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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11 views

Show that MLE estimator equals when mean = variance, show that its consistent [on hold]

I have posted my question as I picture, I hope it wont be any problem.
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41 views

Maximum Likelihood for Negative Binomial _where the r parameter is any positive values

I'm trying to estimate negative binomial parameter using MLE method. I have just known that the parameter 'r' need not to be a positive integer. Let the pdf of NB $(r,\theta)$ be: ...
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1answer
18 views

MLE asymptotic properties in non-regular families

I am working with asymptotic results about the MLEs and I know that if the family of distributions to whom the pdf of my sample belongs is exponential the regularity conditions for the asymptotic ...
3
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16 views

Method(s) to avoid overfitting model parameters for pre-determined model structure?

I'm using maximum likelihood estimation to fit a model of a pre-determined form to some data. To test this fitting method, I decided to generate some simulated data using the precise model form and ...
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8 views

Using statistics for map matching

I have given some road network (segments of two coordinates each) and a position which is given by a coordinate (lon/lat) and an angle 0 <= angle <= 359. I would like to find the segment which ...
2
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16 views

Delta Method vs. Lognormal

I have a single parameter $\theta > 0$ of a probability model I estimate with MLE on i.i.d. data. To get rid of the positivity constraint I instead estimate $\log \theta$ for which MLE gives me an ...
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19 views

Why is Fisher's information the *negative* of expected second derivative?

According to Wikipedia, A "blunt" support curve (one with a shallow maximum) would have a low negative expected second derivative In my mind, a blunt support curve has slow-changing slope, ...
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20 views

Why does the sim function in Gelman's arm package simulate sigma from inverse chi square?

In getMethod(arm::sim, "lm"), the source code shows that $\sigma$ is simulated from inverse chi square: ...
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1answer
26 views

What is the asymptotic distribution of the variance of the error term (in MLE linear regression)

In most treatments of the MLE linear regression, the author focuses on the asymptotic normality of $\hat \beta_{MLE}$. To estimate $Var(\hat \beta_{MLE})$, which relies on $\sigma^2$, they also show ...
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15 views

Estimating the effect of wrong input parameters in a model estimation

I've got a physical system that detect counts in an array of detectors. In each detector $y_i$ I expect to measure $\bar y_i = f_i(\bar \lambda)+\bar b_i$ counts. $b$ represent the vector of of counts ...
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18 views

Choosing the good initial value of the Newton-Raphson iteration method for Maximum Likelihood Estimation

I want to estimate the four parameters of Exponentiated Modified Weibull Extension (EMWE) distribution introduced by Sarhan and Apaloo (2013) with the Maximum Likelihood Estimation. Because the first ...
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20 views

Observed Fisher Info as an estimator of Expected Info

When I construct an asymptotic confidence interval for a parameter $\theta$, taken from a sample iid distributed with a generic pdf/pmf, I usually implement the mle $\hat\theta$ instead of $\theta$, ...
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31 views

Is there any real statistics behind “the Pythagorean theorem of baseball”?

I'm reading a book about sabermetrics, specifically Mathletics by Wayne Winston, and in the first chapter he introduces a quantity that can be used to predict the win rate of teams: ...
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1answer
31 views

Calculate confidence interval for hazard ratio given maximum likelihood and standard error

I'm doing a meta-analysis and one of the studies presents the hazard ratio (HR) with the maximum likelihood estimate (MLE) with its standard error (SE). The rest of the studies give the HR and the ...
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24 views

Maximum Likelihood Estimation for Bivariate Burr III Copula parameters

The Copula of Bivariate Burr III Rodriguez distribution is: $$ C_{xy}(u,v) = ({{1+\alpha (u^{-1/{\epsilon}}-1) (v^{-1/{\epsilon}}-1)+(u^{-1/{\epsilon}}-1)+(v^{-1/{\epsilon}}-1)}})^{-\epsilon} $$ ...
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13 views

MLE: Does the scale of predictor variables affect whether the hessian is positive definite?

