Questions tagged [estimation]

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Estimating the parameters when only characteristic function is known

Recently I was working with a process named Variance Gamma with Stochastic Arrival (VGSA) and trying to fit this process on a given data. To obtain VGSA, as explained in Carr et al. [2001], we take ...
Starlord22's user avatar
6 votes
3 answers
507 views

Unable to understand what confidence interval means

I seek to understand what confidence interval is with the aid of following example (which I know how to solve but do not understand the rationale behind it); Suppose it is known that the weight of ...
Quorthon's user avatar
3 votes
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Cramer-Rao / Wolfowitz bound with nuisance parameter

Let $F$ be a distribution with two parameters, $\theta$ and $\phi$, whose values are non-random but unknown. Consider a sampling procedure in which $N$ samples $x_1, \ldots x_N$ are obtained from i.i....
Luis Mendo's user avatar
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How to manually evaluate a parameter estimate using the first few values of a time series?

I'm working on a problem (I paraphrase), Consider the $\text{AR}(2)$ model $$y_t=\alpha y_{t-1}-(1-\alpha)y_{t-2}+\epsilon_t, \hspace{1em} \epsilon_t\sim N(0,\sigma^2).$$ The conditional least ...
mjc's user avatar
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How to combine soft-max value from two or more neural networks

Consider a scenario where we have some input variable $X$ (maybe an image), which goes through several noisy path and we generate $K$ noisy observations: \begin{align} Y_i = X_i +Z_i, i \in \{1,\ldots,...
Boby's user avatar
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1 answer
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When using Weighted Estimating Equations (WEE) to estimate a linear regression model with missing data, what can do if missing probability is 1

When using Weighted Estimating Equations (WEE) to estimate a linear regression model with missing data. One way is to assume the missing at random and then compute the missing probability using some ...
Fangzhi Luo's user avatar
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Maximum Likelihood Estimate not in Parameter Space

The observed value of mean of random variable from N($\theta$, 1) distribution is 2.3. If the parameter space is {0,1,2,3} then the maximum likelihood estimate of $\theta$ is? a) 1 b) 2 c) 2.3 d) 3 I ...
Rhea Agarwal's user avatar
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Estimating variance of Poisson Binomial random variable

Let's say I have a weighted coin, with probability $p_i$ of being heads. I flip $N_i$ times, and estimate $P_i$ and the variance on $p_i$ using the relevant formulas for a Binomial distribution. Call ...
KHAAAAAAAAN's user avatar
2 votes
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121 views

Efficiency of chi-squared denoising

Suppose my measurement $\theta+\epsilon$ is corrupted by IID additive noise $\epsilon$ distributed as chi-squared with (known) $d$ degrees of freedom, what is the efficiency of pooling multiple ...
Yaroslav Bulatov's user avatar
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Number of data to perform parameter estimation

I found a rather old post (How large should a sample be for a given estimation technique and parameters?) about a rough estimate of the number of data needed when performing parameter estimation via ...
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Literature on GP with kernels having no closed form

I have to use GP regression on a complex time series, and the kernel function is not known in closed form. I have found a numerical approximation with the Gauss-Laugerre quadrature. It takes the ...
CfourPiO's user avatar
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3 answers
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When should one control for covariates?

Suppose that one wants to estimate the effect of X on Y in the following causal diagram Should one take Z as a covariate (and why/why not?) For example, suppose that one wants to estimate the effect ...
Sam's user avatar
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Does the confidence interval for Poisson rate contain the sample mean?

Let $X_1, X_2, \dots, X_N$ be iid random variables from $Poisson(\lambda)$. The confidence interval for $\lambda$ with confidence level $1-\alpha$ is $$ \frac{1}{2N} \chi^2 \left(\alpha/2; 2 \sum_{i=...
mathslover's user avatar
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1 answer
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Verifying mean and covariance estimators of a two-dimensional normal distribution

Here I try to verify estimators of the mean and covariance matrix of the two-dimensional normal distribution $N(\mu, A)$ with $\mu=[-2,3]^T$ and $A=\begin{pmatrix} 5 & 11\\ 11 & 25 \end{...
H.Y Duan's user avatar
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Check data consistency with prior in Bayesian setting

Let's say we are given an informative prior on $\theta$, preferably estimated from previous data. Given some new observations, suppose the $\hat{\theta}_{MLE}$ is very deviating from what the prior ...
Kaiwen Wang's user avatar
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Exponentially Weighted Covariance Matrix with Ledoit Wolf Shrinkage

The Ledoit Wolf paper "Honey, I Shrunk the Sample Covariance Matrix" presents the formulation for the shrinkage intensity parameter estimate in Appendix B. The formula for a weighted ...
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Is there a method to estimate the distribution of error term in linear model?

