a method of estimating parameters of a statistical model by choosing the parameter value that optimizes the probability of observing the given sample.

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44 views

When to divide data into training & test set in logistic regression?

I am using Logistic Regression in a low event rate situation. Overall universe: 46,000 Events: 420 Conventional logistic regression models divide the data into ...
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19 views

Likelihood Ratio Tesr [on hold]

Let X1;X2; :::;Xn be a random sample from N(0; 2 = ) distribution where 0 < < 1 and 0 is known. Show that the likelihood ratio test of H0 : = 0 versus H1 : 6= 0 can be based upon the ...
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1answer
53 views

A case of understanding customer behavior

Suppose I have a big online company, and many of my customers churned (i.e. they were paying, and then stopped). My goal is to understand why each of them churned. First I identify the complete set ...
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1answer
16 views

Does the estimated overdispersion parameter of Negative Binomial depend on mean

Negative Binomial distribution can be parameterized using mean, $\mu$, and overdispersion $\psi$, so that the variance of NB is $\mu + \frac{\mu^2}{\psi}$. We know there is no analytical solution for ...
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23 views

MAP Estimator with Laplacian Noise

I need to calculate the MAP estimator of $ x $ in the following case: $$ \left [ \begin{matrix} {y}_{1}\\ {y}_{2} \end{matrix} \right ] = \left [ \begin{matrix} x\\ x \end{matrix} \right ] + ...
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0answers
39 views

Maximum Likelihood Estimation with Known Parameter Distribution

Consider i.i.d observation vector ${\bf x}$ from a distribution $F$ depending on vector of parameters $\boldsymbol{\theta}$ and single parameter $\alpha$. We would like to estimate parameters ...
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0answers
9 views

Model selection and parameter estimation in forecasting with a Dynamic Linear Model

I am implementing a general purpose prediction tool for time series. I want to tolerate missing values, so I decided to settle for DLMs. To make it as relevant as possible on a large number of ...
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12 views

What is the proper way to compare two estimated densities using sample data?

Say if have a dataset $X \subset \mathbb R^d$. I have two candidate probabilistic models M1 and M2 (e.g., M1 is a mixture of 2 gaussians and M2 is a mixture of 3 gaussians). I want to know which model ...
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24 views

Iterative solving of ML estimators

I have derived this likelihood function \begin{equation} \begin{split} &-\frac{1}{N}\log L(\eta,\beta,\mathit{\Omega})\\ &=\frac{1}{2}\log ...
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0answers
38 views

Package ‘fitdistrplus’

I am trying to use the package ‘fitdistrplus’ in R to fit one non standard distribution to my data set. I am trying to copy the methods the package creators used in their tutorial for specifying a ...
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0answers
13 views

sub-questions with likert scales choices

I want to determine compliance to a certain standard in ISMS and to determine that, I have the standards started and it has sub-questions (say 2,3,4 questions), with each having a 5 point likert type ...
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1answer
39 views

Finding the MLE

Let $x_1,\ldots,x_n$ be a random sample with pdf $$f(x)= \begin{cases} (\alpha+1)x^\alpha, & 0 \le x \le 1, \\ 0,& \mbox{otherwise}. \end{cases}$$ Find the MLE of $\alpha.$ So, I've found the ...
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11 views

Maximum likelihood hypothesis vs Expectation maximization

Maximum Likelihood is given by the formula $h_{ML}=arg\space max_{h \in H } \space\space p(D/h)$ I want to transform it in terms of mechanism involved in Expectation maximization. $h_{ML}=arg\space ...
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0answers
56 views

Understanding the derivation of a ML-estimator

I have the following likelihood function: I'm given this information about the $\Omega$ matrix ($\boldsymbol{1}$ is a $T \times 1$ vector of ones): I would like to be able to show that the ...
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0answers
21 views

MLE or instrumental variables

I'm trying to estimate a model in which one of the explanatory variables is correlated with the error term. As I see it there are two alternatives, specify the likelihood function and maximize it to ...
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0answers
31 views

Stata: ml versus nl

I need to estimate an equation using some iterative method to optimally choose the coefficients. I won't go into the reasons that I can't use a simpler method like OLS, GLS or instrumental variables ...
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1answer
62 views

construct the maximum likelihood estimator

Let $a_{1},a_{2},a_{3}$ be independent with a normal(0,1) distribution. Define $X_{1},X_{2},X_{3}$ by $X_{1}=a_{1}$, $X_{2}=\theta X_{1}+a_{2}$ and $X_{3}=\theta X_{2}+a_{3}$ Find the MLE for $\theta$ ...
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18 views

Maximum likelihood estimation (MLE) for Markov Chain initial distribution?

