# mathematical-statistics's questions - English 1answer

3.970 mathematical-statistics questions.

### 1 Log-normal returns

Let $P_t$ denote a stock price distributed as $\operatorname{lognormal}(\mu , \sigma^2 )$. Suppose we construct simple returns $R_t=\frac{P_t-P_{t-1}}{P_{t-1}}$. My question is: What is the ...

### 3 Minimal sufficient statistics of increasing dimensionality (not equal to the number of observations)

Restricting the attention to the case of fixed parameters support, it's my understanding that (minimal) sufficient statistics of fixed dimensionality, i.e. a fixed number of of them, exists in, and ...

### 3 Asymptotic Distribution of function of $\bar{X}$

1 answers, 37 views mathematical-statistics inference
$X_i \stackrel{iid}{\sim} N(\mu,\sigma^2)$ i=1,2,...,n $Z_n=\sqrt{n}(\bar{X} - \mu)$ I believe the asymptotic distribution of $Z_n$ is $N(0,\sigma^2)$. So what would the asymptotic distribution of ...

### -1 p-value, literature request for the notion of p-value,statistical hypotheses testing [duplicate]

I would like to know the name of a statistics textbook in which the notion of $p$-value is treated as detailed as possible.An Amazon link will help.Thank you.

### 8 When does a UMP test fail to exist?

I have a sample $X=(X_1, ...,X_n)\sim N(\mu,\sigma^2)$ with $\sigma^2$ known. The hypotheses are $H_0: \mu=\mu_0, H_1:\mu \neq \mu_0$. I know that in such a case an UMP test does not exist and so ...

### Proving the convergence of k-means algorithm using fixed point theorem

I'm learning machine learning and functional analysis this semester. When I learn the k-means algorithm , it came to me that the stopping criterion is very similar to the fixed point theorem thought. ...

### Uniform integrability does not imply integrability of stopped variable

Tried but failed to prove the following assertion: if $(X_n)_{n \ge 0}$ is a process adapted to a filtration $( {\mathcal A}_n )_{n \ge 0}$ such that the family $\{ X_n : n \ge 0 \}$ is ...

### Variance estimates of Grand Mean and Treatment Effect in ANOVA

0 answers, 15 views mathematical-statistics anova
Suppose a random sample of size $n_i$ is taken from $i = 1,2,...k$ and $k$ is the number of populations to be compared, the ANOVA Model is given by $Y_{ij} = \mu +\tau_i + \epsilon_{ij}$. I would like ...

### 3 Calculation of relative distance

I have 100 term triplets as shown in the below mentioned figure. Each triplet contains 3 objects namely x, y and z. I want to rank the triplets according to the following two properties. y should be ...

### prerequisites to algorithms and then to python and Machine Learning

I spent the last 5 months studying full-stack web development using the MERN stack, that is (MongoDB, Express, React and NodeJs). Now that I have seen the full picture of what I would be doing ...

### 2 Is it bad practice to shift traffic distributions for test experiences during the run of a test?

I have recently come across a testing design that Adobe uses in their "Adobe Target" tool that they call "Auto-Allocation". Here is their article on the test design. https://marketing.adobe.com/...

### 1 two sided test convenience and p-value

I have a serious doubt about one characteristic of the two-sided test: Suppose we have a random variable: $X \sim \mathcal{N}(\mu,\,\sigma^{2})$ where $\sigma = 0.4$ but $\mu$ is unknown. We ...

### When to update a model

This is an open question that I have - when should a model be updated? In practice, the modelling process could take a number of weeks/months to update and I would just like to know what some of your ...

### Why is one-hot encoding required? [closed]

I'm trying to work out why one-hot encoding is required, rather than, for example, assigning a different integer to each of the classes. Eg, in an machine learning image classification task, why can'...

### 2 How to calculate divergence from standard deviation

I have 20 people I wish to give performance score every 6 months. I want to identify the weakest performers in the bottom 10 and remove them from the group but only those from the point of the most ...

### -1 Variance proof for the stochastic estimator for trace of a matrix

I'm reviewing the proof the estimator of the trace of a matrix and am having trouble reconciling a jump in the proof of the variance of the estimator. The paper with the proof is found here. The ...

### 3 Asymptotic Distribution of the Wald Test Statistic

I am trying to understand the asymptotic distribution of the Wald test statistic, specifically under the alternative hypothesis which I've found little reference to. For clarity, the binary ...

### Estimating excess count

0 answers, 14 views mathematical-statistics inference
I have values of sales made for 20 months over two months period. The values are recorded as count per month and we have a hunch that the values were under-reported. I am trying to build a ...

### 1 R2 - contribution of explanatory variables x1, x2 and x3 to the variance of the explained variable y

I wish to look at the contribution of explanatory variables x1, x2 and x3 to the variance of the explained variable y. To summarize the contribution of the explanatory variables alone to the ...

### 3 Difference between a translationary invariant and a stable distribution

I understand that a stable distribution is a distribution whose linear combination of two independent random variables with this distribution has the same distribution (ignoring location and scale ...