I am trying to fit a regression via maximum likelihood estimation, one of the regression terms involves $\beta_0e^{(\beta t)}$ where $t$ is measured in hours and has a range of 0 to 90 days. The ...
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39 views

How to define a likelihood function for an EM algorithm

Assuming $A$ a set of vectors from a normal distribution, and $X$ a projection matrix and $B$ a set of projected vectors of $A$ using $X$: $B=A*X$ Using an EM approach and by initializing X from ...
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1answer
17 views

Likelihood for dependent data above a threshold

Let $(Y_t)$ a real-valued stationary Markov chain and $u$ some positive threshold. We assume that for $y>u$, $$Y_{t+1}|\{Y_t=y\}\sim\mathcal{N}(\alpha y+\mu y^\beta,\sigma^2 y^{2\beta})$$ I want ...
4
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2answers
58 views

Is it better to use a MLE or a MME to build an asymptotic confidence interval for a real parameter $\theta$?

I thought that the answer was pretty straightforward given that the MLEs possess some strong asymptotic properties, i.e. normality, efficiency and consistency. But then, I have found that also MME ...
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0answers
25 views

MLE Uniform X∈(N,N+1,…,N+10) [duplicate]

I am trying to find N by MLE for several discrete uniform distributions involving a parmeter N∈Z. If the interval X is defined on is X∈(N,N+1,...,N+10) then I think N^=min{X1,X2,...Xn}.But this ...
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1answer
48 views

MLE for discrete uniform distribution [closed]

I am trying to find $N$ by MLE for several discrete uniform distributions involving a parmeter $N\in \mathbb{Z}$. If the interval $X$ is defined on is $X\in (N,N+1,...,N+10)$ then I think ...
3
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1answer
40 views

Meaning of “likelihood ratio criterion is distribution free”

This is in ref to pp. 54-55 in McDonald,R.P (1985) [1] in the context of exploratory factor analysis (EFA) estimation: I am confused as to the meaning of: "(the likelihood ratio criterion) is a ...
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52 views

How can I prove that the log-likelihood function for logistic regression is globally concave?

For my master thesis, I have to show/prove that the log-likelihood function for logistic regression is globally concave. My supervisor told me that one way to show this is to use the fact that $X'X$ ...
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27 views

Is MAP and MLE the same if MAP uses uniform priors?

would MAP = maximum a posterior and MLE = maximum likelihood estimation be the same if the priors were uniform? since maximizing p(x|y) would be basically the same as p(x|y)c where c is some ...
3
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1answer
114 views

MLE uniform distribution

Let $X_1, X_2, \ldots, X_n$ be a random sample of discrete random variable with Uniform distribution on set of integers $\{-\theta, -\theta+1, ... ..- 1, 0, 1, \theta-1, \theta\}$ where $\theta$ is ...
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1answer
33 views

How do you fit the ordered logit model?

I am reading the wikipedia article on ordered logit models. As I understand it, the model is specified by: $\Pr(y \le k | \mathbf{x}) = \frac{1}{1 + e^{\mathbf{w} \cdot \mathbf{x} - \theta_k}}$ ...
3
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1answer
35 views

Using method of maximum likelihood find the estimator for $\mathcal N(m,1),m<0$ and $\mathcal U(\theta, 1), \theta<0$

Using method of maximum likelihood find the estimator for $\mathcal N(m,1)$-normal distribution and $\mathcal U(\theta, 1), \theta<0$ From what I understand, if the parameter is negative it is ...
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10 views

How to calculate AIC for multiple participants

I have a number of competing models that I fit separately to each participant's data. What is the correct way to calculate AIC in this case? Can I just write $AIC = 2nk-2\sum_{i=1}^n{LL_i}$, where $n$ ...
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1answer
83 views

Negative variance in a log normal distribution

I'm currently trying to solve a maximum likelihood estimation of a random variable which is assumed to be log normal distributed. For this I compute the log of all sample values I have in order to ...
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1answer
38 views

What is the difference between partial likelihood and maximum likelihood?

I don't understand these terms. They both have "likelihood". How are they different? Can someone provide an intuitive explanation of them?
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22 views

Data's Effect on Optimization Algorithm running into a Saddle Point

I am working with a non-linear model that uses seven independent variables to estimate a Bernoulli probability. To estimate the parameters of the model, I am optimizing a likelihood function using ...
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19 views

Reestimating prior probabilities after making assumptions about them

Imagine that I have $M$ observations, and each of them can be classified in two different ways: it belongs to one of the classes $A = \{A_1, A_2\}$ and to one of the classes $B = \{B_1, ..., B_n\}$. ...
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1answer
26 views

Bayesian approach and ML approach for distributions

Suppose that we have two sets of discrete random variables X ~ f(θ), Y~g(θ) where X and Y are independent, and the parameter θ is the same in both cases. We are interested in predicting Y on the basis ...
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42 views