I am working on using MLE to estimate a Markov Chain, I have successfully estimated the transition matrix $A$, using the method provided in ...
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1answer
28 views

Likelihood function of a sample selection model

I'm having some problems with the following assignment: I have a sample selection model (tobit II model) which however does not have the standard tobit II representation but rather the sample ...
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2answers
481 views

Why maximum likelihood and not expected likelihood?

Why is it so common to obtain maximum likelihood estimates of parameters, but you virtually never hear about expected likelihood parameter estimates (i.e., based on the expected value rather than the ...
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1answer
42 views

Link Functions where MLE=OLS

This is a follow-up of a question that I posted previously. I'm trying to get parameter estimates from two different SAS functions (Proc REG and ...
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2answers
60 views

SAS - REG vs GENMOD; OLS vs MLE

I'm using a very simple data set from an article in trying to further my understanding of GLMs. I've input the data using SAS, and I've run both the PROC REG and PROC GENMOD procedures on the data. ...
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2answers
49 views

Can I think of the level of a hypothesis test as being the probability the null hypothesis is true? [duplicate]

I am trying to understand the level of a test better and was wondering if the level of a hypothesis is essentially equal to the probability that the null hypothesis is true. I have been trying to ...
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1answer
47 views

What is it meant by the “rejection region” and “power” of a likelihood ratio test?

Suppose that $X_1,...,X_n$ are i.i.d. data from a $N(\mu, 100)$ distribution. I am trying to find the rejection region for the likelihood ratio test for level $\alpha= 0.10$ of the test: $H_0: \mu = ...
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0answers
17 views

Asymptotic Property of the Likelihood surface

I have a questions which I am not quite sure how to frame, so I apologies if it does not make sense, but I will try my best to make it interpretable. I have been running some network models in R, ...
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26 views

Unique or multiple maxima of log-likelihood function?

How can I find out if the log-likelihood function has only one global maximum or if it has multiple local maxima?
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1answer
42 views

Maximum likelihood of two Poisson distributions

Suppose I have two sets of samples $\{a_i\}$ for $i=1, \ldots, n_a$, and $\{b_j\}$ for $j=1,\ldots, n_b$, drawn respectively from two Poisson random variables $A \sim\textrm{Poiss}(\lambda_a)$ and $B ...
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1answer
91 views

Method of moments and maximum likelihood problem

I would like to ask a question on a practice problem from a textbook. The practice problem is about finding estimators of $\theta$, first by using method of moments and then by using a maximum ...
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0answers
25 views

How to include number of not-yet-decayed radioactive atoms in MLE? [duplicate]

Since this question received absolutely zero attention, here's a complete rephrase with the aim of significantly shortening it. I have a potful of $n$ radioactive atoms. I spend $t_\text{max}$ = 1 ...
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13 views

Simple Maximum a Posteriori for Matching Points in Two Sets

I have been studying about Maximum a Posteriori and I tried to apply this concept to the problem of matching points, i.e. given two point sets $X$ and $Y$, I would like to find the most likely ...
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27 views

Is it possible to estimate the convex combination of parameters in the IRLS-Framework?

Suppose I want to estimate the parameter $\mathbb{E}(Y)=\mu \ge 0$ with $\mu = a(\alpha)\mu_1(\gamma_1) + \Big(1-a(\alpha)\Big)\mu_2(\gamma_2)$ where $a(\alpha)\in (0,1)$ Using the usual ...
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1answer
69 views

estimate a distribution parameters only by data mean and std. dev

I need to estimate a truncated gamma distribution parameters (shape , scale). But, I only know the data mean and std. dev. I do not know the data set. Given the mean and std. dev. of a data set from ...
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2answers
37 views

how to find out the likelihood of a model given data

If i have a non-stochastic model that predicts the following dataset: [.2, .2] and the actual dataset found empirically (averaged over participants) is [.3, .3] How would I determine the ...
3
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2answers
133 views

How to decide on the MLE when pmf is 0?

