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

learn more… | top users | synonyms (1)

2
votes
1answer
37 views

Excess Bunching - Bunching Estimator (Saez 2010)

Saez (2010) defines excess bunching at the kink as the area under the density in the dominated region: $$ B = \int^{z^*+d z^*}_{z^*} h(z)dz \approx h(z^*)dz^* $$ where income $z$ is distributed ...
0
votes
0answers
22 views

How would you categorise a matrix into high and low levels? [on hold]

I have a matrix of data consisting of over 30000 rows and 2000 columns. My rows are different samples and my columns are different conditions that those samples were measured. I want to assign the ...
-1
votes
0answers
20 views

How to categorize users based on their movie views?

Apologies for cross posting. I have a dataset of size (61573, 25). The rows represent users whereas the columns represent ...
1
vote
1answer
13 views

sample from a mixture

Suppose I have two types of students, male or female. Suppose a test score of a male student follows a distribution $F_m$ and suppose a test score of a female students follows a distribution $F_f$. ...
0
votes
0answers
27 views

Statistics Analysis [on hold]

A drug was administered to 456 males, out of a total 720 in a certain locality to test its efficacy against typhoid. The incidence of typhoid is shown below. find out the effectiveness of the drug ...
0
votes
0answers
25 views

Are all variables random in probability? [on hold]

Probability means what is the likelihood that the given event would occur. Are all variables random in probability ? If so that is probability always talks about stochastic. And if so, Why is ...
0
votes
0answers
17 views

What is the number of sample points when a pair of dice is thrown once

What is the number of sample points when a pair of dice is thrown once. How can we calculate it using permutation?
0
votes
0answers
172 views

A practical question in simulating real world outcomes

PredictWise aggregated polling data and, for each state, estimated the probability that the Obama or Romney would win. Here is the polling data. The data frame has 51 rows(51 states). the name of this ...
0
votes
0answers
11 views

Inter-rater aggrement measuring among multiple participants in classed data

I have 100 items where for each item, multiple facts are given. I want to find the related facts for each item from the given multiple facts using human subjects. So basically I want to categorize ...
5
votes
0answers
152 views

A tricky question about correlation [duplicate]

$X$, $Y$ and $Z$ are three random variables where their pairwise correlations are the same, i.e., $corr(X,Y)=corr(Y,Z)=corr(X,Z)=\rho$ what are the possible values of $\rho$? I was asked this in an ...
-2
votes
1answer
36 views

What is the Mean Squared Error for this estimator?

I understand that to find the MSE, i must find the variance and bias and add them together. I've had trouble calculating either of these so a breakdown would be immensely helpful. The estimator is: ...
-1
votes
0answers
11 views

How to find F(t) in a Poisson process? [on hold]

I've been given the following scenario: There's a bar in positions "A" and position "B" that receives 6 patrons per hour. Position A has 2x the capacity has position B. Find the marked Poisson ...
1
vote
0answers
12 views

should we check for multicollinearity when building a discrimination analysis?

In fact, I have two questions: 1- do we need to check for the multicollinearity when we deal with linear discrimination analysis? 2- how to solve those variables which are multi-collinear? Lets ...
1
vote
0answers
28 views

QQ plot in Python

I generated a qq plot using the following code. I know that qq plot is used to check whether the data is distributed normally or not. My question is what do the x and y axis labels indicate in qq plot ...
0
votes
1answer
23 views

What do you mean by pollster bias in an election?

I came across harvards election poll data science question. I which they ask: Is there a pollster bias in presidential election polls? What exactly is a pollster bias? can some one explain it to me in ...
-1
votes
0answers
38 views

Is the question of outlier detection to fit a model better? [closed]

I was searching to find a package in R which has outlier detection since i am a Matlab User; Anyway, I found several questions in this website which the answers disappointed me very much. this is one ...
-5
votes
1answer
32 views

What is the standard error of the mean? [duplicate]

I don't know anything about this topic. Can you explain and describe standard error of the mean?
1
vote
0answers
32 views

what is the differences between LDA and MLR? [duplicate]

I know that Linear Discrimination Analysis (LDA) is used for classification and Multiple Linear Regression (MLR) is for regression. Lets say I have a matrix X (independent variables) and Y(dependent ...
0
votes
1answer
40 views

what should be the null hypothesis?

