# Questions tagged [point-estimation]

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

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### Extract systematic and random variation

I am working with the data from some manufacturing line. The parts are processed in batches of say 20. In order to control process, we do measurements on manufactured parts. We know that the ...
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### Recall and precision point estimates (statistical inference)

Let's say I have a population of 1M objects. I want to make a binary classifier to use on that data, but I can't manually classify all the 1M to create training data because that would take too long, ...
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### Is it legit to use a point estimate along with a conformal predictive interval from a quantile regressor?

I have a quantile regression model that gives me prediction intervals (PI), and I also need to have a point estimate for all sorts of reasons (or at least something as close to a point estimate in a ...
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### Can I reasonably estimate the population mean and standard deviation from a large sample all taken at a single percentile?

I am currently looking at a dataset of Fair Market Rents which are determined at different percentiles over the years - for example, nationally in 1983 they were all set at the 40th percentile, and in ...
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### How to solve non-identifiability problem in point estimation

I am working with a normal model $X \sim N(0, \sigma^2(\theta))$, where $\sigma^2(\theta) = \frac{1}{e}\cos^2(\theta)+e\sin^2(\theta)$. My goal is to estimate $\theta$ within the range $[0, 2\pi]$. My ...
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### Distribution of the point estimator of a sample

We know that point estimator is defined over a sample and is said to be unbiased if its expectation value is same as that of some parametric function $g(\theta)$ where $\theta$ is a parameter for the ...
222 views

### Unbiased estimator for binomial random variable

On internet, I was reading about the point estimators. I am attaching the screenshot of the relevant portion. Suppose we have a sample $X_1,\;X_2,\;...,\;X_n$, then the point estimator is a function ...
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### Find an estimator of linear regression when errors variance is correlated with one of the K regressors

I need to answer to the following problem: In an heteroschedasticity setting, let $n$ be the index of the n-th statistical unit with $n=1, \dots, N$. Suppose a multiple linear regression setting with ...
1 vote
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### Estimation with MCMC [closed]

I would like to ask some high-view questions about MCMC. I do not have a specific example, I just want to get a general intuitive idea. Suppose I have a data set $X$ and a rather complex model with ...
1 vote
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### Why Do Distributional Forecasts Need to Produce Normally-Distributed Forecasts to be Ensembled/Combined?

I am forecasting a collection of different types of items, using many different forecasting techniques. Some of the techniques I use take the input data as is to produce a distributional forecast. ...
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### Winsorized mean - trimming furthest points instead of both endpoints

I'm wondering if the Winsorized mean can be improved by trimming the 5% farthest points from the mean instead of trimming 5% on each endpoint. Concretely: Consider the Winsorized mean, where we ...
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### Estimating Means of a Bivariate Normal Distribution where some parameters are known

I am trying to figure out how to estimate means of a bivariate normal distribution from a sample when some of the parameters are already known. let  \boldsymbol{x} = \begin{bmatrix} x\\ y\\ \end{...
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### Unbiased estimator and getting estimate from estimator

I got a unbiased estimator but I don't know how to interpret it and adjust it to get estimate. The original problem is to find out the unbiased estimator for $\lambda$ in Zero-truncated Poisson ...
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### Trimmed, weighted mean

The trimmed mean (or truncated mean) is a robust version of the mean, designed to be robust to outliers. I am wondering what is the right trimmed version of a weighted average. If I have a sample ...
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### Mean-square convergence of maximum likelihood estimators: Examples?

From what I've gleaned from the literature, Cràmer, in his 1947 monograph Methods of Mathematical Statistics, proved convergence in probability of an MLE under certain regularity conditions. ...
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### Point estimate and confidence interval for the difference in $x_1$ between two groups for which a particular $y$ is achieved

I have two variables (continuous $x_1$, control/treatment $x_2$) that I want to use to predict a probability. Domain knowledge suggests that the relationship is roughly linear in the log-odds, so I am ...
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### Expression for the Likelihood Function in Point Estimation

I came across this question in my statistics textbook, but I'm struggling to come up with an expression for the likelihood function. Here is the question: Assume that there are three possible traits ...
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### Determining the minimum number of tosses, for heads to be twice more likely than tails in the next toss

I would like some help with the following statistical problem. We have a coin with probability $\theta$ for heads, with prior for $\theta$ being a Beta(a,a) distribution (a is a known parameter). ...
This is similar to Mean Squared Error and Mean Absolute Error but in this case the loss function assigns estimates to $0$ when they are a possible estimand and $1$ when they are impossible. As a ...