Any statistical process which seeks to approximate an unknown value, such as a distribution, a point estimate (e.g. mean), or confidence interval.

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11 views

Showing that moment estimates are asymptotically bi-variate normal

Let $X_1,\dots,X_n$ be iid $\Gamma(p,1/\lambda)$ with density $g_\theta (x) = \frac{1}{\Gamma(p)} \lambda^p x^{p-1} e^{-\lambda x}$, $x>0$, $\theta = (p,\lambda)$, $p > 0$, $\lambda > 0$. ...
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12 views

Existence and Uniqueness of an Estimator

The object to be observed consists of B cubes $(b_{1},\ldots,b_{B})$. The detector consists of $D$ parts namely $(d_{1},\ldots,d_{D})$. Let $p(b_{i},d_{j})$ denote the probability of detecting a ...
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4 views

Estimation using empirical distribution to get parameter estimation

how to get estimation using empirical distribution to estimate the standard force of mortality. ? assumed standard force of mortality is Gompertz law
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28 views

Estimate Probability of being in a time interval

​You arrive at a bus stop in an unfamiliar part of town. Assume that buses arrive at the stop with an unknown (to you) distribution and wait in the bus stop for a few ​minutes. The wait time ...
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1answer
33 views

What is “Targeted Maximum Likelihood Expectation”?

I'm trying to understand some papers by Mark van der Laan. He's a theoretical statistician at Berkeley working on problems overlap significantly with machine learning. One problem for me (besides ...
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5 views

Extract predicted values for latent variables in sem [on hold]

I have used the 'sem' package to create a structural equation model with the aim of better understanding the formation and measurement of structural complexity in natural habitats. The objective was ...
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1answer
10 views

Estimate parameters of three parameters gamma distribution

I need to estimate parameters of three parameters gamma distribution. Can anybody please give me a clue in which software and by which commands I can do it? Thank you
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19 views

Estimate E[x|A,B]: alternatives to bucketing for non-parametric estimation

I have a set of products. I would like to estimate Expected Value of items sold of the products wrt product price and age of the purchaser. One alternative is to assume a distribution and fit it. ...
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30 views

How to estimate mean and standard deviation of a normal distribution from noisy data?

I have $n$ observations, $x_i$ following a normal distribution. I would like to estimate $\mu$ and $\sigma$ from my samples. Normally I would simply estimate $\mu=(\sum x_i)/n$ and $\sigma^2=\sum ...
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11 views

Defining the probability distribution of a Random vector given the probability over a “sub-vector”

Suppose I want the probability distribution over a random vector $X={X_1 ,X_2 ... X_n }$. What I already have with me is the distribution over a subvector $X_i , X_{i+1}...X_m$, $m<n$ which I ...
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13 views

Idea on how to estimate a cost function

I shall appreciate ideas in solving the following problem : I need to find a maximum likelihood estimate for the distance function given in paper ...
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1answer
10 views

Estimating counts from sampled data

I am working on counting events from sampled web logs. To formalize the problem, consider a random process in which we randomly record an event with known probability $r$. Say we have $n$ recorded ...
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28 views

Fixed effects regression when explained variable is used to compute explanatory variable

In a fixed effects model I attempt to explain stock returns with a number of variables. Among these variables are the book-to-market ratio (BM) and the price-earnings ratio (PE). The computation of ...
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62 views

How does one create a confidence interval for the ratio of the means of two non-normal bounded distributions?

Suppose $X$ and $Y$ are known to take values in the interval $[a,b]$ and $[c,d]$ respectively, but that beyond that nothing is known about their distributions. If $(X_i, Y_i)_{i = 1}^n$ is an i.i.d. ...
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21 views

A simple approach to maximum likelihood estimation for a model with no closed-form solution

I would like to estimate the best fitting parameters of a parametric model, $f(\theta)$, that does not have a closed-form solution. There are $n$ i.i.d. environmental observations and the aim is to ...
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17 views

M-estimators: textbook examples

I would like to practice with solving M-estimators problems, but I cannot find where they are easily explained. Could you please recommend me something? Thank you very much for any help!
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8 views

Acceptable Use of the Term “Critical Value”

