Questions tagged [estimators]

A rule for calculating an estimate of a given quantity based on observed data [Wikipedia].

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1answer
17 views

Method of moments estimator, $P_\theta(X = x) = \frac{1}{\theta}$

I am struggling with finding a method of moments estimator for (seemingly) simple situation: pdf is given by $P_\theta(X = x) = \frac{1}{\theta}$, $x \in$ {1,2,...$\theta$}, where $\theta \in N$. My ...
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1answer
56 views

Bias-Variance Trade Off with Cauchy Estimator

I'm having a look at the bias and standard error of a set of estimators. I expected to see the trade off when varying the parameter of the estimator, but I see that both the bias and the variance ...
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2answers
82 views

Is $\hat{\sigma^2}=\hat{\sigma}^2$?

In simple linear regression $$Y_i=b_0+b_1X_i+\varepsilon_i$$ where $$\varepsilon_i\sim N(0, \sigma^2)$$ is it true to say that the estimator for variance and the estimator for SD squared are equal? I ...
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26 views

More efficient estimator in this situation?

I am thinking about the following situation (it is an example): There are N families in a city and we have a simple random sample of size n. In that sample we know that there are $x_{0}$ families with ...
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48 views

Keeping track of the variance of a Metropolis-Hastings estimator

Let $(E,\mathcal E,\lambda)$ and $(E',\mathcal E',\lambda')$ be measure spaces, $p,q$ be probability densities on $(E,\mathcal E,\lambda)$, and $\varphi:E'\to E$ be bijective and $(\mathcal E',\...
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30 views

Error while fitting Pareto type 2 distribution

I am trying to fit a pareto type 2 distribution using the following code: ...
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1answer
49 views

How to fit Weibull distribution using “MME” method and find the estimates in R [closed]

I am trying to fit a Weibull distribution using Moments Matching Estimation (MME) method. Specifically I am trying to estimate the shape parameter $k$ and the scale $\lambda$. I am currently using R ...
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1answer
17 views

Is it possible to scale the mean and std of estimated rate/period, to another period?

Hello, all. When it comes to calculating the average from some time-spanning date, let's say the average of 20 weekly sales records from a specific store - while also calculating the standard ...
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68 views

What is the estimate of $\mathrm{Var}\left(\frac{nM}{X}\right)$ where $X$ is hypergeometric?

Consider the classical capture-recapture method, where we are to estimate the number of deer (say) in a sanctuary. So a certain number of deer is captured, tagged and released. Then a random sample is ...
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18 views

How do I interpret the posteriors in a skew-normal mixed model?

I ran in brms a model with "skew-normal" link function. I would like to know how to interpret the model output. All my independent variables are scaled. If it was a model with normal link function I ...
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0answers
23 views

How to compare SEM estimation methods in R? [closed]

I would like to use several estimators in SEM (e.g. ML vs Yuan-Bentler vs DWLS) and then by using Monte-Carlo approach compare: (a) average relative bias of the estimators, (b) average relative ...
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2answers
45 views

Consistency of estimators vs sample size

I understand that consistency of an estimator is large sample property, but does it make sense to talk about consistency in small samples as well? Can I say about the estimator that it is consistent ...
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76 views

Estimator, Bias and asymptotic distribution

I have a model; $$y_i = \beta_1 + \frac{1}{\beta_2}x_i+\epsilon_i$$ To simplify I use OLS to regress on; $$y_i = \delta_1 + \delta_2 x_1 + \epsilon_i$$ Thus I obtain the two estimators $\hat{\...
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1answer
25 views

Estimate mean of Poisson from binary data

If you assume that counts in sample units would be distributed according to a Poisson distribution, but the data that you have are observations of only presence (count would be 1 or more) or absence (...
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1answer
33 views

nonexistence of a sufficient statistic

Let $X_1,X_2,\dots,X_n$ be a random sample from a $\Gamma(\theta,\theta)$ distribution. Then $$ \prod_{i=1}^n f(x_i;\theta) = \frac{1}{\Gamma(\theta)^n\theta^n}(\prod_{i=1}^n x_i)^{\theta-1}e^{-\frac{...
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1answer
275 views

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....
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33 views

Derive the Bayes estimator of this loss function with indicator. bayesian inference statistic?

