Questions tagged [estimation]

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39 views

Determine probability of an event using maximum likelihood estimation

Problem I have a bag of many red and green balls. To find out the ratio between the two, I randomly picked balls with replacement. Out of the 100 outcomes, 60 were red balls and 40 were green balls. ...
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Involving data length as a decision variable in a optimization for parameter estimation

Consider I have $N$ historical data as outputs from a unknown time-varying system. Assuming within any small time interval $T$, the time-varying system can be approximated by a linear time invariant (...
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How do I choose between regression methods for inference?

Suppose my goal is to understand the relationship between variable $y$ and covariates $X$. Let's say $y$ is a rate, the number of success in $n$ trials, therefore bounded between $0$ and $1$. Now I ...
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2answers
87 views

Why do OLS and logistic regression coefficients have opposite sign?

I have data $y$ which is the rate of success in $n$ trials. I also have covariates $X$ that I want to regress against $y$ to understand the relationship between them. I tried 2 different approaches. ...
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1answer
38 views

Where plus 1 came from in variance estimation [duplicate]

While $$ \mathrm{E}(\tilde{\mathrm{y}})=\alpha+\beta \tilde{\mathrm{x}} $$ Subject is Regression Analysis and this formula is from the "Features of Estimation ". and y is a neutral variable. ...
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49 views

How are the number of actual rape cases estimated?

I see in news articles of number of rapes reported and an estimate for actual number of rape cases. I am interested in knowing about statistical techniques used for making such estimations. Also, are ...
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1answer
50 views

Practical method to do MLE for natural parameters in exponential family

I encountered the following question in my research and I hope this is the correct place to post it. I'm following the notation in this lecture note by Michael I. Jordan. Assume random vector $X$ ...
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10 views

estimating the total number of balls (n) after 2 draws of k balls

The problem is predicting the total number of balls (n) after 2 draws of k balls. After the first draw of k balls, we have marked them so we can see if we had them before. The balls are returns and we ...
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20 views

Is the mundlak estimator equal to the within estimator?

Mundlak has proposed to estimate the following correlated random effects model: $$ y_{i t}=\boldsymbol{x}_{i t}^{\prime} \boldsymbol{\beta}+\overline{\boldsymbol{x}}_{i}^{\prime} \gamma+\omega_{i}+u_{...
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Giving a job lecture on “minimax statistical estimation”. What kind of questions to expect?

As part of a job application process, I am giving a short "mock lecture" for students on minimax estimation in statistics. I will introduce the basic concept and give an example. I am able ...
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Estimating parameters of correlated random variables

Let's say there are two correlated random variables $X$ and $Y$ with coefficient of correlation as $r$. Assume during some hypothesis testing we found that due to some change in the environment mean $\...
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24 views

How to weight samples in a subsample of a stratified sample?

Suppose I'm first interested in computing the percentage of people in a certain town with brown eyes. However, due to some constraints I end up with the following stratified sampling set up: $$N = ...
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1answer
39 views

Is there a word or phrase to describe a model that is basically unidentifiable in practice?

So suppose we have a model $f(x|\theta)$ that is theoretically identifiable, so that $\theta_1 \neq \theta_2$ implies $f(x|\theta_1) \neq f(x|\theta_2)$. However, suppose that data collection is very ...
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Re-weighting after sampling?

After arriving at a sample size in order to achieve a population estimate with a 90% confidence interval, significantly fewer sample results were obtained. Is there any way to re-weight what was ...
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11 views

Real applications using estimation of parameters

In the first classes of statistical inference we learn about parameter estimation of some classical statistical distributions (Bernoulli, Binomial, Poisson, Geometric, Normal, etc). I would like to ...
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39 views

How to evaluate the likelihood of a conditional MAXENT estimation?

