# Questions tagged [mathematical-statistics]

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

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### Is the consistency of plug-in estimators needed?

In generalized least squares, the regression parameter estimate is a minimizer of the following quadratic form, $$\hat{\beta} = \text{argmin}_\beta(y - X\beta)^T\Omega(\theta)^{-1}(y - X\beta)$$ ...
19 views

### Properties of cumulative sum of a random walk?

A random walk can be generated by computing the cumulative sum of a list of random numbers. ...
1 vote
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### Looking for a predictive prior for what I thought to be Bayesian Analysis

I need a prior with 2 parameters location (μ) and scale (σ) (a transformation of mean and standard deviation). My distribution is over discrete values, equally spaced with distance $c$ between ...
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### difference in p-value in simple vs multiple linear regression

Suppose we have have 3 variables: Y , X , Z. then we have : Simple Regression : $Y = aX+b$ Multiple Regression : $Y = aX + bZ + c$ I know that in simple regression we can have a low p-value(showing ...
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### Create a synthetic dataset from the measures of spread

I have certain measures of spread (p50, p66, p75, p80, p90, p95, p98, p99, p99.9, p99.99, p100, Median, Mean, Min, Max)as my attributes. Can I regenerate a data distribution from these? Use case: I ...
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### Is $f(\widehat{x})$ ($\widehat{x}$ is a random sample of $x$) equivalent to $\widehat{f(x)}$ (a random sample of $f(x)$)? [closed]

Assuming $f(x)$ is an injective function, is sampling $\widehat{x}$ from the distribution of $x$ then calculating $f(\widehat{x})$ equivalent to directly sampling from the distribution of $f(x)$? Note ...
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### Can I fix one end in Gaussian Process Regression (GPR)?

I just learnt some basics about Gaussian process regression and how to do it for X-Y data via the GPy package. I wonder whether I can fix one end of the regression curve (or in other words I'm 100% ...
366 views

### Nonparametric Order Statistics - Does this Exist?

I was reading about Order Statistics (https://en.wikipedia.org/wiki/Order_statistic) : Apparently, if we have a sample with "k" number of elements (e.g. x1, x2, ...xk) and assume a ...
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### A question about the expected value of real-valued random variables

Given two not independent r.v. $X,Y$ such that $\mathbf{E}[X]=1$, ¿Is it true that $\mathbf{E}[XY]\approx \mathbf{E}[Y]$? And in that case, ¿can we stablish the rate of approximation? I think that ...
1 vote
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### Central limit theorem with sorted samples

I recently encountered a strange situation while dealing with sampling : Let's suppose I have X1 ... Xn random samples drawn from a population. Then I sort every samples and I make the sum of every ...
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### For a N x 2 matrix, is there a difference between R squared and NS efficiency?

I came across a similar question in the forum yet I failed to understand any practical difference between the two coefficients. To me it seems like it's pure semantics when a prediction is a ...
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### difference between stratification and blocking in experimental design

What is the difference between stratification and blocking in experimental design(or randomized control trial)? Blocking is to obtain homogeneity in a controlled factor. However, I can block more than ...
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### How to calculate the most likely time spent per customer category based on this data set?

I know how many customers of each customer-size group each sales representative handles on an annual basis. Is it possible to calculate the likely time/effort required by each customer size based on ...
1 vote
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### For a block randomized experiment how many possible unique assignments are there?

In a block randomized experiment say of 4 individuals split into 2 even blocks with 1 individual in each block getting assigned to treatment and the other control, how many possible unique assignments ...
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### Why not always use CI's from LRT since they don't require symmetry?

I'm confused on why anyone would appeal to asymptotic normality of mle, $$\hat{\theta} - \theta_0 \rightarrow^D N(0,I^{-1}(\theta))$$ When we can simply invert the likelihood ratio test L(\hat{\...
1 vote
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### A method to find the proportions within each combination of 3 categorical variables

I have three categorical variables that describe each item, and I know how many items I have for each combination of a pair of variables. I am looking to find out exactly how many items I have for ...
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### Statistical inference question evaluating a joint probability mesure w.r.t. a distribution

Note: I have edited this question and delted my old question after following the guidlines to be more clear. I hope this new question is clear and well posed. I attempted this question but I got stuck ...
1 vote
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### Which regression model to chose?