The Stat Trek page for margin of error http://stattrek.com/estimation/margin-of-error.aspx says that Margin of error = Critical value x Standard deviation of the statistic. After looking at a ...
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21 views

Modeling of Multivariate Data

Suppose I have a multivariate data set. For the sake of example, lets say that the dimension of my data set is $p=7$ and I have a matrix which contains samples of this multivariate data set. Now ...
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260 views

Mean of the bootstrap sample vs statistic of the sample

Say I have a sample and the bootstrap sample from this sample for a stastitic $\chi$ (e.g. the mean). As we all know, this bootstrap sample estimates the sampling distribution of the estimator of the ...
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15 views

How is GARCH's p estimated in software?

From what I know, the GARCH(p,q) model is estimated via MLE and through an iterative process. Let's say if i wanted to recreate a GARCH(1,1) parameter estimation with excel solver (through maximizing ...
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10 views

Smoothing of a 2D Empirical Distribution

I have a number of data points $\theta \in \mathbb{R}^2$ with corresponding values $x \in \mathbb{N}$. I am assuming the $x$ are realisations from a distribution $f(X | \theta)$. Given I have a lot ...
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1answer
43 views

Confidence interval in a nonlinear model

Thanks for your suggestions.Actually i have the following model that i explains to you. Suppose i have observations structure like $$\begin{align} y_1 &=&v_1+e_1 \\ y_2 &=&v_2+e_2 \\ ...
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1answer
26 views

Working with the bootstrap sample vs the original sample

Consider a sample of real numbers. Say we want to estimate the central tendency of the population and get a sense of our uncertainty around this estimation. Let's put assumptions about the population ...
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9 views

How to write a program to find Hellinger distance in R [migrated]

So, I recently learned about the Hellinger Distance. Now, I wanted to generate a random sample from Poisson distribution using R, and then use this to estimate $\lambda$. Now, generating a sample, and ...
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1answer
67 views

Finding an unbiased estimator with the smallest variance

I will state the question then my methodology. Q: We have 3 random variables, $X1,X2,X3$ that are independent and identically distributed (iid). We would like to estimate $\theta = E[X1]$. Suppose ...
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14 views

Ranking estimation with partial data

Consider a problem where we ask a number of people to select and rank their top three choices out of a number of options. The set of options is the same for everyone, and they all have to rank their ...
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64 views

Estimate The Rate At Which Standard Deviation Scales With An Independent Variable

I have an experiment in which I am taking measurements of a normally distributed variable $Y$, $$Y \sim N(\mu,\sigma)$$ However, previous experiments have provided some evidence that the standard ...
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68 views

Estimate mass of fruit in a bag from only related totals?

An instructor at my university posed a question like this (not for homework since the class is over and I wasn't in it). I can't figure out how to approach it. The question concerns 2 bags each ...
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13 views

Estimate posterior distribution for a group given aggregate data

I have data describing over a 15 million individuals where each item includes variables like these: A. Amount spent on airfare last year B. Brand of shoes C. Number of times visited some website in ...
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34 views

Modeling a national dataset at a lower level of census geography

I want to build a model from a set of a over 100000 individual survey responses. Then, from the distribution of new responses (not found in the training set) on a subset of questions from the survey, ...
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18 views

Parameter estimation in lottery with some unique and some non-unique prizes

Let's consider this lottery: Each time a player plays he gets a prize. Either it's one of the normal prizes $a, b, c, ..$ or one of the unique prizes $A, B, C, ..$. Here "unique" prize is such that ...
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8 views

using EM for parameter estimation when there is no missing value or hidden variable

I am trying to estimate the parameters (conditional probabilities) for a Bayesian Network (each node corresponds to a discrete variable). There is no missing values in my data and there is no hidden ...
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205 views

Why $\sqrt{n}$ in the definition of asymptotic normality?

A sequence of estimators $U_n$ for a parameter $\theta$ is asymptotically normal if $\sqrt{n}(U_n - \theta) \to N(0,v)$. (source) We then call $v$ the asymptotic variance of $U_n$. If this variance is ...
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23 views

Bayesian update with multiple parameters

In the past I have been able to do Bayesian updating when there is just one parameter which I am trying to estimate. I know a bit about Bayesian methods but I am confused by how to extend them to ...
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1answer
27 views

Why are estimation results sharply different from the actual population (exponential distr.)