How to calculate the distance between clusters using log-likelihood in two step clustering? [closed]

Log-Likelihood Distance (TwoStep clustering algorithms) How to calculate the distance between clusters(i.e record and cluster) using log-likelihood in two step clustering using the below mentioned ...
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1answer
42 views

probability mass function and maximum likelihood estimator

I am revising for stats exam and have come across this question. I don't understand how to get the probability mass function in part a and am struggling with part b as well. For b I have found the ...
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1answer
36 views

maximum likelihood estimate as the root of a polynomial

I have worked out the log likelihood to be The next question says what i have tried to do is follow the normal procedure of setting the first derivative of the log-likelihood equal to zero but am ...
3
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2answers
117 views

Asymptotic properties of MLEs

Are there any relationship between the asymptotic properties of MLEs (assuming that the regularity conditions hold)? I mean, once I know that the MLE for $\tau(\theta)$ is asymptotically efficient ...
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1answer
46 views

How should I estimate the variance using a sample (not knowing the mean)?

The unadjusted sample variance is biased, yet it has a smaller mean squared error. Also, if we assume the sample comes from a normal distribution, the maximum likelihood estimator for the variance is ...
3
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1answer
30 views

How is it logically possible to sample a single value from a continuous distribution?

For example, suppose I am told that 10 data points come IID from a normal distribution with some mean and variance. Isn't the probability of realizing each of these values zero? Shouldn't the fact ...
3
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0answers
65 views

Expected and observed Fisher information?

Studying asymptotics, I bumped into the concept of Observed Fisher Information, as a way to compute Fisher Information when the parameter $\theta$ is unknown. I am also aware that it is related in ...
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0answers
77 views

AIC comparison for models without maximum likelihood

AIC is a popular model comparison measure (despite of its potential shortcomings). I am wondering whether it is legit to compare AIC (or Akaike weights) for models that were fitted without requiring ...
6
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1answer
129 views

Is ANOVA relying on the method of moments and not on the maximum likelihood?

I see mentioned in various places that ANOVA does its estimation using the method of moments. I am confused by that assertion because, even though I am not familiar with the method of moments, my ...
2
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2answers
51 views

Cramér-Rao inequality and MLEs

I know that if it exists, a regular, unbiased estimator $T$ for $\tau(\theta)$ attains the Cramér-Rao Lower Bound (next, CRLB) if and only if I can decompose the score function as follows: ...
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1answer
23 views

MLE on a restricted paraameter space and its behavior [closed]

Suppose $X_1,\dots,X_n$ are a random sample from a normal distribution with mean $\theta$ and variance 1. Find the maximum likelihood estimator of $\theta$, under the restriction that $\theta\geqslant ...
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12 views

MLE for normal distribution with same mean and variance/standard deviation [duplicate]

Could someone please let me know how to find the MLE of $\theta$ when we have a random sample from pdf $N(\theta,\theta^2)$ and from pdf $N(\theta,\theta)$? I found an old thread that referred to ...
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41 views

Estimate GARCH parameters using maximum likelihood pseudocode

I have to estimate the GARCH parameters using maximum likelihood in Scilab. I have tried many ways and so far nothing works properly. I have $$ x_t = \sigma_t y_t, \ \ \ \ \ y_t \sim N(\mu, \sigma) ...
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22 views

Stochastic Gradient on the Simplex

I have a probability density function defined over $x_1,...,x_K$ with a simplex constraint $\sum_{k=1}^K x_k = 1$. I'm trying to perform stochastic gradient descent on this density. I know I can keep ...
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21 views

improve performance of finding rolling window maximum likelihood

There is data indexed by time: $$ D_1, D_2, D_3, ..., D_T $$ I have a model that I assume the parameter $\theta_t$ changes with time $t$. As a result, I adapt a rolling window strategy: $$ ...
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1answer
45 views

Estimate $m$ using method of maximum likelihood

Estimate $m$ using method of maximum likelihood. In the box there are $91$ balls, where $m$ are red, and the rest are blue. To estimate unknown parameter $m$, at once $19$ balls are drawn, $7$ being ...
6
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1answer
67 views

How robust is the maximum likelihood estimator in structural equation modelling to non-multivariate normality?

In a Structural Equation Model, one often uses the ML estimator. In the case where the variables are not multivariate normal, can ML be used? Often times the indicators you have available to work ...