Suppose I have a random variable $Y$ (the outcome) and a set of random variables $\mathbf{X}$ (the input variables). I don't have access to observations of the joint distribution of $P(Y, \mathbf{X})$,...
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11 views

Discrete choice model estimation for unique items

I want to estimate the parameters of a discrete choice model for an item (let's say a piece of stone). In the end, I want to predict a stone's attractivity or utility. Let's say there are 4 variables ...
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30 views

Estimation of joint modeling of binary and continuous random variables via shared parameter

I am trying to fit a joint model of a binary and continuous outcome with repeated measures. I am trying to fit it using a shared parameter model that induces all the correlation between outcome and ...
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Prove that MLE for this distribution is a biased estimator

Let X1, . . . , Xn be a random sample from a normal distribution with mean µ and variance 1. It is known that µ ∈ (0, 1] ∪ [2, 3). Prove that the MLE of µ, if it exists, is a biased estimator of µ. Ok,...
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1answer
49 views

Bootstrap for probability of observing certain data

I am working with years data and I want to see how likely it is for something to have happened for the first time in, say, 1997 given other dates as well. Let me explain. I have something (a lab ...
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1answer
14 views

Estimate a sum using proportional sampling

I have some set of items. Each item has a weight and I can sample the items from the population with probabilities proportional to their weights. I know the size of the population. I want to estimate ...
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1answer
20 views

In simple linear regression, is the estimator of an individual response unbiased?

I am using linear regression. $Y_i = \beta_0 + \beta_1 x_i + \varepsilon_i$ $\varepsilon_i \overset{iid}{\sim} Normal(0, \sigma^2)$ At $X = x^\ast$, let's define the mean response as $\mu^\ast = \...
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1answer
112 views

How to show that $X_{(1)}-\frac1n$ is the unique minimax estimator of $\theta$?

Let $X_1,\ldots,X_n$ be i.i.d shifted exponential with pdf $f_{\theta}(x)=e^{-(x-\theta)}\mathbf1_{x> \theta}$, where $\theta\in \mathbb R$. I have to show that $X_{(1)}-\frac1n$ is the unique ...
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1answer
74 views

R: How does GLM deal with zeros in Poisson regresion?

How are zeros passed into Poisson regresion? I mean the log of 0 is -infinity, so it shouldn't be able to provide zero counts as the dependent variable. Does it use some kind of analytic technique to ...
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1answer
75 views

About computation of Brier score

Assume that we have some count data $x_{1}, \dots, x_{n}$, generated by probability mass function $\textbf{p} = \{p_{1}, \dots, p_{s} \}$. Let $\hat{\theta}$ be some estimator of $\textbf{p}$. In ...
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1answer
37 views

How to estimate the change of rate of COVID-19 infections when accounting for vaccine effectiveness and increased transmissibility of mutated strains?

The world has reasonably accurate numbers of the transmissibility of the strains of COVID-19 that have ravaged humankind. Now, two changes are afoot: Some wealthy regions have access to limited ...
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1answer
41 views

Estimating population parameter from bootstrapped sample distribution, other than mean value

I'm a rather novice to statistics, so my terminology here might not be totally correct. But I will do my best to explain my question clearly. My question is about understanding whether it is making ...
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9 views

Bayesian network: graph synthesis & data sampling

Input (What I have): some Bayesian networks (both graph structure and conditional probability distribution (cpd)) and corresponding categorical datasets (e.g. bnlearn repo). Output (What I want): ...
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7 views

Eliminate signal caused by panel changes

I have a timeseries that I am trying to eliminate signals caused by a changing panel size. Essentially I am trying to get the real predicted values from somewhat noisy reported values with the noise ...
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1answer
33 views

What is an explicit formula for the seventh moment? [duplicate]

I am trying to perform an analysis using the seventh moment but I can't seem to find an explicit formula for anything past the fourth moment. What is an explicit formula for the 7th moment similar to ...
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1answer
52 views

Is it acceptable to use Boostrap/Jackknife to estimate the variance of an MAP estimators?

Suppose we obtain a point estimate using a maximum a posteriori estimator $\hat{\theta}_{MAP}$. Note that I'm aware Bayesian approaches generally do seek point estimates, but suppose this is an ...
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1answer
44 views

ML estimator of $\theta>0$ is $\hat{\theta}_n=\frac{\sum_{i=1}^nX_i^2}{n}$ and $I(\theta)=\frac{1}{\theta^2}$. Show $\hat{\theta}_n$ is consistent

In this problem we have that $I(\theta)=\frac{1}{\theta^2}$ is the Fisher information for a general probability density function $f(x;\theta)$ and $X_1,..., X_n$ are IID random variables from this ...
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10 views

Using linear model to predict unknown time series values with partial data

I have the following data (the actual dataset is much bigger) ...
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1answer
28 views

how to estimate epidemic real infection data from partially observable new infections

I am not a Statistician and I would like to ask for help in understanding how to model the Italian Covid-19 infection data. In particular, in Italy, every day t the number of new detected infections I(...
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2answers
54 views

How to manually fit MA1 model with OLS?

