Tagged Questions

Any statistical process which seeks to approximate an unknown value, such as a distribution, a point estimate (e.g. mean), or confidence interval.

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Are empirical risk minimization and M-estimators the same thing?

Would it be true to say that Empirical Risk Minimization and M-Estimation are the same thing?
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How to estimate a pdf of x under the model of y = x+n, when the pdf of y and the pdf of n are given

I guess I come up with a classic question, but I failed to find any useful solutions by far. My question is about the following model $$y=x+n$$ where $x$ is a hidden random variable that cannot be ...
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How to get exact distribution of estimated p for binomial distribution?

This question is kind of a follow up of another question I had: Asymptotic normal distribution via the central limit theorem There I had to calculate the estimator for $p$ (meaning $p$ for success) ...
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Given tolerance intervals for multivariate hypergeometric, estimate a mean

Suppose we have a multivariate hypergeometric distribution on balls in $k$ colors. Let $n_i$ be the number of balls for the $i$-th color, so that we are drawing from $N = \sum_i n_i$ balls. Each ...
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How to calculate Pareto parameters

I'm trying to calculate the parameters for a Pareto distributed variable in R. I use the following model: form = rank~bet*(downloads)^(-alp)+eps, which is widely ...
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How to compute the maximum a posteriori probability (MAP) estimate with / without a prior

I am a newbie in this area so I hope someone could explain the following problem to me in plain English. Assume I want to use MAP to estimate some parameters on the basis of some observations. I know ...
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Bayesian MMSE estimators from a transformation of the observations

Consider a random variable X whose value we want to estimate using a Bayesian MMSE estimator. Let $O_1(X)$ be a set of observations which depend on $X$ in some complex way (captured by $P(O_1|X)$) ...
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when is an estimator consistent?

Say there are parameters $\theta$ such that $\theta_i > 0$ and $\sum_i \theta_i = 1$ and a model such as $p(x) = \sum_{i=1}^n \theta_i p_i(x)$ where $p_i(x)$ are fixed and defined over a domain of ...
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What's the value of information when we decrease the entropy of a probability distribution?

Suppose you have to choose between actions $A_1,\dots,A_n$. You have a probability distribution over each $U(A_i)$, i.e. over the utility of choosing each action. So you should choose the $A_i$ that ...
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What is the proper way to estimate the probability (proportion of time) a rare event occurs?

Often, I need to estimate the probability (proportion of time) a rare event occurs. The standard MLE estimate often gives me extreme estimates since the denominator is usually 1, and the numerator is ...
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How to aggregate human estimates?

I'm working on a program that involves people estimating numbers. For instance, when estimating $X$, one person says that $X$ is the product of two numbers over which he has probability distributions ...
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Generating random variable from density function

How can I generate a random variable of size n= 2914 if I have the density function?. So the problem is that I have the density f(x) (function well defined) ...
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Single sample versus multiple sample

I have a jar with white and black balls. Total number of balls in the jar is 100000. I want to estimate the proportion of white balls. My constraint is that the sample size for estimation should be ...
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Estimate the parameters of beta exponential distribution via L-Moments

Estimate 3 parameters of beta exponential distribution in the case of censored type 1 samples via L-moments
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Expected maximum given population size, mean, and variance

How would one estimate the maximum given population size, a few moments, and perhaps some additional assumption on the distribution? Something like "I'm going to do $N_s≫1$ measurements out of ...
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How to estimate the confidence interval using sample average and sample size ONLY? [duplicate]

Suppose there is a population, with goods and bads. The bad rate of the population(=bads/(bads+goods)) is of course unknown. Now, I have a sample of $N$ from the population and I know the bad rate ...
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On how to formulate and apply maximum likelihood

I have just delved into the basics of maximum likelihood estimation and expectation maximization. The latter is really difficult to follow and I am having a tough time in figuring how I can apply the ...
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Estimating the slope of the straight portion of a sigmoid curve

I have been given this task and was stumped. A colleague asked me to estimate the $x_{upper}$ and $x_{lower}$ of the following chart: The curve is actually a cumulative distribution, and x is some ...
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Maximum likelihood estimate: Is this possible to solve?

I have the following problem: Formulate the likelihood function, the log-likelihood function, and the maximum-likelihood estimate as well as the Fisher information and the observed Fisher information ...
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Relation between best fit line and eigenvector of maximum eigen value of an estimated covariance matrix

(This question is from my pattern recognition course.) There is this exercise: Imagine we have $N$ samples with $n$ dimensions. First it asks to find a point $m$ where the summation of Euclidean ...
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Dimension independent regression/interpolation methods?

Hopefully this question is not too simple or too general. I am working on a problem right now in which I am given different sets of data. Each data set consists of some number of samples (sampled at ...
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componentwise boosting based on fisher scoring

componentwise boosting dates back at least to Bühlman and Yu (2003), where in each boosting iteration a set of base-learners (e.g. simple linear models) depending on a subset of the covariates are ...
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Fitting data in a generalized Pareto distribution and parameter estimation

I have log(return) data as time series, how I can fit this data in a Generalized Pareto distribution and estimate the parameters of this distribution, any kind of resource pointer with clear code ...
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Bernoulli random variable parameter estimation

Suppose $\theta$ is the probability that a Bernoulli random variable is one (therefore $1-\theta$ is the probability that it's zero). I have a sequence of $n$ of these i.i.d. Bernoulli random ...