Point estimation is the application of an estimator to the data in order to learn about a certain population parameter.

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How to find conditional distribution for Rao-Blackwellizing an estimator?

Let's say I have an unbiased estimator $u(\underline x)$ for function $v(\theta)$ where $\theta$ is a parameter of the distribution of $x$, and $T(\underline x)$ which is a sufficient statistic for ...
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63 views

Cramer-Rao bound for $\chi^2$ distribution parameter estimates

I've struck an unpleasant problem with the noncentral $\chi^2$ distribution. I work with random variables, distributed as $\chi^2_{\nu}(\lambda)$, where $\nu$ is the degree of freedom and $\lambda$ ...
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22 views

Biased but consistent estimator for the mean of Gaussian distribution?

$(X_1,X_2,\ldots,X_n)$ is a random sample from $\mathrm{N}(θ, 1)$. We know sample mean is a unbiased estimator that is consistent. What would be a biased but consistent estimator for θ? Would it be ...
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49 views

Comparing two estimators for accuracy using empirical bootstrap

I am trying to figure out the proper way to compare the quality of two estimators of a parameter based on data. The basic approach I've taken is to compute the MSE of the empirical bootstrap ...
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23 views

EM Algorithm - Expectation w.r.t. a subset of current parameters

Suppose I want to make inference on a parameter vector $\theta $=$(\theta_{1},\theta_{2},\theta_{3})$ and I have some missing data $Y_{mis}$. I would like to use the EM algorithm to find the mode of ...
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38 views

Show that $\mathbb{E}(g(T-p)) < \mathbb{E}(g(S-p))$ for any convex function $g$ if $T$ and $S$ are estimators of $p$

The more detailed question. I'm kinda having some trouble starting out with answering this question. My initial approach would be to $g(x)= x^2$ since that is a convex function and find the ...
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15 views

Given the 6 criteria, show that criteria 1 - 5 are transitive while criteria 6 is not. Assume the parameter theta = 0

Here are the criteria and the more detailed question. I'm not sure how to really proceed on answering this question. The problem set provided this hint but I'm not sure what to make of it. ...
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2answers
68 views

Why we shouldn't be obsessed with unbiasedness

In my Bayesian statistics class, my professor makes the remark that we should not be obsessed with unbiased estimator. First: I understand this statement in the sense of trading biasedness for ...
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39 views

Estimation of unknown vector's amplitude with Gaussian noise

I have the following model: y = P v + n Where y is the vector of observations, v is a unit vector and n is a Gaussian random noise whose covariance matrix is the identity matrix. P is a positive ...
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49 views

Calculating point estimates from model-averaged parameters

I'm using an IT-approach and multi-model inference with some count data. I have used model averaging to obtain parameter estimates from several GLMMs with Poisson-lognormal errors (Poisson family ...
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1answer
231 views

Confidence Interval for a Random Sample Selected from Gamma Distribution

Working on a homework question and having some trouble... Any help would be greatly appreciated. Based on a sample 1.23, 0.36, 2.13, 0.91, 0.16, 0.12 from the GAM$(2,\theta)$ distribution, find an ...
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97 views

How to use a point estimator on an interval?

I got part a and part b just fine, but I am confused on how to do part (c), (d), and (e). I don't really understand what the question is asking, nor do I understand how to do that sort of interval ...
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61 views

Complex-valued estimator of Real Parameter?

I was in statistics class today and the professor wrote "consistent estimator". The first thing I thought of was that the range of the estimator should be a subset of the set of plausible population ...
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59 views

Yet another “Bayesian vs Maximum Likelihood” question

In the fully Bayesian approach, the predictive distribution is: $$ P( Y|X ) = \int P(\theta | X ) P( Y | \theta ) d\theta $$ When the integral is difficult to compute, we might resort to the Maximum ...
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42 views

Why do matching algorithms use point estimates rather than intervals?

