# Questions tagged [estimation]

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### 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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### 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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### 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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### 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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### 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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### 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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### 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 ...
8 views

### 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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### 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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### 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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### 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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### 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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### 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 ...
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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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 ...