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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Estimating number of unique people

Assume from a prior experiment with have a known truth table of misclassification of logins on an individual basis. $$ \begin{array}{c|lcr} \text{Truth}/\text{Observed} & \text{Al (M)} & ...
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20 views

What is the difference between ex ante and a priori, if any?

In the context of estimating geophysical quantities from remotely sensed data (inverse theory), what do the terms ex ante and ex post mean? For context, see for example this paper by T. von Clarmann ...
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13 views

Unbiased Estimator of Days Until Completion?

I'm trying to get an estimate of average number of days until some event occurs (the event is guaranteed to eventually occur). I have some sample where this event has already occured for most ...
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15 views

Probability of 'Chance of winning' given a set of wins [on hold]

Let $p$: chance of success and $q = 1-p$ Then given that there are m wins of the n games. What is the probability that p>q. Assuming p is normally distributed.
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8 views

In inverse theory, how do I transform the averaging kernel matrix to a new grid?

Rodgers and Connor (2003) describe how measurements by remote sounders can be properly compared, taking into account differences in averaging kernels and error covariances. They make the assumption ...
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29 views

variance of doubly truncated binomial

I am in need of variance of doubly truncated binomial distribution (equation number 3.69 on page number 137 of third edition of Johnson, Kemp and Kotz Discrete Probability Distributions). Thanks. ...
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8 views

Estimating Distribution from Intervals

Say that I get an attendance list of people in a party. From another source I know the minimum and maximum age of each person with a name e.g. "John" must be between 19 and 55 or "Mary" must be at ...
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13 views

Efficient scale & shape parameter estimation for generalized secant hyperbolic distribution needed

the (symmetric) generalized secant hyperbolic distribution GSHD is very flexible but I found not much at all on how to estimate its 3 parameters. Given the location, I need to obtain scale & shape ...
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19 views

Maximum Likelihood through a noisy channel

I have a random variable $X$, which can take $n$ values and is distributed according to multinomial $\Theta=(\theta_1, \theta_2, \cdots, \theta_n)$. I observe a random variable $Y$, where I have that ...
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33 views

Question about using a multiplicative dummy variable

In many econometrics model, the changes in the response variables in certain intervals are more difficult than other intervals. But I believe this is often not considered when estimating the model. ...
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39 views

Predicting the impact point of a moving object

Suppose we have a moving object (a horizontal projectile motion as one of the most basic examples). Is there any way to predict where it will hit finally? Please note that I'm looking for a machine ...
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1answer
9 views

Parameters estimation of non-stationary random process using different runs

Let $X(t)$ be a non-stationary continuous time-dependent random process with a known model but unknown parameters. I'd like to know if it's possible to estimate the parameters of $X(t)$ not by using ...
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33 views

Estimating a joint distribution from observed max and min samples

Suppose that you have jointly distributed $N$ (~100) random variables, $\{X_1,\ldots,X_N\}$, and this distribution is unknown to you. However you do know that their sum is zero by construction. Having ...
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31 views

Maximum likelihood estimator for variance in two linear models

I am learning MLE's at my inference class and this is a problem I came accross. Consider two simple linear models. $y_{1j}=\alpha _1+\beta_{1}x_{1j}+\epsilon_{1j}$ and $y_{2j}=\alpha ...
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1answer
116 views

Estimate average percentage error based on another gaussian measurement

I have a model where the error is proportional to the throughput. This is, the observations I got come from a measurement instrument that has some error and it measures material going through in ...
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27 views

UMVUE for normal distribution $\sigma$

Let $X_1,X_2,...,X_n$ be a random sample from a normal distribution with mean $\mu$ and variance $\sigma^2$. I showed that $(\bar X,S^2)$ is jointly sufficient for estimating ($\mu$,$\sigma^2$) where ...
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1answer
18 views

Partial Parameter Estimation (MLE/LMMSE)