conduct a test hypothesis to show that it takes longer for people with average fitness to successfully complete physical therapy as compared to those with above average physical fitness. Test at ...
5
votes
2answers
66 views

Why is the standard deviation defined using differences^2 instead of differences^4? [duplicate]

I've read some post about why to take the std. deviation and its benefits, here's one of them: Why square the difference instead of taking the absolute value in standard deviation?, and another by ...
0
votes
0answers
37 views

“All of Statistics” questions [closed]

I am not able to solve a couple of questions asked in the exercise 10.11 of book - All of Statistics. Question 1 Question 2 How do I start ? Any hints would be helpful ? I do not want complete ...
2
votes
1answer
21 views

Adjusting Monte Carlo estimates to generate correct even moments - improving on antitthetic draws

If I want to generate a matrix 10,000 (row) samples of 3 uniform (uncorrelated) variables it is trivial to use antithetic draws to ensure the odd moments such as the mean equal their "true" value. ...
0
votes
0answers
23 views

t-student distribution [duplicate]

I've got this problem: Here, if $Z,W$ are independent random variables, and $Z$ has normal standart distribution and $W$ has $\chi^2$ with $n$ degrees of freedom, $T=\frac{Z}{\sqrt{\frac{W}{n}}}$. I ...
0
votes
2answers
41 views

Predictive Accuracy formula in Excel or R [duplicate]

I have posted this question, not sure how to move that question to this stats.stackexchange.com. ...
5
votes
2answers
277 views

Example for a prior, that unlike Jeffreys, leads to a posterior that is not invariant

I am reposting an "answer" to a question that I had given some two weeks ago here: Why is the Jeffreys prior useful? It really was a question (and I did not have the right to post comments at the ...
0
votes
0answers
10 views

How can I prove the variance of residuals for an unbalanced one-way layout?

How can I prove the variance of residuals for an unbalanced one-way layout? var($e_{ij}$)=$σ^2$($1- \frac{1}{n_i})$ here i = 1,...., a j = 1,....$n_i$ where $e_{ij}$'s are the residuals. where ...
0
votes
0answers
20 views

Level of a time series and adding daily dates to plot

just wondering if you can help me with explaining this plot Just wondering what does level tell me? is it the trend of the data with seasonality taken out, which is the slope right? Can't seem to ...
1
vote
0answers
40 views

Calculating $E\big((X_1X_2)/(\sum_{i=1}^n X_i^2)\big)$ [closed]

Let $X_1,X_2,...,X_n$ be a random sample of $N(0,\sigma^2)$. How can I calculate $$ E\bigg(\frac{X_1X_2}{\sum_{i=1}^n X_i^2}\bigg)\ ? $$
0
votes
1answer
51 views

finding upper bound for $P(T=0)$

Let $X_1,X_2,...,X_n$ is a random sample of Poisson distribution with parameter one. if $T=\bar{X}(n-\bar{X})$ how can find upper bound for $P(T=0)$
-1
votes
0answers
17 views

How to show invariance for this test statistic

$$ \frac{|s^*M^{-1}z|^2}{(s^*M^{-1}s)\big[1+\frac{1}{K}(z^*M^{-1}z)\big]} \:\:\:----->1 $$ $$K \text{is real scalar},\: \quad s,z \in \mathbb{C}^{N \times 1} \quad \: and \quad M \in ...
0
votes
1answer
34 views

bias and sampling

This was an interview question I encountered. can some one answer this When you sample, what bias are you inflicting? How do you control for biases? What are some of the first things that come to ...
1
vote
1answer
51 views

assumptions made for a normal distribution- a interview question

I was asked in my interview: What assumptions can you make? Why and when? (i.e When is it safe to assume "normal"). Can some one answer this .
-1
votes
1answer
43 views

What does z* represent in statistics?

Could somebody please give me an explanation as to what Z-star means for statistics, where it's used, and how to calculate it? My book is very confusing and I don't really know what it means. Even a ...
0
votes
0answers
20 views

how to calculate Kolmogorov-Smirnov test for one sample in R [migrated]

I have a matrix in which I would like to calculate Kolmogorov-Smirnov test on each column separately. Let's say my matrix is like below ...
4
votes
2answers
114 views

What does an error in ANOVA indicate?

