Questions tagged [mathematical-statistics]
Mathematical theory of statistics, concerned with formal definitions and general results.
4,503
questions
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20 views
Posterior predictive
The posterior predictive distribution is always defined by the densities.
Assume $X_1,X_2,...$ are conditionally i.i.d. given $\mu$ according to measure $P_\mu$, where $\mu\sim Q$. Let $\mu\mid X_1,\...
0
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1answer
8 views
Calculation of critical values
Are the critical values for the two-sample t-test with unequal variances calculated the same as for the two-sample z-test?
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0answers
27 views
Problem on sufficient statistics
Let the distribution of $X_1,X_2,...X_n$ depend on two parameters $a, b$ such that there exists a single sufficient statistic, for either parameter when the other is fixed/known.
Show that there is ...
2
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0answers
50 views
Correlations between two sequences of irrational numbers
If $x$ is an irrational number and $b$ an integer, let's define
$g(x,k) = \mbox{Correl}(\{nx\},\{nb^kx\})$.
Here $k=1,2,\cdots$ is an integer. The brackets represent the fractional part function. ...
0
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0answers
12 views
A pharmacologist is interested in determining whether or not three different psychoactive drugs differ in [on hold]
A pharmacologist is interested in determining whether or not three different psychoactive drugs differ in how long they remain in the body before they are excreted or metabolized. The pharmacologist ...
0
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0answers
13 views
What is the difference between lasso and WOE encoding in logistic regression?
I know lasso is one of the best method to select important variables and make variables sparse. But WOE encoding does the same thing, making variable smooth.
I would like to know what is the ...
3
votes
1answer
36 views
A basic question about a randomized test involving the error type I
I have a basic question in the context of testing statistical hypotheses, more specifically, about randomized tests. Suposse that I have two actions (altenatives) about a certain unknown parameter $\...
0
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0answers
7 views
Make exclusive class intervals from given class intervals [on hold]
Expenditure(Rs): 0-19 20-39 40-59
No of families : 4 8 12
Note :Be sure you don't make class interval from -0.5 as Expenditure is on Rs which cant be negative.
0
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1answer
34 views
Minimizing an Integral of function by derivation
Currently I am reading ESL. I am struggling to unterstand the step 2.15 to 2.16 in Chapter 2.4.
The authors mention that the stationary function can be found by differentiation. The commentary by ...
0
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1answer
27 views
Determine the highest values in a set [on hold]
Let's say I have a set of 5 values:
[0.1, 0.3, 1.2, 1.6, 2.3]
What statistical technique could I use to return the highest values, say ...
0
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0answers
10 views
How to define a good threshold based on a numbered dataset
I have a set of ordered number list as follows.
25789, 20500, 18888, 15000, 13200, ...., 118, 8, 1, 0
In my dataset most of the values are in the range of (1000-...
0
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0answers
21 views
Pooled variance versus pooled standard deviations squared?
Typically, one estimates the pooled variance using something like
$$ \sigma^2 = \Sigma_i^n \ w_i \sigma_i^2 $$
where $w$ corresponds to some kind of weight. Note how we average variances here. ...
10
votes
2answers
2k views
Solution to German Tank Problem
Is there a formal mathematical proof that the solution to the German Tank Problem is a function of only the parameters k (number of observed samples) and m (maximum value among observed samples)? In ...
2
votes
1answer
18 views
Why does the intercept of Principal Component Regression differ from the orginal regression?
I am comparing two regressions:
$y= \beta_0+ \beta_1 x_1 + \beta_2 x_2 + \epsilon $
and
$ y = \gamma_0 + \gamma_1 PC_1 + \gamma_2 PC_2 +\eta $.
The regressors in the second regression, $PC_1, ...
1
vote
1answer
24 views
What is a good measure of the similarity of 6 different time series?
Essentially, I have 6 different data time series that were each generated first using an industry standard methodology (call it method m.A) and then again using my technique (call it method m.B). ...
5
votes
3answers
170 views
Which likelihood function is used in linear regression?
When trying to derive the maximum likelihood estimation for a linear regression, We start by a likelihood function. Does it matter if we use either of these 2 forms?
$P(y|x,w)$
$P(y,x|w)$
All pages ...
0
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0answers
33 views
How many classmates does a freshman have?
The freshmen at East China Normal University has just received their student ID. Let the last three digits of a student ID be ABC, then A is the class he is in, whereas BC is his number in the class.
...
