# Tagged Questions

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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### Error in estimation with continuous data

Is there a way to correlate error in a fit (MSD) to the error of the a calculation performed with the parameters associated with the fit? My specific problem is dealing with spectroscopic data. I ...
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### Help in formulation of maximum likelihood estimation

I need to find the minimum of the distances $D(X_i,X_j)$ provided that $||X_i-X_j|| \le l_0$ where $l_0$ is the maximum scaling distance. The points are the samples on a reconstrcuted attractor of a ...
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### Estimating successes while obtaining Bernoulli samples

I have a process which, after fixing the values of some parameters, generates samples from a Bernoulli distribution with unknown $p$. The value of $p$ is typically small, and what I want to do is to ...
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### Variance of a difference in marginal proportions in a three-way contingency table

Let a multivariate distribution be given by $P(Y,S_1,S_2)$, where all three variables are discrete, $Y$ is multivalued, $S_1=(0,1)$ and $S_2=(0,1)$, respectively, and all may be dependent. Define the ...
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### How to use profile likelihood?

I am new to profile likelihood and do not really understand what advantages it may have. Lets say I have the following results estimating the means of three groups. What can I say about them? R ...
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### Normalize a periodic parameter

I am using inverse modelling software (PEST) to estimate a periodic parameter for the direction of anisotropy, $\hat{\theta}$, which is somewhere in $[0^{\circ}, 180^{\circ})$ (i.e., has a wavelength ...
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### Maximum likelihood estimation of volume

Can somebody explain to me how to find the maximum likelihood of distances, $U_i$ for all dimensions D, with 2 nonlinear signal points $u_{id} - u_{jd}$, where $d =1,2\ldots,D$ . The 2 points lie ...
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### Disadvantages of the Kullback-Leibler divergence

I'm working on a calibration problem which involves the usage of the Kullback-Leibler divergence as an error between some empirical distribution $p$ and a theoretical distribution $q$. In the model, ...
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### Estimating the distribution from partially aggregated data

I have a dataset that consists of a list of tuples: (1, .5), (3, .7), (1,.1), (23,.8),... In each tuple, the second element is the average price, and the first ...
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### Combining bootstrapped non-normal statistics across multiply imputed data sets

I am analysing data that have been multiply imputed (MI). One of my statistics to test a particular hypothesis is defined as the difference in two absolute values ($\theta=|X|-|Y|$). There is reason ...
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### Combined individual error

This is from my college project management course. Reading through an example question here it says: When estimating in parts, the total error will be less than the sum of the part errors. ...
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### Bayesian estimation of Dirichlet distribution parameters

I want to estimate parameters of Dirichlet mixture models using Gibbs sampling and I have some questions about that: Is a mixture of Dirichlet distributions equivalent to a Dirichlet process? What ...
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### Confusion: different definitions of MAP estimation in Graphical Models (MRFs)

The "classical" MAP estimation: $$\hat\theta = \arg\max_{\theta}P(\theta|\mathbf{x})$$ where $\mathbf{x}$ are the observations and $\theta$ are the parameters. In this book chapter (page 6, second ...
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### Low intensity Poisson estimation

I have a collection of Poisson processes each with an unknown $\lambda$. I would like to estimate $\lambda$ for each process. for each process I could take either the total number of event over the ...
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### Sequential linear estimation: Is MSE non-increasing?

Suppose we estimate $x$ from $y_1=ax+z_1$ and get $x_1$. Then suppose we receive $y_2=bx+z_2$ and reestimate $x$ using both $y_1$ and $y_2$ and get $x_2$. Is the means squared error (MSE) of $x_2$ ...
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### Variable selection for Linear Regression using Robust or Least Squares Estimation

I have a data set consisting of one continuous response variable and about 70 predictors. Using this data, I want to construct a linear regression model. However, I don't know what predictors are ...
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### Estimation of mean of ratio of empirical distributions

I am trying to estimate the mean of the ratio of two empirical count distributions $f(x)$ and $b(x)$ defined on the limited range $[-1, 1]$ $$\left<\frac{f(x)}{b(x)}\right>$$ $f(x)$ and ...
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### Estimation of the shape parameter of gamma distribution in Winbugs

I want to estimate the shape parameter of gamma distribution in Winbugs. I select gamma distribution as prior for shape parameter. Data set is generated using MATLAB as: ...
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### How to present the results of numerical comparisons

I ran a comparison where I estimated the parameters of a model using $S$ different methods several times. More specifically I simulated $M$ datasets $\boldsymbol{y}_1, \dots, \boldsymbol{y}_m$ from a ...
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### Does Bayesian data analysis take into account estimates' bias?