We can manually fit AR1 model using linear model, as discussed here. But how to manually fit MA1 model? following code seems incorrect .., but how can we write the explanatory variable $w_t$ and $w_{t-...
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1answer
30 views

How to manually fit AR(1) model?

I am trying to fit an AR(1) model using linear model fitting (lm in R). Why am I not getting the correct coefficient? (Ground truth from sim is ...
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0answers
20 views

Using McNemar's test in a Nested Cross Validation

I have developed a nested cross-validation (11x10) routine to compare two alternative deep learning architectures. By running the algorithm, I saved the accuracy values obtained by the two models on ...
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10 views

Sample size for standard deviation estimation

There are lots of videos/sources talking about how to define a sample size in order to estimate the population's mean, given a standard deviation. But no one talks about the sample size needed to ...
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25 views

estimation of covariance of function of two i.i.d. data points

Given i.i.d. data: $X_1,\dots,X_n$ living in some space $\mathcal{X}$ and drawn according to distribution $P$, and symmetric functions $f,g: \mathcal{X} \times \mathcal{X} \to \mathbb{R}$, I want to ...
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24 views

Are the Generalized Least Square (GLS) and Maximum Likelihood (ML) two different ways of estimation?

I was taught, that OLS and ML are two different ways of estimation. ML gives OLS estimates under met assuptions, but it doesn't change the fact the two approaches differ. If so, how is that possible ...
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27 views

Monte-Carlo Estimation of conditional expectation term

I want to ask if my approach to estimation of the following quantity is correct: I have $n$ i.i.d. draws $\{(X_i,Z_i) \}_{i=1}^n$ and I want to estimate for a fixed $(i,j)$ pair the quantity: $$ \...
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5 views

How to calculate and compare ML models Recall estimators from stratified sample?

Let's say that I have 2 machine learning models for a disease (binary) classification task. I would like to estimate Recall for both models and compare it (show statistically that for example Recall ...
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1answer
16 views

Recovering factor level estimates from contrast estimates

Using R I have fit some data to a model of the form y~A*B where A is a factor with levels A1, A2, ..., A5 and similarly with B. I am using a different contrast than the default, so the results do not ...
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0answers
17 views

How to estimate the weight of the kilo?

Wikipedia has an article on the International Prototype of the Kilogram, which also includes a graph of the relative weight of its copies. Because there is (were) no independent unit to measure weight,...
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7 views

Choose strata size so that dispersion of an estimator is the least

The reseacher has 20000 dollars in their disposition to run a survey. It's known that from all households, 90% have stationary phones. Interview by phone costs 10 dollars per household. Each ...
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11 views

Estimate the support (~ confidence interval of the output) for a linear regression

Consider a linear regression model like this: I want to draw two margins, say upper- and lower-bounds, which contains 95% of the data. Formally, given a regression model ($\hat{y} = Ax+B$), I want to ...
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1answer
24 views

Standard error for total population ratio estimate bigger than the estimate of the population total itself

I have a sample of $n=100$ counties and I'd like to estimate a total number of veterans in a country (U.S.A.) of 3414 counties. To do that I use ratio estimate. The sample is drawn eith simple random ...
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22 views

Autocovariance-ergodicity of the autoregressive process of order 1

I wonder if the autoregressive process of order 1 is an autocovariance-ergodic process (https://en.wikipedia.org/wiki/Ergodic_process): hence, if the time average estimate of autocovariance converges ...
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6 views

explanation for a difference between GMM and SMM based on a closed-form equation

It is always said that GMM is used when closed-form estimating equation can be written, whereas in SMM case, there is no closed-form relationship. I am a bit confused about what this sentence really ...
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1answer
42 views

To estimate the total amount of veterans in U.S. with total population given as auxiliary variable, should I use regression or ratio estimation?

There is a sample of size 𝑛=100 of counties in U.S. where for each county a total population and amount of veterans are given. The sample is drawn using simple random sampling. What would be the best ...

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