For my work, I analyze the field failure data sometimes and make decisions accordingly. (spare parts quantity, optimum preventive replacement point, ...) I made an experiment in Excel. Using inverse ...
2
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1answer
40 views

Can Hidden Markov Models be used to predict next observation?

I am reading up on Hidden Markov Models (HMMs) for my research and would like to know if it is applicable to the problem I wish to tackle. My problem is to detect/estimate the next value of a ...
2
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1answer
36 views

Estimate normal distribution from small sample with rankings

If I have n samples from an $N(\mu,\sigma)$ distribution, how can I estimate the distribution from a subset of m of these n samples where the order within those n is known. For example, if n = 100 ...
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13 views

Multivariate Bernoulli, Covariances for Categorical Data

I need to find outliers in multidimensional, categorical, 1-hot encoded, binary data. Data might look like, 0,1,1,0 1,1,0,0 1,1,1,0 0,1,1,1 0,0,1,0 I toyed with ...
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1answer
121 views

How to estimate the true distribution by using bootstrap method

I would like to estimate the true distribution of the following data set by making use of bootstrap method. ...
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1answer
192 views

Determining demographics by restaurant visits

Note: The edits below phrase the problem better, but I kept the original post as is. My apologies if not explaining the problem coherently Assume Person X likes to visit different restaurants at ...
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2answers
76 views

Self-study: Finding the maximum likelihood estimates of the parameters of a density function

Consider a random sample $x_1,x_2,...,x_n$ from a newly-generated distribution, whose probability density function is given below \begin{equation} f(x|\alpha,\beta,\sigma)=\frac{1}{\Gamma \left( ...
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55 views

Hayashi yoshida estimator for correlation not coming between -1 to 1

I took two time series data with 141 data points in total with time stamps. i found out actual correlation between them which is about 0.97. Now i find the Hayashi Yoshida estimator for correlation. ...
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685 views

What is the logic behind method of moments?

Why in "Method of Moments", we equate sample moments to population moments for finding point estimator? Where is the logic behind this?
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45 views

Prove that the MLE $\hat{p}(1-\hat{p})$ is a asymptotically efficient

Consider when $X_1, ..., X_n \sim $ Bernoulli($p$). We want to estimate $p(1-p)$. Suppose $\hat{p}=\frac{1}{n}\sum_{i=1}^nX_i$. Prove that the MLE $\hat{p}(1-\hat{p})$ is a asymptotically efficient ...
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10 views

How to prove that the permutation of the points are the minimal sufficient statistics for Cauchy distribution?

I see this everywhere that the permutation of the samples $X_{(1)}, ..., X_{(n)}$ is the minimal sufficient statistic for the Cauchy distribution [1]. It is clear that it is a sufficient statistic,but ...
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44 views

Correctness of a proof for Hodges' estimator

We know the following is Hodges' estimator: $$ \delta_n = \begin{cases} \bar{X}_n & |X_n| \geq n^{-1/4} \\ a\bar{X}_n & |X_n| < n^{-1/4} \\ \end{cases} $$ where $X_1, ..., X_n \sim ...
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1answer
24 views

Horvitz-Thompson estimator for two-stage cluster sampling

So I want to apply the Horvitz-Thompson (H-T) estimator to two-stage cluster sampling. The H-T estimator is defined as: $$\sum\frac{Y_i}{\pi_i}$$ where $\pi_i$ is the probability of including the ...
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2answers
66 views

estimating the value of a property (real estate) using the hedonic regression

I'm trying to estimate the value of a property depending on the property characteristics. I did some research and I found out, that it would be better to use the Hedonic Model/Regression instead of ...
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1answer
55 views

Predicted lm() means of log-transformed and untransformed data not equal

Why is the back-transformation of the predicted values so different from the observed when the observed are log-transformed? Sample data: ...
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1answer
70 views

Error bars on log of big numbers

I am calculating a quantity of the following form: $\mu = \log( \frac{1}{n} \sum_{i=1}^{n} e^{\phi(X_i)} )$ via MC. $X_i$ are iid and I can sample them. I want to give error bars\ confidence ...