When I came across ANOVA, the instructor talked about df(Error), ss(Error), etc. What do these error terms indicate? Do error terms differ for two-way ANOVA with dependent and independent variables? ...
1
vote
0answers
35 views

Huber's M estimator for contaminated Gaussian noise

Huber discussed in this seminal paper "Robust Estimation of a Location Parameter" link that if we have some observations $x_i$ as follows: $$y_i = \theta + \nu_i, ~~i=1,\cdots,N, \tag{1}$$ where ...
0
votes
0answers
24 views

Two-way ANOVA: negative interaction sum of squares?

I am doing a two-way ANOVA. The two variables are both categorical, one with 3 and the other with 2 categories. The count for each category is not equal. The data (only category means) is here: ...
0
votes
0answers
21 views

decomposing distribution function of sum

I am thinking about decomposing distribution function of sum of two random variables into sum of distribution function. Let assume $Y_1\sim F_1$ and $Y_2 \sim F_2$ and $Y_2\in \mathbb{R}$ and ...
0
votes
0answers
22 views

What is the reason behind lift measure?

While reviewing some slides I see the following formula for calculating lift (which is defined as "measure of dependent/correlated events"): $$lift(A,B) = \frac{s(A\cup B)}{s(A)\cdot s(B)}$$ which ...
0
votes
0answers
16 views

Multivariate Gaussian, rearranging means

Looking through the the matrix cookbook, a collection of matrix identities, I came across this one called "rearranging means" in the multivariate Normal distribution (Sec. 8.1.5 or Eq. #356, also ...
0
votes
0answers
16 views

Fisher information matrix of an arbitrary statistic

I have a proof (that is a bit long) that shows that for a single parameter $\Theta$, $J_\mathbf{X} (\Theta) \geq J_\mathbf{T} (\Theta)$ where $J_\mathbf{X} (\theta)$ is the fisher information of the ...
2
votes
5answers
328 views

What are the appropriate Statistical tests when dealing with two or more categorical outcome variables in a model

I'm familiar with GLM techniques when dealing with continuous outcomes and categorical or continuous predictors. I've used Logistic regression with a single dichotomous categorical outcome variable ...
1
vote
0answers
6 views

Confidence Interval for mean difference with non-mutually exclusive 1 to many matches in R

This is somewhat both a programming question, and a stats question. So sorry for the overlap (although it seems that there is a large overlap between the realm of stats and programming of ...
1
vote
1answer
30 views

Hazard function for proportional odds model

The Cox proportional hazards model for survival data with covariate ${\bf z}$ is defined through the hazard function $h(t,{\bf z})$ by $$ h(t,{\bf z}) = h_0(t)~\cdot\theta~~,~~~\theta = \theta(\beta, ...
0
votes
0answers
10 views

Conjugate Distributions

I read one way to derive saddle point approximation uses the so called conjugate distributions densities $h_t(x)$ for a given density function $f(x)$. It is defined as follows. $$ h_t(x) := ...
0
votes
1answer
17 views

Accounting For Increase In Volume

I'm not very good at statistics but today at work we were in a meeting where manager stood at the top of the room and told us our quality performance in manufacturing our goods had dropped but our ...
0
votes
1answer
22 views

Variance calculation RELU function (deep learning)

weight initialization is important for modern deep learning. To understand [1,2], I would like to understand the following: $$ E[x^2] = 0.5 Var[y], $$ where $x= max(0,y)$, $E[.]$ is the expectation, ...
0
votes
0answers
13 views

Alternative answer to choose k people out of n, then choose 1? [migrated]

The question is fairly simple, we first choose k people out of n, that is $C(k,n)$ as the combination function, then we choose 1 person out of k, we have k choices. The total number of choice is given ...
0
votes
2answers
17 views

Division of vectors [closed]

In R: aff<-c(4,8,12) bff<-c(2,4,6) aff/bff [1] 2 2 2 But vectors' division is undefined. Where I am wrong?
1
vote
0answers
12 views

Implementing the Bivariate survival function (Dabrowska estimator etc)

I am trying to implement the Dabrowska estimator to apply to some data that has been collected and I am wondering if anyone can help. The original paper is Kaplan-Meier Estimate on the Plane by Dorota ...