I'm developing a matching algorithm, and I am wondering why websites choose using point estimates, e.g. "You match 60% with person X". Given that there will be most likely be missing data, rather ...
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119 views

Differntiate between point estimate and interval estimate in terms of assumptions for making such estimates?

interval estimate is common. However, point estimate appears to be based on simple theorem of central limit theorem.
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Invariance property of MLE: what is the MLE of $\theta^2$ of normal, $\bar{X}^2$?

Invariance property of MLE: if $\hat{\theta}$ is the MLE of $\theta$, then for any function $f(\theta)$, the MLE of $f(\theta)$ is $f(\hat{\theta})$. Also, $f$ must be a one-to-one function. The ...
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118 views

Prove/counter example: A minimax decision rule is always Bayes wrt some proper prior

Not sure whether the claim is true or false. If claim is true, intuitively, it might have something to do with "least favorable priors", but am not able to figure out the connection. If claim is ...
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1answer
38 views

What does “I” represent in this context?

I'm trying to work on a problem which contains a symbol that I don't recall seeing before - I. I assume it has some special significance but I'm having a hard time looking it up. Relevant portion of ...
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248 views

Extract data points from moving average?

Is it possible to extract data points from moving average data? In other words, if a set of data only has simple moving averages of the previous 30 points, is it possible to extract the original data ...
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4answers
636 views

Inference for the skeptical (but not math-averse) reader

I just watched a lecture on statistical inference ("comparing proportions and means"), part of an intro to stats online course. The material made as little sense to me as it always does (by now I ...
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1answer
95 views

Given MCMC samples, what are the options for estimating posterior of parameters?

Markov chain Monte Carlo (MCMC) is a class of algorithms for sampling from probability distributions. In the end, given a parametric model explaining the data, MCMC could also be used for parameter ...
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175 views

Determine an unknown number of real world locations from GPS-based reports

I'm working on some software which should determine real world locations (f.e. speed cams) from several GPS-based reports. An user will be driving when reporting a location, thus the reports a very ...
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1answer
189 views

Estimated error variance $\sigma^2$ for MCMC estimation in a high-dimensional space

Let $f$ be a function such that: $$f~:~(x,~\theta)\in\mathbb{R}^{3}\times\mathbb{R}^{12} \rightarrow f(x,~\theta)\in\mathbb{R}^3$$ My observations $y$ are noisy values taken by the function $f(\cdot ...
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481 views

How to describe the differences in skewed data with same median but statistically different distribution?

I am comparing length of stay after laparoscopic and open appendectomy in over 160000 patients. LOS is typically a skewed variable so I use the median and interquartile range and ranksum test to ...
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1answer
216 views

Why do we rely on the standard error? [duplicate]

Possible Duplicate: Difference between standard error and standard deviation I cannot come to terms with the fact that the standard error is used to describe the accuracy of a point ...
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264 views

Sufficient, Complete Sufficient, UMVUE, Rao-Blackwell, Admissible. What are ties between these?

I am taking stat inference course. I have some trouble understanding some these terms: Sufficient Statistics: a stat that does not depend on the parameter, say $\Sigma X$ for normal distribution ...
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1answer
57 views

How to estimate 5 percent breaking point of a sample of ropes?

The breaking strengths in pounds of five specimens of rope were 660, 460, 540, 580, and 550. How can I estimate the point at which only 5 percent of such specimens would be expected to break?
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1k views

How to find an unbiased estimator?

Suppose $X_1, X_2, ...,X_n$ are samples from a uniform discrete distribution with probability 1/3 on each of the points $\theta-1, \theta, \theta+1$, where $\theta\in\mathbb{Z}.$ From "Theory of ...
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582 views

Is the theory of minimum variance unbiased estimation overemphasized in graduate school?

Recently I was very embarrassed when I gave an off the cuff answer about minimum variance unbiased estimates for parameters of a uniform distribution that was completely wrong. Fortunately I was ...
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35 views

Improving an estimate of mean with observations of sign

Suppose $x_i$ are drawn i.i.d. from a $p$-variate Gaussian, $\mathcal{N}\left(\mu,\Sigma\right)$. Suppose one observes $x_1,x_2,\ldots,x_n$. One also observes $s_{n+1},s_{n+2},\ldots,s_{n+m},$ where ...