# mathematical-statistics's questions - English 1answer

3.823 mathematical-statistics questions.

### 4 Deriving the Maximum Likelihood Estimation (MLE) of a parameter for an Inverse Gaussian Distribution

Given the following likelihood function $$f(y|x,\tau) = \prod_{i=0}^Nf_T(u_i-x_i-\tau) \tag{1}$$ where, $f_T(t)$ is the probability density function of an Inverse Gaussian distribution given by ...

### 3 Time series analysis textbooks for mathematicians

As a former mathematics student, when reading any math-related materials I tend to care about their mathematical rigour very much. Such high attention to mathematical details might be a good habitat ...

### 1 Determine AR term from PACF plot

I have the a time series data, the acf and pacf for which have been displayed below: I get that MA term is 1. But I'm confused about AR term since it is geometrically decaying from 7th lag. Do I need ...

### Application of Factor Analysis to a table of count data

I am being asked to apply a statistical technique that I do not think is optimal. I have asked before, but was told my question was vague. I have re-worded it appropriately here. I am being asked to ...

### -1 Estimation of Maximum Likelihood Estimate [on hold]

This is from a very cool paper about horse racing, I tried it at Excel much time, but all failed, I mean cannot estimate the likelihood. https://imgur.com/WsC95aC "formula" My Excel is like this: ...

### Confidence Interval for 10 unit change in hazard ratio?

I'm fitting a Cox model with one predictor, X. That is, $$h(t) = h_0(t) exp(X_i \beta).$$ I'm an interested in getting a confidence interval for the hazard ratio of a 10 unit change in X instead of a ...

### -2 Using time series with data of only one part of the year [closed]

I have a data set containing sales data per day for Jan-April 2017 and Jan-April 2018, I need to forecast the sales values for Jan-April 2019. What would be the best method for this? Example of the ...

### 1 How can we get the weights of ridge regression if there is bias term?

2 answers, 33 views regression mathematical-statistics
For ridge regression I learned before, $\hat{w} = argmin_{\theta}||y-Xw||_2^2 + \lambda||w||_2^2$. Thinking about if the bias is added, so the new $X$ become $[1,X]$, and we have a new weight $\theta$...

### 16 Does a “Normal Distribution” need to have mean=median=mode?

I've been in a debate with my graduate-level statistics professor about "normal distributions". I contend that to truly get a normal distribution one must have mean=median=mode, all the data must be ...

### 1 How to force a neural network to have Gaussian hidden activations

Let the task be classification and the neural network under discussion to have Sigmoid activation functions and be trained by Backpropagation and SGD. How can I force the networks hidden activations ...

### 6 How to find the deterministic function representation of a random variable?

For any random variable $X$ whose density is $\mathbb{P}(X=x)=p(x;\theta),$ where $\theta$ is a parameter, its deterministic function representation is $X=f(\theta, \omega)$ where $\omega$ is a random ...

### 2 Conditional correlation, copula, portfolio optimization and diversification

I have a data set which consists of > 500 hedge funds, their historical monthly returns, and their benchmark (index) monthly returns. The number of data points (# of monthly returns) differs from a ...

### 1 What is the meaning of the coefficient ($z_{\alpha/2}$) in Acceptance Intervals fomula?

Introduction: I'm studying "Statistics-Business-Economics-Paul-Newbold", chapter 6, topic: "Acceptance intervals" (page: 260). (https://www.amazon.it/Statistics-Business-Economics-Paul-Newbold-ebook/...

### 3 Prove $E[{E[(Y|X)^2}] + E[Y^2] - 2E[Y*E[Y|X]] + E[{E[Y|X]}^2]$

3 answers, 207 views self-study mathematical-statistics