., X_n$ are independent and identically distributed Poisson($\lambda$) random variables.
What is a good approximating distribution for $\sum_{i = 1}^{200} \frac{(X_i - \lambda)^2}...
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0answers
11 views
What is the discrete equivalent of a truncated normal? [on hold]
Let random variable X be distributed with a truncated normal with unspecified mean, unspecified variance, a(the lowest limit) = 0 and b some fixed natural number greater than 0.
With the Y axis we ...
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1answer
22 views
Why is the infinite-population perspective usually taken in sampling? What underlying bias/convergence implications are there?
In sampling literature and causal inference literature, there usually is a distinction made about how to view observed data. The first is usually to view some observed data as having come from a ...
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1answer
7 views
Hidden Markov Model probability of producing a sequence
Suppose that we have two models for a 2-state HMM and both have two output symbols: $A$ and $B$.
Model 1:
Transition probabilities: $a_{11}=0.6$, $a_{12}=0.4$, $a_{21}=0.0$, $𝑎_{22}=1.0$.
Output ...
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0answers
7 views
How to find the standard error of a sample of measurements each with their own uncertainity
I have a scale that has a resolution of +-0.01 grams. I have assumed that it has a standard error of +-0.005 grams. I would like to measure the mass of an Samsung INR18650-30Q battery. I would like to ...
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0answers
19 views
How to average columns having varying lengths? [on hold]
I am trying to plot the average of a set of columns. However, since the columns have unequal lengths, the shape of the plot at the end has abrupt shifts. I am thinking of re-sampling all the columns ...
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23 views
A question about the definition of sample
Let $(\Omega,\Sigma,\mu)$ be a measure space. The definition of a sample is that it is a sequence of iid random variables $X_1,\ldots,X_n$. Usually random variables are real valued and the ...
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10 views
How to test the validity of Fitt's law in R
I would like to use the Fitt's Law to test some hypothesis. Anyway, it's the first time I use it, and I have some doubts.
Then aim of my experiment is to test if in a certain situation the Fitt's law ...
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1answer
26 views
How do you verify independence of a pair of uniform random variables in MATLAB? [on hold]
If $A$ is a subset of $R$ and $X$ is a random variable. I have two variables $X_1$ and $X_2$. $I$ being $1$ if $X$ in subset $A$, and $0$ if not in $A$. Let $U$~$U(0;1)$ and determine if this pair ...
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1answer
333 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
4 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/...
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0answers
19 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
27 views
Minimal Sufficiency for Two Parameters [on hold]
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 ...
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1answer
59 views
Rao-Blackwell Problem [on hold]
Let $X_1, .. X_n$ be iid Bernoulli($\theta$).
I want to estimate $\lambda = \theta(1-\theta)$ using $\delta$ (unbiased estimator for $\lambda$) where
$\begin{cases}
\delta = 1 & X_1 =1 \...
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1answer
30 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
31 views
cumulative distribution functions (CDFs) [duplicate]
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
11 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
35 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
14 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 ...
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0answers
22 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? [closed]
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
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(\...
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0answers
23 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 ...
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0answers
30 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
29 views
How do you confirm whether null hypothesis can be rejected in decision rule? [closed]
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 ...
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0answers
26 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 ...
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1answer
19 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 [closed]
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
44 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
49 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 ...
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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,...
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0answers
29 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
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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 ...
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0answers
16 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 ...
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0answers
12 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.
...
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2answers
85 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
32 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
22 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 ...
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0answers
13 views
Tree pruning & cost-complexity
This is a question in cost complexity pruning that I want to learn about.
I am given $A ≥ 0$ to be the tuning parameter, where $t_0$ is the full tree, and $t$ is a subtree. We then have $|t|$ as ...
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0answers
13 views
Tree Pruning: SSE
Can someone show me an instance of a data set where a no split causes a reduction of SSE, however can be modeled by a tree with 3 splits?
Basically, an example that shows that it's sometimes needed to ...
1
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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
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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 ...
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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 ...