I need derive the Bayes estimator of this loss function with indicator. I have a sample of n distribution Bernoulli($\theta$) , and a priori distribution Beta(a,b). So, the a posteriori ...
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1answer
72 views

MLE as an expectation over the empirical distribution

I am reading Ian Goodfellow "Deep Learning" book. At page 128, it writes the maximum log-likelihood estimator and then says it is equivalent to the expectation over the empirical distribution To ...
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2answers
63 views

Why is $\frac1n\sum_{i=0}^{n-1}\sum_{j=0}^i1_{\{\:X_i\:=\:Y_j\:\}}f(Y_j)$ an equivalent representation for the usual Metropolis-Hastings estimator?

At the beginning of section 2 of the paper A Vanilla Rao-Blackwellization of Metropolis-Hastings Algorithms, the usual Metorpolis-Hastings estimator of $\int f$ given by the ergodic average $\frac1n\...
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15 views

Why do we use sample mean in ratio estimator of a population mean?

To estimate the population mean of a parameter, one of the estimators we can use is the ratio estimator: $$\hat{\mu_{y}} = \frac{\bar{y}}{\bar{x}} \mu_{x}$$, where we use the ratio estimate $$\frac{\...
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22 views

Expectation of Sample Variance

This is a question from the book Casella and Berger: where $ES$ actually means $\mathbb{E}(S)$ (expectation of S) So, I manage to use the Jensen Inequality to prove that $\mathbb{E}(S) \leq \sigma$,...
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2answers
52 views

Show that a linear combination of UMVU estimators is also a UMVU estimator

Suppose I have two estimators $\delta_1$ and $\delta_2$ with finite second moments, and they are UMVU estimators of $f_1(\theta)$ and $f_2(\theta)$, respectively. Now, for some real numbers $n_1$ and ...
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34 views

When does the MLE have a p-value equal to 1?

Suppose we have data $X_1,\ldots,X_n$ that is independently and identically distributed from a distribution $\mathbb{P}_\theta$, with unknown parameter $\theta \in \Theta$. Consider the hypothesis $...
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17 views

Expected value of the parameters in linear regression (trying to understand which part is constant and which isn't and why)

I'm studying Linear Regression and trying to proof/demonstrate some properties of the parameters. When I started working with the expected value of the slope, I got confused with something. I actually ...
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1answer
29 views

Why is having low variance important in offline policy evaluation of reinforcement learning?

Intuitively, I understand that having an unbiased estimate of a policy is important because being biased just means that our estimate is distant from the truth value. However, I don't understand ...
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27 views

Which is the better estimator for standard deviation?

Let $X_i \sim^{\textrm{iid}} N(\mu, \sigma^2)$. If I have measured $n$ values of $\textrm{std}(X_i)$ as $\sigma_1,\cdots,\sigma_n$, then what is the better estimator for $\sigma$: $$\hat{\sigma}_1 = ...
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5 views

How to estimate an activity based on self reported activity in a social network

I help run a social network for rock climbers who self report what they have climbed on a specific day, and optionally who they climbed it with. These climbers who self report are a perfect lower ...
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31 views

Comparison of GMM and ML estimators for regression with correlated errors

Consider a linear model with normally distributed, autocorrelated errors \begin{aligned} y&=X\beta+\varepsilon \\ \varepsilon&\sim N(0,\sigma^2_{\varepsilon}) \text{ and autocorrelated.} \end{...
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10 views

Are there differentiable estimators for Entropy?

I have recently came across a paper on estimation of Information theoretic measure such as Entropy, Mutual Information and divergence, using a Mean Nearest Neighbor approach. Since, the estimator is ...
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29 views

Questions on BLUE and MMSE estimators for a linear observation model

I have this observation model $$ \begin{cases} Y_i = X + V_i, \quad i=1,\dots, p \\ V_i \perp V_j, \quad \forall i,j \\ V_i \sim (0, \sigma_i^2) \end{cases} $$ where $X$ is a scalar random variable $...
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31 views

Difference between “Within” estimator for $Y_\textit{diff} = Y_{t_i} - Y_{t_{i - 1}}$ vs “First Difference” estimator for $Y_{t_i}$

I am using a diff-in-diff strategy and have a few question. I am not getting equivalent coefficient estimates for the two following regressions on panel data: a panel regression with a fixed ...
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0answers
36 views

Are a distribution's higher-order features harder to estimate?