Consider the linear model where $A$ is not known $$ y = Ax + \epsilon $$ where we want to estimate the distribution $\epsilon$ from a set of samples. To prevent over-fitting, we want to impose some ...
Ma Joad's user avatar
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Determine if Poisson process rate changes

Imagine a person, P, calls into a call center multiple times an hour. With 50% probability, P will call with some low rate (like an average of ~3 calls an hour) the whole time. With 50% probability, P ...
KHAAAAAAAAN's user avatar
2 votes
0 answers
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What is a 2-stage estimator?

I thought I would quickly find the answer to this, and maybe my capabilities of using the sites search function are very poor, but I didn't find an answer to the definition of what a 2-stage estimator ...
Lynchian's user avatar
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Iteratively Training an ARIMA model

The Context Let's say for argument's sake that I have a time series dataset, $X_t$, that is stationary, exhibits strong autocorrelation and is a good candidate for an ARIMA-type model. I have a series ...
Andy Smith's user avatar
2 votes
1 answer
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What are the mechanisms for the propagation of effects across stages in a structural model?

I have an SEM question to which I have not found an answer anywhere. I have used SEM a bit already but my difficulties with this question suggest I lack some basic understanding. Question: In a ...
Patrick A's user avatar
2 votes
2 answers
209 views

Can I estimate the mean of a dataset if I have its standard deviation and a portion of the full data that is higher than some threshold?

I have a partial set of measurement data that is limited due to my tool's sensitivity. I know that the data is approximately normally distributed and I have a standard deviation from another data set ...
Shuesh's user avatar
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Is this a typo on P.75, Theorem 5.52 of the book "Asymptotic Statistics" by Van der Vaart?

Let $\Theta$ be a compact metric space, $\theta \in \Theta.$ Let $m_{\theta}:\mathbb{R}^d\to \mathbb{R}: x\mapsto m_{\theta}(x)$ be a family of measurable function indexed by $\theta \in \Theta.$ Let $...
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How does the training set size affect the uncertainty (variance) of performance estimation?

I am reading this paper which discusses the factors that affect the uncertainty (variance) in the performance estimation of a learner. The authors say (p. 2, "The monotonicity of the learning ...
ado sar's user avatar
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1 answer
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Estimating the Joint and Conditional probability distributions for discrete variables

I read the proof the of the law of large numbers where its states that the the sample mean converges in probability to the population mean and it its proven by Chebyshev's Inequality Here I am curious ...
Moh's user avatar
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1 answer
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Unable to estimate AR(p) coefficients and $\sigma^2$

I am currently trying to solve this problem pertaining to the Yule-Walker equations: Let $\{X_t\}_{t\in Z}$ be a causal autoregressive process given by $$X_t = \varphi X_{t−2} +W_t$$ with $\{W_t\}_{t\...
Patrick O'Rourke's user avatar
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0 answers
13 views

Efficiency terms in Stochastic Frontier Analysis can be greater than 1?

Let us consider a Cobb-Douglas production function with $Y$ being the output and $X$ being the input (assume for simplicity only one input) and a composite error term: $$ Y = e^{\beta_0}X^{\beta_1}e^{...
Barbab's user avatar
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0 answers
80 views

Estimating expected value with respect to posterior

I have a neural network and I need to calculate the following: $$\mathbb{E}_{P(\theta|D)}[f(\theta)]=\frac{\sum_\theta P(D|\theta)P(\theta)f(\theta)}{\sum_\theta P(D|\theta)P(\theta)}$$ Where $f$, ...
Feri's user avatar
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Standard deviation of standard deviation under non-normality

In this post, an unbiased estimator for the standard deviation of the standard deviation under normality is provided. I would be interested in such an estimator without the normality assumption, i.e., ...
Hiro's user avatar
  • 303
2 votes
1 answer
42 views

What standard references discuss the differences between hypothesis testing, estimation and prediction? [closed]

I am trying to understand the ramifications of this three-way distinction, particularly when it comes to model building. Could someone point me at the standard references on the subject?
1 vote
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Covariance calculation in a DiD estimation

I am estimating a difference-in-difference model estimating the effect of a parental leave reform on female wages. It is not possible to take the logarithm of the varaibles as a lot of wages are 0. I ...
Rstrobaek's user avatar
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0 answers
42 views

How do random effects affect fixed effects (or just other coefficients) within a model

I have found that random effects terms can affect other coefficients within a model from here. I see how in this example the coefficients change with the addition of a random effect; I'm still not ...
Geoff's user avatar
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2 votes
2 answers
258 views

Cramer-Rao bound for biased estimators

So the Cramer-Rao bound gives us a lower bound on the variance of an estimator, now if the estimator is unbiased then we have a bound on the mean square error. While I can see the utility of the bound ...
delta_99's user avatar
1 vote
0 answers
54 views

