Questions tagged [estimation]

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Linear relations between statistics in exponential family of distributions

I am reading about point estimation from Theory of Point Estimation by Lehmann and Casella (1999). I couldn't understand the following point mentioned in p.24, under the exponential family of ...
286 views

Trying to find estimators for 3 parameters in a simple equation

I came across the following equation (source):￼ $$y=ax^be^{-cx}$$ where a, b and c are parameters, and x, y are variables. I was curious to estimate the parameters a, b, c for a dataset of x,y pairs,...
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Small sample size fails to approach inverse CDF

When sample size $n$ gets large, we know that a sorted set of the $n$ samples approaches the inverse cumulative distribution function (CDF) sampled at $\frac{1}{n}, \frac{2}{n}, \dots, \frac{n}{n}$. ...
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Optimal sampling rate for forward algorithm

I have a system with a binary-state. The system state is estimated by an HMM forward-algorithm. Also, the system allows a varying sampling rate. Considering that the system state transition takes a ...
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Burg's method for estimation of AR-models

I am trying to get an intuitive understanding of Burg's method for estimation the coefficients of an AR-model. Say we have an AR(1)-process with \begin{equation*} X_t = a X_{t-1} + \varepsilon_t \...
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Can a Bayesian estimator perform better than an MVUE?

According to wikipedia: In statistics a minimum-variance unbiased estimator (MVUE) or uniformly minimum-variance unbiased estimator (UMVUE) is an unbiased estimator that has lower variance than any ...
582 views

Why is $R_t$ (or $R_0$) and not doubling rate or time the go-to metric for measuring Covid-19 expansion?

In my head, the natural way to measure the expansion speed of an epidemic across populations of different sizes is simply fitting an exponential over recent infection numbers (with any strategy), ...
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Control for common factors

Hi I have a question about how to control for common factors. I used people of a state as the sample to investigate a causal relation between two variables, y and x. Although there are a lot of ...
2k views

Revisiting the Rule of Three

The rule of three is a method for calculating a 95% confidence interval when estimating $p$ from a set of $n$ IID Bernoulli trials with no successes. My understanding from its derivation is that the ...
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Making sense of MLE

Since we were taught MLE (Maximum Likelihood Estimation), a number of questions often bothered me. Why does Maximum Likelihood Estimation work ? Why does it always produce almost accurate results ...
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How to find the time complexity of an MLE based algorithm

How to calculate or what is the time complexity (big-Oh) for this method? Based on my understanding, MLE depends on number of datapoints, $N$ so time complexity for MLE is O(N). However, there are ...
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OLS estimators are independent of the scale of the predictor data

The title says it all: How can I see that OLS estimators (linear regression) do not depend on the scale of the predictor data? I am reading my lecture notes about lasso estimators, where it is ...
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How to combine confidence intervals of a regression when calculating a mean of estimated value

I am facing the following problem: I have a regression similar to the following: fit <- lm(I(hp > 100) ~ cyl + wt + disp + am,data = mtcars) The idea is more ...
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Cramer-Rao bound in case of non-invertible Fisher Information matrix

I am learning about the Cramer-Rao lower bound (CRLB) and Fisher Information matrix (FIM), and started trying to apply it to some simple toy models from physics. However, even for a simple example I ...
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A problem about confidence interval

How can I solve this? Two new drugs were given to patients with hypertension. The first drug lowered the blood pressure of $16$ patients an average of $11$ points, with a standard deviation of $6$ ...
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Bootstrapping the time until an event happens

Assume I have some measurements $\{(y_i, t_i)\}^n_{i=1}$, where $y_i$ is a real number (measured quantity) from some unknown random function $y_i = f(x_i)$, $x_i$ are inputs to that function and $t_i$ ...
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Test whether the theoretical model estimated from the sample predicts the same mean

I have a sample of experimentally observed data and a parametric distribution model which is expected to explain the data. I estimated the model parameters by the maximum likelihood. Now I need to ...
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How to estimate mean and variance for rate of change when I only have state data at different ages

I'll give you the intuition behind my problem first. I have data on whether children ($n \approx 200$) can read and their age in integers from 0 to 14. For each age, it is straightforward to ...
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Randomly Sample M samples from N numbers with replacement, how to estimate N?

Can you estimate $N$ with MLE or method of moment or whatever strategy? $N$ numbered balls are in a bag. $N$ is unknown. Pick a ball uniformly at random, record its number, replace it, shuffle. After ...
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How to obtain standard error of parameters in maximum likelihood when reparametrized/transformed?

Sometimes parameters in the maximum likelihood estimation process are reparametrized for numerical convenience. As an example if I'm fitting maximum likelihood estimation (MLE) to a data that is ...
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Risk of loss function Bernoulli random variable

Can anyone help me with the part b of the question? I understand the risk is expected value of the loss function, but how to incorporate expected value in the piece-wise function. I will be grateful. ...
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standard techniques for picking a rolling window to estimate the mean

I have a time-series of noisy estimates of an observable. To get a better estimate (let's ignore stationarity issues), I can take an average of the past N values. But it seems, that instead of ...
38 views

Complete and Sufficient Statistic for Discrete Distribution

I have a single observation X from the following distribution: $$𝑃(𝑋=−1)=\dfrac{𝑝}{3},𝑃(𝑋=0)=(1−𝑝),𝑃(𝑋=1)=\dfrac{2𝑝}{3}$$ I'm trying to find a complete and sufficient statistic for p based on ...
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Recursive estimation

I'm trying to assess the stability of the parameters of an MA(2) model on unemployment data using recursive estimation. However, I'm in doubt how to interpret the outcome of the code I'm using: ...
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Why might the functional form of a distribution be “inappropriate” for a particular application?

Working through Bishop's Pattern Recognition and Machine Learning(a great read so far!) and on page 67 he says: "One limitation of the parametric approach is that it assumes a specific ...
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How to model errors around the estimation of proportions - with measurement error?

I have a situation I'm trying to model. I would appreciate any ideas on how to model this, or if there are known names for such a situation. Background: Let's assume we have a large number of movies (...
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MLE for the number of samples given $k$ largest values

I have the views on the top 100 videos using a tag in TikTok and want to estimate the total number of videos in that tag. I know the distribution for other tags so I can make a guess as to what it is ...
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How to estimate SEIR model parameter in R via RSS?

I tried to estimate the SEIR MODEL parameter in R by using the following code .Unfortunately I couldn't get it because I get the following error : "Error in names(parameters) <- c("...
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Calculating the trimmed mean as an estimator

My book provides the following steps to calculate the $100 \alpha$ percent trimmed mean for a sample data of $n$ measurments: 1-Order the measurments. 2-Discard the smallest $100\alpha$ percent and ...
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Why can't we have a $100 \%$ confidence level?

As the title implies, why can't $1 - \alpha = 1$ , so that we have a $100 \%$ confidence level? I saw these two answers, but want a more mathematical proof: How to estimate 100% confidence interval ...
777 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 ...
What does the term "Uniformly" mean in UMP(Uniformly Most Powerful) test and in UMVUE(Uniformly Minimum Variance Unbiased Estimator)? So far I have learnt, it means for all $\theta$(...