Suppose you have $\theta=\{1,2\}$ and the sample of (0,1,2) with the task of finding MLE: \begin{array} {|c|c|c|} \hline x & p(x|\theta=1) & p(x|\theta=2) \\ \hline 0 & 1/2 & 1/4 \\ ...
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0answers
10 views

parameter estimation in bivariate autoregressive sem with individual heterogeneity - troublesome likelihood surface

I am working with models for panel data of individuals, wherein: my latent variables Yt= $\beta$Yt-1+Ai+Q Individuals level of the process A~N(l,h) Innovation of the latent Q~N(0,q) observed variables ...
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1answer
30 views

Trouble in comprehending question: Simple linear regression - LS and MLE

I've been given the simple linear regression model: $y_i = β_0 + β_1x_i + ε_i$ Under the assumptions of a simple linear regression model, the question they ask is: Assuming the usual model ...
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0answers
21 views

likelihood of a model

the likelihood of a model is defined as the probability of data given model: Likelihood(Model) = p(DATApoints | Model) which is equivalent to the product of all p(datapoint | Model) for each ...
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0answers
19 views

Can someone help me with the derive the MLE for the parameter in the SARIMA model?

My reseach topic is modeling the Inflation Process in Liberia, a SARIMA approach. I need to determine the property of the general SARIMA model and to derive the maximum likelihood estimators for the ...
3
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1answer
72 views

Summarising simulations on a transformed parameter

Let $\theta > 0$ be some model parameter for which properties (bias, ...) of an estimate are studied via simulations. For a given data set, an estimate $\hat{\theta}_i$ of $\theta$ can be ...
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25 views

Solving a difficult equation for a variable?

I'm trying to obtain the maximum likelihood estimate of the parameters for a model I'm building. I have constants $\sigma$, $\mu$, and $q_0$; a boolean matrix $\alpha$; and vectors $A, \beta, r, d,$ ...
2
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0answers
28 views

Estimator of Bessel function?

I am trying to estimate the parameters of the modified Bessel function of the first kind for integer order case. $I_n(wt) = \sum\limits_{m=0}^\infty \frac{1}{m!(m+n)!}(\frac{wt}{2})^{2m+n}$ In ...
2
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1answer
105 views

ML vs WLSMV: which is better for categorical data and why?

I was wondering which is a better estimator to use for categorical data: ML or WLSMV. I saw on a discussion on the Mplus website that they recommend WLSMV for categorical data but didn't explain why. ...
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0answers
33 views

Wrong parameters for GEV

I am doing some data analysis involving fitting datasets to a GEV distribution, but I'm getting some weird results. I'm using scipy, which uses MLE for fitting the parameters. My data is ...
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3answers
436 views

Intuitive reasoning behind biased ML estimators

I have a confusion on biased Maximum Likelihood estimators. The mathematics of the whole concept is pretty clear to me but I cannot figure out the intuitive reasoning behind it. Given a certain ...
3
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1answer
47 views

Seeking a Theoretical Understanding of Firth Logistic Regression

I am trying to understand Firth logistic regression (method of handling complete or quasi-complete separation in logistic regression) so I can explain it to others in simplified terms. Does anyone ...
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1answer
63 views

MLE of an exponential distribution in discrete case

Consider the one parameter exponential family on a finite sample space $S$: $$p(x;\theta)=\frac{e^{\theta x}}{\sum_{x\in S} e^{\theta x}}, \theta\in \mathbb{R}.$$ My objective is to find an MLE for ...
3
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2answers
134 views

What is meant by the standard error of a maximum likelihood estimate?

I'm a mathematician self-studying statistics and struggling especially with the language. In the book I'm using, there is the following problem: A random variable $X$ is given as ...
4
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2answers
117 views

Maximum Likelihood Estimator of the exponential function parameter based on Order Statistics

The following question is part (1/4) of a 2.30h written exam for the course "Probability and Statistics" in a school of engineering. So, although tricky and difficult (because the Professor is really ...
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0answers
38 views

Figuring out quantiles in quantile regression

Suppose I have a dataset $\{y_i,x_i\}$ $i=1,2,...n$. For the response variable, $y_i$ as per quantile regression I have the following likelihood: $$p(y_i|\beta,\alpha_i,\sigma) ...
2
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1answer
65 views

relation between confidence interval and likelihood function

I once meet the following question,which is also listed by book written by Cosma Rohilla Shalizi ...