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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31 views

Best linear unbiased estimator

I have a sample of N stocks. I have the following information: For each stock i, I have an estimate of variance (of returns) $\hat{\sigma}^2_{i}$. I also have a fitted variance, denoted by ...
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0answers
10 views

combine normal and binomial probability distributions [on hold]

Asume we combine 2 sets of data properly. one set has normal destribution and another has poisson or binomial destribution. Can we define a new destribution for new population? How can we estimate ...
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0answers
9 views

Estimating a Poisson process when arrivals occur out of order?

TL;DR: Given a Poisson process with constant intensity $\lambda$, but you are hearing about arrivals out-of-order, how would you (sequentially/iteratively) estimate $\lambda$? What if the problem is ...
2
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0answers
32 views

Does Hoeffding's inequality apply to sampling from finite populations?

Based on Hoeffding's theorem, one could easily find the minimum number of samples required for the inequality $\Pr \left(|\bar{X} - \mathrm{E} [\bar{X}]| \geq t \right) \leq \delta$ to hold as ...
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1answer
16 views

Fit stochastic differential equation to data

Could I have some review of the method I used to fit following SDE: dX = f(t) dt + s X dW Fitting method: Calculated sample for sdW from our data as: sdWt = ...
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1answer
18 views

Estimate effect on mean of dependent variable of an increase in the independent variable in a linear regression

Suppose I have the linear regression equation: Y = B0 + B1(x) How do I find the estimated effect on mean Y of an additional 50 to x? I believe this is the multiplicative effect.
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0answers
57 views

Can Chebyshev inequality be used to bound the error of the sample mean?

Can the probability of error of the sample mean, i.e., $\Pr(|\bar{X}-E[X]| \geq \epsilon)$, be bounded using Chebyshev inequality (or something similar)? $X$ is a discrete random variable with an ...
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0answers
12 views

Basic questions about stochastic gradient descent / Robbins and Monro algorithm

I have a LOT of time series observations and I would like to estimate a simple AR(1) model $$ y_t =c+ \phi y_{t-1}+ \varepsilon_t \qquad \varepsilon_t \sim \text{N}(0, \sigma^{2}) $$ with parameters ...
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1answer
34 views

proving the asymptotic distribution of the mean

Let ${X_t} = \mu + \sum\limits_{j = - \infty }^{ + \infty } {{\psi _j}{\varepsilon _{t - j}}}$ with $\varepsilon$ is a white noise iid with variance $\sigma^2$ , $\sum\limits_{j = - \infty }^{ + ...
5
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3answers
108 views

Fast density estimation

Suppose you are trying to estimate the pdf of a random variable $X$, for which there are tons of i.i.d. samples $\{X_i\}_{i=1}^{n}$ (i.e. $n$ is very large, think thousands - millions). One option is ...
1
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1answer
25 views

Estimate of Coefficient Variance in multiple regression

I'm trying to compute an estimate for the variance of the estimated coefficients in a non-linear regression using the formula described in link. I can't figure out how to build $F_{ij}$ Let's ...
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0answers
10 views

Estimator for a function depending on a random variable [duplicate]

Let $X$ be random variable in $m$ dimensional space. The distance between each pair of vectors $x_i^m,x_j^m$ is $D_{i,j}^m =d(x_i^m,x_j^m)$. Correlation Sum, $C(r)$ represents the probability of the ...
3
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1answer
67 views

Robust estimates of the covariance matrix in the big data space

I am trying to compute the robust estimates of the covariance matrix (and also the mean) in the big data space. I am aware of FastMVE and FastMCD (Minimum Covariance Determinant and Minimum Volume ...
2
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1answer
44 views

What's the statistical method where you add a certain number to each sample to make the distribution slightly more uniform?

Please forgive my lack of knowledge - it's been a while since I've taken classes in statistics, and even then, it was not my strong point. I'm trying to recall a method used to upweight all values in ...
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0answers
15 views

How to estimate Extreme value distribution parameter

Assume that I have non-negative Gamma random variables $\{X_i,i=1\dots n\}$ and I want to find $M_n=\max\{ X_i\}$. I want to apply generalized extreme value distribution (GEV), but how to find $\mu$, ...
2
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0answers
10 views

Evaluating survival models in the presence of covariate-dependent censoring

I have a censored survival analysis problem with the following characteristics: Failure times are discretized The censorship distribution depends on certain covariates I don't have a ...
1
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1answer
27 views

Is there any method to quantify parameter estimation uncertainty of method of moments fitting technique?