Marginal means (or "adjusted predictions") with categorical predictors

Goal My analysis goal is to estimate the expected value of the outcome variable under three different conditions defined by a set of 3 categorical explanatory variables with two levels each. However, ...
user3084100's user avatar
1 vote
0 answers
40 views

Standard errors for fixed effects having only the model estimates

I am trying to joint model longitudinal data with informative observation times. Taking the simpler case, where the outcome and time processes are associated through a random intercept, I already ...
adrimsvieira's user avatar
2 votes
2 answers
85 views

Distribution of the minimum of a pair of random observations

A test results interpretation question, which I think boils down to this: what is the distribution of the minima of pairs of values sampled at random from a known distribution (say, Gaussian) and can ...
Maciej Tomczak's user avatar
1 vote
1 answer
46 views

ARIMA parameter estimation from scratch

I am implementing ARIMA from scratch, and I am trying to understand how to estimate the parameters by the MLE + innovations algorithm approach. The likelihood is given by (as in Shumway and Stoffer: ...
Student's user avatar
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2 votes
0 answers
79 views

What method should I use if I want to estimate proportions in a 2xc contingency table (where c >2)?

This is a theoretical question, but it's been in the back of my head for a while now. Let's say I have two groups A and B, and I already know that they differ relative to their distribution on a ...
Daniela's user avatar
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1 vote
1 answer
62 views

How to estimate how heavy a tail is?

Suppose I have data coming from a single variate distribution. I want to estimate how heavy the tail of the distribution is. For example, if the data comes from the Zipf distribution, I would want the ...
user2316602's user avatar
11 votes
4 answers
219 views

How best to estimate regression parameters subject to constraints?

The setting Consider a least squares model for $y$ as a function of $x,$ possibly nonlinear in the parameters. Abstractly this can be expressed as $$y = f(x;\theta) + \varepsilon$$ with the usual ...
whuber's user avatar
  • 321k
7 votes
4 answers
265 views

Unbiased estimation of $\mathbb{P}(X < Y)$

Suppose that I observe i.i.d. draws of two independent variables, $X$ and $Y$. My goal is to estimate $\mathbb{P}(X < Y)$, preferably in a consistent and unbiased way. How exactly should I do this? ...
afreelunch's user avatar
1 vote
0 answers
29 views

Strong consistency of kernel density estimator

I am studying the book Nonparametric and Semiparametric Models written by Wolfgang Hardle and have difficulty with the following exercise: $\textbf{Exercise 3.13}$ Show that $\hat{f_h}^{(n)}(x) \...
graham's user avatar
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0 answers
95 views

UMVUE for a Uniform distribution [duplicate]

How did we derive the PDF and CDF highlighted in green? Thanks
learn_to_code1's user avatar
1 vote
0 answers
56 views

Estimating a secret with before/after interchanging noises

$\newcommand{\Var}{\mathrm{Var}}\newcommand{\E}{\mathrm{E}}$ For $n+1$ iid "noise" variables $X_0,\dots,X_n$ from the normal distribution $\mathcal{N}(0,1)$ and a "secret" $s$ ...
Nathan's user avatar
  • 11
0 votes
0 answers
27 views

KDE-like technique to learn a continuous distribution from samples subject to specific noise

There's a continuous-valued random variable $X$ with distribution $f_X$. Normally, we're given a bunch of i.i.d. samples $X_1, \ldots, X_n$, and we try to give an estimate $\hat{f}_X$ of the ...
chausies's user avatar
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0 answers
45 views

Why is the statement "the bayes estimator is bayes optimal" profound?

I'm trying to understand why people make a big deal about the optimality of a Bayes estimator. Certainly, if I have a Bayes estimator, then my expected loss is minimized, almost by definition. So, $$ \...
Y. S.'s user avatar
  • 1,277
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0 answers
17 views

Scoring races + ranking index, with Bayesian approach

Challenge: Is this the best approach for scoring multicompetitor races? How do I account for both uncertain prior & uncertain evidence when scoring? Case: athletes getting scores in each race, ...
Daniel Westergren's user avatar
0 votes
1 answer
58 views

Extrapolating a Discrete Distribution to a Continuous one

Say I have a list of the letter grades of a class (meaning some number of As, Bs, Cs, Ds and Fs). Is there any way for me to take this discrete distribution and extrapolate it to the most likely ...
Ghull's user avatar
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0 votes
1 answer
59 views

Estimating the mean of a Poisson process from data

My data shows the daily number of logins per person over the last three months. I am modelling the number of events per person per day as a Poisson process. I am interested in estimating the ...
Arturo Sbr's user avatar
0 votes
0 answers
22 views

How to estimate the effect of time series on a variable sampled irregularly and much less frequently for multiple subjects

I’ve been struggling for several days to find the proper statistical analysis tools for my problem, and I’m hoping for some valuable tips and insight from the internet. I’ve read up on ARIMA(X), ...
timeSerious's user avatar

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