Questions tagged [point-estimation]

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

Filter by
Sorted by
Tagged with
2
votes
0answers
13 views

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 ...
2
votes
1answer
28 views

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{...
0
votes
0answers
14 views

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 ...
-3
votes
0answers
20 views

What is the difference between point estimate and a random variable?

I was reading this answer. I wanted to understand how to comprehend these two terms.
0
votes
0answers
20 views

Consider N independent RVs having identical binomial distribution with parameters θ and n=3. Estimate θ by method of maximum likelihood

Consider N independent random variables having identical binomial distribution with the parameters θ and n=3. If n0 of them take on the value of 0, n1 take on the value of 1, n2 take on the value of 2,...
4
votes
1answer
76 views

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 ...
1
vote
0answers
17 views

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. ...
0
votes
0answers
17 views

Maximum Likelihood Estimation - parameter estimation

I must find the relation between a group of categorical features and a Target (label) variable T. A proxy of the dataframe I am using is the following: ...
1
vote
1answer
20 views

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 ...
0
votes
0answers
26 views

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 ...
2
votes
1answer
30 views

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). ...
0
votes
0answers
22 views

I need help finding an original reference for estimating random sampling error from an isolated sample

I have read many times, particularly in texts on meta-analysis and sampling theory, that it is impossible to estimate the sampling error of a parameter estimate (like an effect size) from an isolated ...
0
votes
0answers
9 views

Is there a term for an estimator's probability of estimating an impossible estimand value?

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 ...
0
votes
1answer
339 views

What's the advantage of a point estimate over an interval estimate?

A point estimate is : A single numerical value that is used to estimate the corresponding population parameter. Whereas an interval estimate is : An estimate that consists of two numerical values ...
2
votes
0answers
38 views

Consistent estimator of $p^2$

$(X_1, X_2,...,X_n)$ is a random sample of size $n$ from $Bernoulli(p)$ distribution. $S_n=\sum_{i=1}^nX_i$. I have to check whether $\frac{S_n(S_n-1)}{n(n-1)}$ is a consistent estimator for $p^2$. $...
1
vote
0answers
14 views

Is the population parameter more likely to occur closer to the sample statistic? [duplicate]

When we use the sample statistic to find a confidence interval, is there any reason to using the sample statistic after that, when we can instead refer to the confidence interval? For example, let's ...
1
vote
1answer
131 views

Most Efficient Estimator and Uniformly minimum variance unbiased estimator

I am studying Estimation theory from "Introduction to theory of statistics" by "Mood and Graybill". After completing I thought I understood UMVUE (uniformly minimum variance ...
0
votes
0answers
47 views

Taking Expectation Over Inverse Sum of Indicator Functions?

I'm working with a zero inflated Poisson distribution that has the following pmf: $$f(y|w,\lambda)=wI[y=0]+(1-w)\frac{e^{-\lambda}\lambda^{y}}{y!}$$ I would like to find the expectation of the ...
2
votes
1answer
13 views

Variance Estimator Change if we know Population Mean? (Normal dist. example)

For a normal distribution $N(\mu, \sigma^2)$ a commonly used unbiased and consistent estimator of variance is $$\hat \sigma^2=\frac{\sum_ix_i^2 + n(\bar x)^2}{n-1}=\frac{\sum_i(x_i-\bar x)^2}{n-1}$$ ...
0
votes
0answers
32 views

Why does the sample mean work as an estimator when we know data is not iid?

Let's say I know that height effects weight. To be more precise, let $H_i$ and $W_i$ be the heights and weights of person $i$ respectively. Let's say the true relationship between these variables is ...
0
votes
0answers
27 views

Can use Factorization criterion for proving given estimator is not Sufficient?