In what sense, if any, are a distribution's higher-order features (e.g., moments, cumulants) harder to estimate than its lower-order features, for at least some distributional families? For example, ...
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1answer
38 views

“Ice skater” / “figure skating” / “ISU” method of discarding outliers

So I need a way of ruling out outliers and "the ice skater method" has been suggested. The person who suggested it has a good deal of experience of doing the task I am doing, so I am certainly ...
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51 views

How do I correctly estimate the size of a subpopulation using noisy observations?

To preface this question: please comment on whether my description of the problem is missing details or the problem itself is not well-posed as I'm seeing a lot of views but no activity. I am trying ...
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31 views

What are the differences between HC estimators and their small sample properties?

I am currently using R to run regression with the following code: ...
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3answers
53 views

“Magical” variance reduction problem

I recently came across this toy problem: You have two sticks of unknown lengths $a>b$ and a measuring device with constant variance $1$ that you can only use twice. How can you construct ...
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0answers
31 views

Parameter estimation by averaging over all high-likelihood possibilities?

I am refereeing a chemistry paper. The authors are trying to interpret some experimental data by comparison with numerical simulations. They have run many simulations using different combinations of ...
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1answer
63 views

Skewed outcome variable, sem model: is it a problem?

My outcome variable is really skewed, and I want to include it in a SEM model (I am using lavaan - R). It is measured with a 7-points Likert scale (agreement) and consists of 5 items. If the model ...
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0answers
62 views

Minimax estimators in Bayesian analysis

I got recently introduced to minimax methods in statistical decision theory. Is there an analogue in Bayesian analysis and some resources related to this?
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1answer
91 views

What may be an inefficient estimator of the population mean?

If the sample mean is an efficient estimator of the population mean, what may be an example of an inefficient such estimator?
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1answer
50 views

quantifying asymmetry on a sphere

I have a scalar quantity that is distributed on a sphere. I would like to quantify the asymmetry in this scalar field. is there any standard method to do this? Let's say that the function on the ...
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1answer
31 views

L1 distance between categorical distribution and any arbitrary estimator?

Given an unknown categorical distribution $p$ over $k$ categories, and any arbitrary estimator of this distribution vector $q$ constructed from $n$ i.i.d samples, can anyone point me to some results ...
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32 views

Is sample mean square is a consistent estimator of population variance?

If x ~Normal with population mean u and population variance (sigma)^2 Then is sample mean square which is asymptotically unbiased estimator for population variance then is it also consistent ...
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1answer
56 views

Proof for how the drift estimator, for a random walk with drift, is unbiased?

Random walk with drift formula is: (Yt = α + Yt-1 + εt ) How do I go about checking that the drift estimator α-hat is unbiased.. which is proving that E(α-hat) = α? Is this something I would need ...
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24 views

variance estimator for a symmetrical two-sides censored normal distribution

Suppose to draw a sample of $n$ observations from $X \sim \mathcal{N}(0,\sigma)$, with observations outside the interval $(-c,+c)$ censored; $c$ is known and one can conveniently set $c=1$, for ...
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0answers
16 views

Taking into account the variance of an estimated population size to construct confidence intervals for count statistics

I had originally posted this on the Math Stack Exchange website, but was justifiably recommended to explore this site instead. When given confidence intervals that are developed for proportions under ...
2
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1answer
28 views

Unbiased estimator when only the magnitude can be measured

given an random variable $x$, which is drawn from a normal distribution $f(x| \mu_x, \sigma_x) = \frac{1}{\sqrt{2 \pi \sigma_x^2}} \exp\left(-\frac{(x-\mu_x)^2}{2 \sigma_x^2}\right)$. We are drawing $...
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23 views

(contextual bandit problem) What does 'identical draw' mean here?

I am currently reading a paper (Learning from Logged Implicit Exploration Data) whose link is below. https://arxiv.org/pdf/1003.0120.pdf The paper supposes we have a set of possibly deterministic ...
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1answer
45 views

Policy evaluation in contextual bandit setting

I am currently reading a paper whose links is (Exploration Scavenging) http://delivery.acm.org/10.1145/1400000/1390223/p528-langford.pdf?ip=128.135.98.49&id=1390223&acc=ACTIVE%20SERVICE&...
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17 views

Bias of Pearson correlation estimator of two Bernoulli variables

Crossposting link: https://math.stackexchange.com/questions/3312349/bias-of-pearson-correlation-estimator-of-two-bernoulli-variables Suppose we have two correlated Bernoulli random variables, $X_j$ ...