0
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0answers
13 views
Random variates generation for disrecte distribution by inverse transform method [duplicate]
I have solved this question but still confused. I don't know whether this method is correct or not and also the answer which I get is right or wrong, as I was told to generate random variates for ...
1
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0answers
25 views
How to perform regression with different error variances? [duplicate]
I have two series of measurements values, first series is X and second is Y.
I need to model Y as a function of X, where I know the method that was used to measure X is two times better then the ...
0
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0answers
44 views
+100
What does it mean if the sobol main and total effects indices are the same?
What does it mean when the total and main effects ANOVA indices are the same?
Does it mean there is zero interaction of the different inputs? Is there some other way to quantify or understand that? I ...
0
votes
1answer
45 views
Proof for how the drift estimator, for a random walk with drift, is unbiased?
Random walk with drift formula is:
(Yt = α + Yt-1 + εt )
How do I go about checking that the drift estimator α-hat is unbiased.. which is proving that E(α-hat) = α?
Is this something I would need ...
0
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0answers
27 views
Better algorithmic solution to find the peaks of multiple number series [closed]
Suppose I have set of number series which can be drawn a multiple line graph like this:
According to what I have learned, peaks can be found using the theory of local maxima. And I found that the '...
0
votes
1answer
17 views
Statistical test to check whether an item meets the specification
I have a data on emission of an automobile which a company manufactures. The emission test was conducted on roads near towns and villages and the data is as follows.
According to a new rule passed ...
1
vote
1answer
34 views
Mean residual life in terms of incomplete moments
In a paper by Braga, Cordeiro, and Ortega 2017, they representing the Mean Residual Life in Terms of the incomplete moments
$$\operatorname{MRL}(t)= \frac{1-m_1(t)}{1-F(t)}-t$$
where $m_1(t)=\int_0^...
3
votes
1answer
59 views
Dealing with NAs in Poisson Regression estimators [duplicate]
I am trying to fit a Poisson regression in some soccer matches. I want to be able to predict matches of the first league for a new season, which means that there will be some new teams that have been ...
0
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0answers
20 views
Variance of Guassian Products [duplicate]
Suppose I have to vectors $w$ and $x$, each of size $[512,1]$. Each element of $w$ and $x$ is an i.i.d sample from a Guassian Distibution with mean 0 and variance 1. So $x_i$ and $w_i$ follow $N(0,1)$...
0
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0answers
24 views
How can I model this?
I have a question about whether I can model in a way that solves this problem:
Suppose a swimming coach has 100 athletes and only cares about the distance they can each swim in 5 minutes. From this, ...
2
votes
0answers
26 views
Statistics books with applications in quantitative finance
I am a Pure Maths PhD. As I would like to venture myself into quantitative finance jobs, I need to pick up statistics, programming and finance.
I have been reading time series analysis by Hamilton ...
0
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1answer
28 views
Time Origin in Survival Analysis
I am new to survival analysis, and I am confused about time origin, or what's called calendar data format and survival data format.
I have the following dataset, subjects were continuously entering ...
0
votes
1answer
30 views
Variance of mean of correlated variables
Page 228 of THIS BOOK provides the formula for the variance of the mean of more than two correlated random variables:
where $m$ is the number of variables, $r$ is the correlation between the ...
1
vote
1answer
57 views
Variance of difference of two correlated variables when working with random samples of each
I know that the variance of the difference of two correlated variables, $Y_1$ and $Y_2$ , is what the below formula shows, requiring $r$ the correlation between the two variables.
But suppose I have ...
0
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0answers
15 views
Bias of Pearson correlation estimator of two Bernoulli variables
Crossposting link: https://math.stackexchange.com/questions/3312349/bias-of-pearson-correlation-estimator-of-two-bernoulli-variables
Suppose we have two correlated Bernoulli random variables, $X_j$ ...
2
votes
3answers
61 views
What would be the outliers in this specific situation? (given in description)
Recently over a phone interview I was asked this:
"I have data consisting of 102 points between 0 and 100 where the first 50 points, starting at 0, are incremented by 0.5 every time. The next two ...
0
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0answers
12 views
Why we really need the concept of “Local” Rademacher complexity?
Recently, I have been studying High-Dimensional Statistics: A Non-Asymptotic Viewpoint written by Martin J. Wainwright. In this book, the author uses a special complexity measure which is called Local ...