I was learning about the Sufficiency of Estimators and Factorization criteria. Now, I noticed that whenever we prove a given estimator is not sufficient, we use a counterexample with concrete values. ...
3
votes
1answer
31 views

Outlier detection in point estimates

I have to perform outlier detection on population estimates for certain variables at the city level. For example, I might be estimating median income for a city and I want to know if there are any ...
1
vote
0answers
30 views

How to estimate a proportion as a step function of time

There is a black-box mechanical process that, at any time, may be either succeeding or failing. It is known that after an initial disturbance, the process will fail $X\%$ of the time for $N$ seconds, ...
2
votes
0answers
21 views

Strong consistency in quantum estimation problem

I'm reading the paper: Strong consistency and asymptotic efficiency for adaptive quantum estimation problems by Akio Fujiwara. In this paper, describes the next adaptive scheme of estimation: "...
2
votes
1answer
283 views

It is possible to find point estimate of population mean and population variance when confidence interval of population mean is given?

Let's say that somehow $100(1-\alpha)\%$ confidence interval of population mean $\mu$ is known as $(a,b)$ and the number of samples is $n$. Is it possible to infer point estimates of population mean ...
4
votes
2answers
138 views

Bayesian Analysis: Point Estimates for a Beta Posterior

I think this is a fairly beginner bayesian analysis question. I have a Beta Posterior with $\alpha = .32$ and $\beta = 1.35$ (estimated using MCMC), that describes a probability. My question is: ...
1
vote
0answers
25 views

Surprising nonlinear variance-based scale est (bias adj) for Laplace Distribution competes with MLE?

Background: Using the quantile function (inverse cumulative distribution) for the Laplace distribution supplied with uniform random deviates (per the RAND() spreadsheet function), I examined an ...
1
vote
0answers
15 views

Better than expected bias corrected estimator for scale parameter of Logistic random deviates based on sample standard deviation?

Background: Using the quantile function (inverse cumulative distribution) for the Logistic distribution supplied with uniform random deviates (per the RAND() spreadsheet function), I was testing ...
0
votes
2answers
48 views

Parameter estimation for random variables where a control parameter is another r.v

Let $\{X_i\}$ a sequence of independent random variables. Each $X_i$ has a p.d.f $p(m, \theta)$. Where $\theta$ is a real unknown parameter and $m$ the outcome of another random variable $M$ with p.d....
1
vote
0answers
69 views

What is an intuitive of definition of “point identification” (point identified parameter) in econometrics?

I've recently come across the notion of point identification in several econometric papers. See, e.g., https://scholar.harvard.edu/files/tamer/files/pie.pdf, who mentions point identification ...
2
votes
0answers
24 views

Derive summary statistic Grouped Data & Frequency Distribution Table

I have the following data from the 2018 American Community Survey for a number of census block groups: ...
1
vote
0answers
72 views

Point estimate and 95% credible interval

The text of the problem as follows: The data follows a normal distribution with $\mu$ and $\sigma^2$ unknown. We wish to perform inference on the mean selling price $\mu$. And our sample data are (...
37
votes
3answers
9k views

What percentage of a population needs a test in order to estimate prevalence of a disease? Say, COVID-19

A group of us got to discussing what percentage of a population needs to be tested for COVID-19 in order to estimate the true prevalence of the disease. It got complicated, and we ended the night (...
0
votes
1answer
108 views

Calculating Confidence Interval for Estimated Parameters of SEIR model

I used a Log-Likelihood Estimation (Poisson) Objective Function to estimate and fit a curve to a data of reported infected cases of COVID-19 using SEIR model in order to estimate its coefficients. How ...
0
votes
1answer
206 views

How to find point estimator for $\lambda$ in Poisson distribution?