For example, the standard deviation is known to have bias that depends on the number of samples observed. If I wanted to do Bayesian inference on the SD of samples from two populations, and have ...
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### What is the proper way to estimate the CDF for a distribution from samples taken from that distribution?

Given $n$ samples from a (continuous) distribution X, the obvious thing to do is sort them, and distribute them equally across $[0,1]$ by taking $(x_{(k)}, (k-1/2)/n)$ as estimates of particular ...
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### How to compute efficiency?

Suppose instead of maximizing likelihood I maximize some other function g. Like likelihood, this function decomposes over x's (ie, g({x1,x2})=g({x1})g({x2}), and "maximum-g" estimator is consistent. ...
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### Estimation method

I am looking for some Statistical estimation method to understand how many errors hidden in a database. Can somebody point me if such estimation method is available? Any online reference, link is ...
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### Why is it claimed that a sample is often more accurate than a census?

When learning the course of sampling, I meet the following two statements: 1) Sampling error leads to mostly variability, nonsampling errors lead to bias. 2) Because of nonsampling error, a sample ...
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### FE shrinkage estimates

In what circumstances can Fixed effects models produce BLUE/shrinkage estimates? I am referring to models discussed in Tekwe et al.(2004)...Journal of Educational and Behavioral statistics. I would ...
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### CLT in a Monte Carlo simulation, small sample

A CLT says that asymptotically the sampling distribution of the sampling mean converges to the Normal. I would like to run a Monte Carlo simulation using information on one of the model's variables ...
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### Difficulty in understanding correlation dimension

I am trying to implement the Grassberger Procaccia algorithm. I have got stuck in how to find the summation of the correlation integral. The following code computes the correlation dimension in the ...
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### Linear regression 3 variables formula for slope coefficient estimates

Okay so I think I found a formula for the coefficient estimates but it is not very concise. It has like 6 sum of squares but it is in a single fraction so it is calculable. I was wondering what the ...
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### Estimation parameters using Generalized Method of Moments and Generalized Empirical Likelihood with R

I have two density functions: $h_{1}(x)$, $h_{2}(x)$. I want to estimate parameters from one dataset using $h_{1}$ and $h_{2}$ andthe GMM estimator or the GEL : from the article "Computing ...
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### Predicting the edges of a graph

I have a dataset of paired relations, indicating whether $a$ is in relation with $b$. It is better to consider this dataset as a graph where each node has a numerical value as its feature. Let's say ...
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### Estimating variance of center-censored Normal samples

I have normally-distributed processes from which I get small samples (n typically 10-30) that I want to use to estimate variance. But frequently the samples are so close together that we can't ...
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### Fisher information $J_y(\theta)$ for transformation $y=F(x)$

Consider a multivariate random variable $x$ with density function $P_x(\theta)$ for a scalar parameter $\theta$. Assume the Fisher information $J_x(\theta)$ is known. Now, for a transformation ...
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### Why do we estimate the mean response in Confidence interval but predict individual outcome in prediction?

I have tried to understand the differences. Just to be clear, I think I understand the two sources of variation in prediction comes from the variation in the distribution of the location of Y and ...
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### Difference between 'ovtest' and ovtest,rhs'

After running an OLS regression, I ran the Ramsey RESET test using the stata command 'ovtest' and 'ovtest,rhs'. Two tests gave the opposite results. With the first one, I could not reject the Null, ...
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### Demonstration of sample quantile bias

While doing some simulations, I realised that the sample quantile is a biased estimator of the true quantile. And, according to my simulations, a potentially very biased one. I was surprised with ...
I'd like to infer the variance of estimated parameter $\hat\theta$ of the density function of $f(x;\theta)$ given only a limited number of samples $X_1,\cdots,X_n$. Bootstrapping doesn't perform well ...