Let's suppose I want to measure the impact of M&A in the hospital sector. I have a dataset containing hundreds of hospitals, a quality indicator and the type of ownership for each over a time ...
1 vote
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### Distribution of rainfall over locations per year [duplicate]

$5.2$ Suppose $X_{1}, X_{2}, \ldots$ are jointly continuous and independent, each distributed with marginal pdf $f(x)$, where each $X_{i}$ represents annual rainfall at a given location. (a) Find the ...
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### Proving a result in maximum likelihood theory: accuracy of the quadratic approx. to loglikelihood

I need help proving a result shown in a paper. I am reading Assessing the Quadratic Approximation to the Log Likelihood Function in Nonnormal Linear Models by Salomon Minkin. The paper defines several ...
1 vote
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### Why does sum cov(Xi,Yi) = n cov(X,Y) [closed]

I am trying to understand how to find cov of two sample means.
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### what statistical test should be used for testing number/proportion of people who agreed in 2 different years

I want to measure if the number of people who agreed on a likert scale (1 strongly disagree - 5 strongly agree), so responded with a 4 or 5 had a statistically significant increase from the previous ...
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### Splitting data to study datsets based on in- and out-of-distribution

I found an interesting paper for which they evaluate the in and outdistribution on different splittings of the dataset. For this they propose four different in distribution settings. The two I'm ...
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### Why do we calculate probability distribution on leaf nodes at Sum-Product Networks (SPN)?

I am new to Sum-Product Networks (SPN) and still trying to understand some concepts. I understand that we need to give inputs at the leaf nodes of SPN. But why do we have gaussian distribution and ...
115 views

### What type of prediction model will be suitable in this case?

We have 100 subjects (A,B,C....) in total. We took 2000 tissue samples from each subject. For each subject, we evaluated the outcome(PASS or Fail), but we only evaluated the outcome on the subject ...
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### Does RCTs imply causation?

Can statistics help to definitively deduce causality? RCTs require that you state the set of variables that you believe influence a given outcome of interest, a priori, therefore if one wants to ...
1 vote
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### Within/Between Multivariate Analysis

I am interested in analysing two dependent variables, let's say Alpha and Beta. I tested 40 participants, divided into two different treatment groups: Group A (n = 20) and Group B (n = 20) Within each ...
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### Calculation of the standard deviation of the power in dB

I wanted to find out the stability of my system so for that i calculated standard deviation of power samples data which is in dB but I am not sure whether i have used correct formula or not. As far as ...
1 vote
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### asymptotic distribution of correlation coefficient in bivariate normal distribution

Suppose \begin{align} \begin{pmatrix} X_i\\ Y_i \end{pmatrix} \sim_{iid} N \begin{pmatrix} \begin{pmatrix} \mu_1 \\ \mu_2 \end{pmatrix}, \begin{pmatrix} \sigma^2_1 & \rho \sigma_1 \sigma_2 \\ \...
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### Comparing the probabilities of 2 different completely separate models that predict different outcomes

You have 2 separate models, one is a binary classifier that predicts whether a customer will pay off their credit card balance on time and another binary classifier (separate model) whether a customer ...
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### F-test and Wald test in time series

Assume we have the time series $X_{1,t}$ and $X_{2,t}$ where $X_{i,t}=(x_{i,1},...,x_{i,T})$. We build two models as (Assume the time series are weakly stationary): \begin{align} X_{1,t}=\sum_{\...
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### This data is related to smog AQI. I want to know which method is applicable here to know the forecasting. Is it seasonal exponential smoothing method?

Mathe The daily average of Air Quality Index in Lahore is plotted in a time series graph