Suppose we have a random sample $(X_1,X_2,...,X_n)$ from a Poisson distribution $Poi(\lambda)$. How to find a point estimator of $\lambda$, and compute the mean and variance of the estimator. ...
3
votes
1answer
529 views

SIR model parameter estimation in R

searched on google about the sir model in r and I came up with the following code. ...
0
votes
1answer
43 views

Minimising Posterior expected loss

I am new to Bayesian statistics. I am not sure how I could find the best point estimator $T(x)$ for $\alpha$ that minimises the posterior expected loss, $$E_{\alpha|x} [L(\alpha, T(x)))] = \int L(\...
2
votes
1answer
41 views

How to interpret a sampling distribution from a Frequentist and Bayesian perspective

I've read multiple of the threads about Bayesian vs Frequentist interpretations of probability, but I'm having trouble trying to reconcile them with the idea of the sampling distribution when ...
0
votes
1answer
12 views

internal process of proc mianalyze procedure [closed]

Does proc mi analyze in sas consider only estimates of imputed values or complete data sets that is imputed values as well as non imputed values?
4
votes
1answer
89 views

The “correct” way to approximate $\text{var}(f(X))$ via Taylor expansion

tl;dr: There are two commonly reported formulas for approximating $\text{var}(f(X))$, but one is notably better than the other. Since it isn't the "standard" Taylor expansion, where does it come from, ...
0
votes
0answers
11 views

Alternative to Point Density

I have the coordinates of a bunch of car crashes and I reasoned that the place where they are the densest is where crashes are the most likely to occur. The solution I found when looking into this ...
2
votes
1answer
189 views

Intuition behind Method of Moments estimators of Binomial distribution

The method of moments estimators of the binomial distributions ($x \sim Binom(n, p)$) are a bit weird... I got $\hat p = \bar x + 1 - \frac{\sum x_i^2}{\sum x_i}$ and $\hat n = \frac{\bar x}{\hat p}$. ...
1
vote
1answer
61 views

How to best characterize uncertainty for an incidence rate? [duplicate]

Here is the scenario I am trying to model. I have a population of people who are susceptible to developing a disease. I observe each person for a different amount of time, summing to a total of 3000 ...
3
votes
1answer
110 views

Simple exercise in point estimation: what did I do wrong?

I wanted to do some exercises to improve my basic stats skills, but the following simple problem from Gelman's "applied regression" exam made me think quite a bit. A multiple-choice test item has ...
2
votes
0answers
84 views

Point estimation, interval estimation, density estimation?

Frequentist statistics textbooks typically consider point and interval estimation but not density estimation of a parameter. Since the density (of the sampling distribution) of the estimator is ...
0
votes
1answer
83 views

Bayesian estimator $\theta(x)$

Given a training set of $(X, Y )$'s where the $X$'s are the source variables and the $Y$'s are the targets, derive an estimator that minimizes the mean squared error between target values and ...
0
votes
0answers
32 views

Show that the MLE of $\theta$ is $\hat \theta = X_2$

Suppose that $X_1$ and $X_2$ are iid $exp(\theta)$ random variables. If we observe only $X_2$, Show that the MLE of $\theta$ is $\hat\theta = X_2$ I've tried to write the joint of $X_1$, $X_2$ and ...
7
votes
1answer
193 views

Question about Casella and Berger's proof of MLE invariance

In Casella and Berger, p. 320, they have a proof of the invariance of the MLE. Let $g: \theta \mapsto \eta$ be a function. They define the induced likelihood as $$ L^*(\eta \mid X) = \sup_{\{\theta: ...
2
votes
1answer
176 views

Fitting a gamma distribution to truncated data

I am faced with the following truncation problem: $$ X_i \sim \Gamma(\alpha, \beta) \\ \delta_i = \chi(X_i \le \tau_i) $$ I can observe only $(X_i, \tau_i)$ where $\delta_i = 1$ and I have no a-...
0
votes
0answers
619 views

MVUE for Poisson Distribution

Let $X_1,...X_n$ be $\text{Poi}(\lambda)$ distributed random variables. I want to construct a minimal variance unbiased estimator (MVUE) for $\lambda$. By the Neyman Lemma, I know that $T:=\sum_{i=1}...