0
votes
1answer
40 views
How to get a unified result on multiple results of a A/B test
I have a A/B test. this test will generate a P_value every day based on the daily data. For example, I had 5 days' significate and 5 days' non-significate. So if I want a unified result from these 10 ...
0
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0answers
9 views
Approximate Value / Policy Iteration (Reinforcement Learning)
I am reading Markov Decision Processes in AI : about Approximate Dynamic Programming.
Would you like to explain the rationale for introducing the API algorithm, how it compares to AVI ?
How would ...
0
votes
1answer
31 views
Jurafsky and Martin (2018) Do not understand formula in naiye bayes classifier
Currently I am reading Language and Speech Processing by , Chapter 4 Naiye Bayes and Sentiment Classification.
At page $7,$ when the authors discuss worked example.
Data set is as follows:
Training ...
2
votes
1answer
80 views
Proof Verification: Joint variance of the product of a random matrix with a random vector
BACKGROUND
QUESTIONS
Is the proof of my claim correct?
How might my proof be improved?
Claim: (1) The joint-covariance matrix of the product of a real random matrix $X$ of dimension $v\times m$...
1
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0answers
29 views
How to defend a probability distribution [closed]
Apologies if this isn't the right place to ask this question. While I was an undergrad, I derived a probability distribution. I tried to get this published along with a professor, but she mentioned to ...
0
votes
1answer
10 views
How to compare two, time based, measurements of the same object
I have 2 rounds of measurements from a set of 10 capacitors. The measurements are with respect to frequency and are all measured at the same 200 frequencies between 1 kHz and 5 MHz. The data is not ...
1
vote
2answers
47 views
How to get the false positive? “1 - true negative” or “1 - true positive”?
wiki gives this Drug testing Example to illustrate Bayes' theorem
${\displaystyle {\begin{aligned}P({\text{User}}\mid {\text{+}})&={\frac {P({\text{+}}\mid {\text{User}})P({\text{User}})}{P(+)}}\\...
-1
votes
1answer
26 views
What are the % Odds?
NEED SOMEONE GOOD IN MATH!
My father, my brother & myself all have AB- Blood Type. According to The Stanford School of Medicine Blood Center around 0.6% of the population has the ABneg blood type....
1
vote
1answer
35 views
Determinants of the sum of two matrices and their eigenvalues
I know some basic property of determinant. I read an article and see this formula:
\begin{equation}
|(\delta-p-1)D+S|=\bigg(\prod_{i=1}^{p}\lambda_{i}(D)\bigg) \bigg(\prod_{i=1}^{p}(\delta-p-1)\...
0
votes
1answer
24 views
What is the conceptual difference between Residual Sum of Squares (RSS) and Residual Standard Error (RSE)?
I am very new to statistics and am currently using the Introduction to Statistical Learning with R book.
I am having some issues understanding the difference between RSS and RSE. From my ...
4
votes
3answers
99 views
What does beta distribution “has support” mean?
This post says
the beta prior has support over all valid probabilities and only over
valid probabilities
About Support, wiki says
In mathematics, the ...
3
votes
1answer
46 views
Probability statistics - probability that 10 or more of the donors are Rh-negative?
In a certain population, 18% of the people have Rh-negative blood. A blood bank serving this population receives 95 blood donors on a particular day.
So my teacher posted a solution to a problem ...
14
votes
2answers
2k views
Does Wolfram Mathworld make a mistake describing a discrete probability distribution with a probability density function?
Usually a probability distribution over discrete variables is described using a probability mass function (PMF):
When working with continuous random variables, we describe probability distributions ...
3
votes
3answers
168 views
Can anyone give a concrete example to illustrate what is an uniform prior?
I googled "uniform prior" and got a link to Prior probability, which uses the term without an explanation or a definition.
anther link is to quora, which does not give an concrete example.
Can ...
0
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1answer
42 views
what is the name of this computation?$e_{10}{(0.1)} = 0.8$
section 1.4.3 of the book "Machine Learning - A Probabilistic Perspective" gives an example about KNN:
the input is two dimensional, we have three classes, and K = 10
which contains a computation
$...
3
votes
1answer
76 views
Variance of beta distribution (fastest way)
Suppose a Random variable $X \sim \mathrm{Beta}(a,b)$
Find the $\mathrm{Var}( \frac{X}{1-X} ) $
My initial approach is to calculate $\mathrm{E}( \frac{X}{1-X} ) $ and $\mathrm{E}( [\frac{X}{1-X}]^...