If I want to fit a distribution (let's say we can be certain about the type) to observations using maximum-likelihood method, I have many options to express the parameter estimation uncertainty due to ...
5
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3answers
37 views
6
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1answer
168 views

Estimating parameters for a binomial

First of all I'd like to precise that I'm not an expert of the subject. Suppose to have two random variables $X$ and $Y$ that are binomial, respectively $X\sim B(n_1,p)$ and $Y\sim B(n_2,p),$ note ...
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1answer
29 views

Point estimation MLE and MME

Consider the family of probability mass functions given by f(x;k) = 3(4^(k-x)) x = k + 1, k + 2,.... and indexed by parameter k E Z. For a random sample of size n, derive with justification: a) ...
2
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1answer
51 views

Conceptual question on estimation : How to calculate the variance of estimation error

EDIT/ UPDATE: I have understood CRLB & why we need it. But my problem is something else. In book ...
2
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1answer
35 views

Average of Dependent Variables

Suppose $X_1, \ldots, X_n$ are dependent varibles with identical marginal distribution. Denote the common population mean as $\mu_0$. In this case, is $\frac{1}{n} \sum X_i$ a reasonably good ...
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1answer
22 views

Inverse Gamma Prior with Scale Parameter set to 1

\begin{align*} X_{ij} \mid \mu_i , \sigma^2 & \sim N(\mu_i, \sigma^2) \nonumber \\ \mu_i & \sim N(\mu_0, \tau^2) \nonumber\\ % S_i^2 \mid \sigma^2 & \iid \chi_{n-1}^2/(n-1) \nonumber \\ ...
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0answers
15 views

Transforming frequency data into a rating system

I'm working on a project for fun using data (items from a persistent video game) I've gathered from the web. At the moment, the data consists of around 180,000 rows which will probably grow quite ...
3
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2answers
51 views

Fitting parametric CDF to ecdf

There is a random variable $X$, but the only data I observed is actually its empirical distribution function (at a suitably fine grid). That is, I only observe $\hat{F}(x)$:=$\#\{x\leq u\}\over N $ ...
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1answer
35 views

On approximating the MSE of an estimator

I'm trying to approximate the MSE of an estimator through simulation, in particular estimators of the form $$ \hat{\theta} = \sum_{i=1}^N w_i X_i $$ Where $X = \{X_1,...,X_N\}$ are i.i.d. samples ...
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1answer
49 views

OLS versus ML estimation of VECM

A vector error correction (VECM) model has an equivalent vector autoregression (VAR) representation. (VECM) $\;\;\;\Delta y_t=\Pi y_{t-1}+\Gamma_1\Delta y_{t-1}+...+\Gamma_{p-1}\Delta ...
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0answers
20 views

Learning the distribution of a phenomenon's occurrence with partial observation

I recently came across this problem: There is a phenomenon, which occurs exactly on one of a set of M (finite) places at every time step t= 1,2,... At each time step t, the place of occurrence is ...
5
votes
2answers
77 views

What's the difference between estimating equations and method of moments estimators?

From my understanding, both are estimators that are based on first providing an unbiased statistic $T(X)$ and obtaining the root to the equation: $$c(X) \left( T(X) - E(T(X)) \right) = 0$$ Secondly ...
4
votes
3answers
45 views

Cointegration - Why can't I estimate a VAR on the differences?

When talking about variables that are I(1) (the first difference is stationary), Lutkepohl book says: "...in general, a VAR process with cointegrated variables does not admit a pure VAR representation ...
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1answer
30 views

Prove that System FGLS is Consistent

In the Systems of Equations framework, such as Seemingly Unrelated Regression (SUR), suppose we have $g=1,\ldots,G$ equations. Let $\mathbf{X}_i$ be a $G \times K$ matrix, $\mathbf{y}_i$ be $G \times ...
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0answers
9 views

Price index - Bill method and Rate method

Can someone explaing the difference between these two methods for calculating price indices, i.e. how is index calculated? Or more precisely, what exactly is determined from the Bill method and the ...
7
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4answers
536 views

How to sample when you don't know the distribution

I'm fairly new to statistics (a handful of beginner-level Uni courses) and was wondering about sampling from unknown distributions. Specifically, if you have no idea about the underlying distribution, ...
0
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1answer
39 views

