Questions tagged [point-estimation]

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

Point estimation is the application of an estimator (a statistic) to the data in order to learn about a certain population parameter. This parameter may be a fixed number as seen by classical or frequentist statistics or it may be a random variable itself as in Bayesian statistics. Common methods of point estimation are ordinary least squares, maximum likelihood, the method of moments or Bayes' estimators.

For further information see:
Lehman, E.L. and Casella, G. (1998) "Theory of Point Estimation", 2nd edition, Springer Verlag Inc., New York

233 questions
42
votes
5 answers

How to derive the likelihood function for binomial distribution for parameter estimation?

According to Miller and Freund's Probability and Statistics for Engineers, 8ed (pp.217-218), the likelihood function to be maximised for binomial distribution (Bernoulli trials) is given as $L(p) = \prod_{i=1}^np^{x_i}(1-p)^{1-x_i}$ How to arrive at…
Ébe Isaac
  • 1,132
38
votes
3 answers

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 (over zoom) arguing about signal detection and…
Industrademic
  • 501
37
votes
3 answers

Is p-value a point estimate?

Since one can calculate confidence intervals for p-values and since the opposite of interval estimation is point estimation: Is p-value a point estimate?
00schneider
  • 1,390
25
votes
2 answers

Shrunken $r$ vs unbiased $r$: estimators of $\rho$

There has been some confusion in my head about two types of estimators of the population value of Pearson correlation coefficient. A. Fisher (1915) showed that for bivariate normal population empirical $r$ is a negatively biased estimator of $\rho$,…
ttnphns
  • 61,413
24
votes
2 answers

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 $f(\hat{\theta})$ . Casella & Berger "Statistical Inference" Also, $f$ must be a one-to-one function. The book says,…
user13985
  • 1,034
19
votes
5 answers

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 points? If so, how?
user16679
19
votes
4 answers

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 must have seen this stuff dozens of times, spread out…
kjo
  • 2,027
  • 1
  • 19
  • 26
19
votes
2 answers

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 immediately corrected by cardinal and Henry with…
Michael R. Chernick
  • 44,121
14
votes
4 answers

Unbiased estimator for the smaller of two random variables

Suppose $X \sim \mathcal{N}(\mu_x, \sigma^2_x)$ and $Y \sim \mathcal{N}(\mu_y, \sigma^2_y)$ I am interested in $z = \min(\mu_x, \mu_y)$ . Is there an unbiased estimator for $z$ ? The simple estimator of $\min(\bar{x}, \bar{y})$ where $\bar{x}$ and…
pazam
  • 141
13
votes
2 answers

Why is the geometric median called the $L_1$ estimator?

My question is simply, why is the geometric median called the $L_1$ estimator? This always reminds of $L_p$ spaces but the distance being minimized in the geometric median's definition isn't $L_1$ but rather the $L_2$ (Euclidean) norm. What does the…
Fixed Point
  • 639
  • 1
  • 7
  • 15
12
votes
1 answer

Posterior variance vs variance of the posterior mean

This question is about the frequentist properties of Bayesian methods. Suppose we have data ${\bf y}$ generated from a distribution with a single parameter $\theta$ , equipped with a prior $\pi(\theta)$ . This leads to a posterior distribution…
knrumsey
  • 9,712
12
votes
1 answer

Sufficiency or Insufficiency

Consider a random sample $\{X_1,X_2,X_3\}$ where $X_i$ are i.i.d. $Bernoulli(p)$ random variables where $p\in(0,1)$. Check if $T(X)=X_1+2X_2+X_3$ is a sufficient statistic for $p$. Firstly, how can we find the distribution for $(X_1+2X_2+X_3)$? Or…
Landon Carter
  • 1,845
11
votes
1 answer

When can't Cramer-Rao lower bound be reached?

The Cramer-Rao lower bound (CRLB) gives the minimum variance of an unbiased estimator. One sentence in the wiki page says "However, in some cases, no unbiased technique exists which achieves the bound. This may occur either if for any unbiased…
Tony B
  • 231
11
votes
2 answers

Proof that posterior median is the Bayes estimate of absolute loss?

It is always argued that the posterior median is the Bayes estimate associated to the absolute loss function. The proofs I have come across rely on differentiating the conditional Bayesian risk and equating this to zero. However, this shows that…
Valley
  • 113
11
votes
2 answers

Rao-Blackwellization of Gibbs Sampler

I am currently estimating a stochastic volatility model with Markov Chain Monte Carlo methods. Thereby, I am implementing Gibbs and Metropolis sampling methods. Assuming I take the mean of the posterior distribution rather than a random sample from…
mscnvrsy
  • 555
1
2 3
…
15 16