Parameter estimation in log linear models

Can anyone explain to me how parameter estimation is computed in log linear models? I followed this paper which is quite good, however I'm a bit confused in the parameter estimation part which is ...
4
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0answers
31 views

asymptotic unbiasedness of weibull mle

It's known that the MLEs of the two-parameter Weibull distribution scale and shape parameters are not available in a closed form. It is, however, known that they do exist, are unique, and moreover, ...
2
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0answers
20 views

Instagram representative sample

I am doing a survey to study both sellers and consumers behaviour on Instagram in Kuwait. My question is how to decide on the sample size? What sampling design should I use since there is no sampling ...
3
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2answers
59 views

Estimator for $E[X]^2$

I'm trying to understand the theory of estimators. As I understand it now, if you have an r.v. $X$ and take $n$ i.i.d. samples then an estimator for $E[X^{2}]$ would be $\overline{X^{2}}$ since ...
1
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1answer
50 views

Definition of Scale median

Lehmann, in Theory of Point Estimation p.212 (and also on p.169), defines scale median as the solution to: $${E(X)I(X\le c)} = {E(X)I(X\ge c)}$$ given $X$ is a positive random variable, and ...
1
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1answer
37 views

Pointwise probability limit

Suppose we have a joint distribution of a random sample $(y_n,x_n)\in R^2$: $$ y_n = \beta_0 x_n + \epsilon_n $$ and the estimator $$ \hat \beta = argmin_\beta \frac{1}{N} \sum_{n=1}^N(y_n - \beta ...
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0answers
16 views

Getting estimates of hospital specific stroke admissions data

I am analysing a small data set on stroke process of care gathered from public sources but don't have access to hospital specific emergency stroke admissions over a period of time data except for ...
0
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0answers
24 views

How to make non-parametric distribution estimation with known, limited number of points of the CDF?

Is there any method to make non-parametric estimation of a cumulative distribution function (CDF) which actual points (not a sample) can be calculated numerically? I have a numerical method which can ...
0
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0answers
24 views

L1 distance between empirical and true distribution for discrete distributions

I have a distribution over the discrete set $\mathcal{A} = \{1, \ldots, d\}$ where the pmf is $p(.)$. That is, $p(i)$ is the probability of obtaining $i$ from $\mathcal{A}$. Given a dataset with $n$ ...
0
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1answer
13 views

Combining two estimates of p in a binomial estimation

I have an estimation problem for a binomial data. I got a sample and from that I can get an estimation. But I also have a kind of prior information about the p. But mind it, this prior is just a ...
1
vote
2answers
36 views

Can you compare probabilities of an epidemic by knowing R0 values?

In comparing two diseases with different basic reproduction numbers (R0), is it possible to use the R0 values to calculate the probability of an epidemic spread through a population? For example, if ...
2
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2answers
138 views

Gaussian noise model derivation

I have the following linear regression model, $y = f(x;w) + n$, where $y$ is the vector of true labels, $x$ is the observed data, $f(x;w) = w^Tx$, and $n$ ~ $N(0, \sigma^2)$ is the noise. Why then ...
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1answer
23 views

Finding $p(\tilde{y}|x)$ given measurement model and error distribution

Given two measurements of a variable $x$: $\tilde{y_1}=x+e_1$ $\tilde{y_2}=x+e_2$ where $e_1,e_2$ are zero-mean random variables following a bivariate normal distribution, with a known joint ...
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1answer
24 views

Maximum Likelihood solution of a zero-covariance process

Let the measurement model be: $\tilde{y}=Hx+v$ $\tilde{y}=H\hat{x}+e$ where $H$ is the basis matrix, $v$ is a constant vector equal to, say, $a$, $x$ is the measurement variable and $e$ is a ...
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0answers
14 views

Need help with importance sampling over HUGE sample space

My underlying problem is fairly simple, but the sheer size is what is causing issues. I would like to use importance sampling, but am unsure about its implementation. Problem statement: We have $N$ ...
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0answers
24 views

Recursive Bayesian Estimation, $p(C_k|\mathbf{x})$ as (discrete) likelihood

I''ve been struggeling with this problem for the last couple of days. The main goal is to use the probabilistic classification output $p(C_k|\mathbf{x})$, from for example a logistic regression, to ...
1
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1answer
61 views

Estimation based on observing sum of two variables

Let $X_1,\dots,X_n$ are i.i.d normal $N(\mu,\sigma^2).$ Suppose that we only observe $$ X_1+X_2,\dots,X_1+X_n,\dots,X_{n-1}+X_n, $$ i.e, $X_i+X_j$ for all $i<j.$ I wish to find the best estimator ...