I have a basic question. MLE/LMSSE is introduced as follows: $$Y = H\theta + W$$ where $H$ is the linear model matrix, $W$ is measurement noise (let's assume it is normal so MLE = LMSSE). $\theta$ is ...
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2answers
21 views

Pivotal to estimate lambda of a exponential

I am studying interval estimation by the method of pivotal quantities. Let $X_1,X_2,...,X_n$ be a random sample from a p.d.f $f(x;\lambda)=\lambda e^{-\lambda x}, x>0,\lambda >0$. I have to ...
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87 views

Advantage of Maximum Likelihood estimation [closed]

We can estimate unknown parameters by Least square, Least Mean Square, Blue estimators and Maximum Likelihood estimation. Q1: What is the advantage of MLE over others and when should MLE be chosen? ...
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39 views

Would two different pivotal quantities of the same parameter give the same confidence interval?

I couldn't think of an example but it would be great if someone could give one.
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48 views

Confidence interval for the standard deviation of a Normal distribution with known mean

Suppose $\textbf{Y} = (Y_{1}, ... , Y_{n})$ is a random sample from the $N(\mu, \sigma_{0}^{2})$ distribution where $\mathrm{E}(Y_{i}) = \mu$ is unknown but $\mathrm{SD}(Y_{i}) = \sigma_{0}$ is known. ...
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49 views

Good Reading/Bibliography

Before posting this question, I searched CV for a similar question that could helped me, but I didn't find one. So, I'm sorry if this has already been asked before. So, I'm self-studying from Keith ...
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63 views

Cramer-Rao bound for $\chi^2$ distribution parameter estimates

I've struck an unpleasant problem with the noncentral $\chi^2$ distribution. I work with random variables, distributed as $\chi^2_{\nu}(\lambda)$, where $\nu$ is the degree of freedom and $\lambda$ ...
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29 views

Standard error of difference of estimates

I have two (non-independent) OLS-parameter estimates each with its own standard error. I'm trying to find out what the standard error of the difference of the estimates should be. Can anyone help? Is ...
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25 views

Estimation of Noise Level in the High-Throughput Cancer Data

Assume that I have made a coverage log ratios signal by dividing the coverage data coming from a tumour sample over the reference sample and then taking the log2 of this division. My question is: ...
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55 views

Estimating ARMA equation using lm() in R

Is there a way to estimate an ARMA equation using the lm() function in R without using arima()?
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159 views

Parameter estimation based on MLE estimate of another parameter

There is a situation explained below where I intend to apply MLE. The problem statement is that I am estimating a measure $X$. This measure is obtained my Maximum Likelihood estimation technique. ...
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46 views

Estimates of regression coefficients are uncorrelated?

Consider a simple regression (normality not assumed): $Y_i = a + b X_i + e_i$ where $e_i$ is with mean 0 and standard deviation $\sigma$. Are the Least Square Estimates of $a$ and $b$ uncorrelated?
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22 views

Biased but consistent estimator for the mean of Gaussian distribution?

$(X_1,X_2,\ldots,X_n)$ is a random sample from $\mathrm{N}(θ, 1)$. We know sample mean is a unbiased estimator that is consistent. What would be a biased but consistent estimator for θ? Would it be ...
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22 views

Relative importance of variables?

The following output is given: The task is to state, which variables, among thoses that are statistically significnat at 0.05, have the greatest and least relative importance on the fitted model? ...
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21 views

Estimate Mean and Standard Deviation from Percentiles

I have a derived dataset that specifies the percentiles from the 10th to 95th in increments of 5 along with the total number of data points. Is there a way to estimate the mean of the original ...
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37 views

temperature prediction algorithm

I found an interesting problem in a contest on temperature prediction: https://www.hackerrank.com/contests/expansion-challenge/challenges/temperature-predictions It is not about forecasting the ...
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21 views

G/G/1 Simulation help

i am a complete nooby in statistics, therefore the question i am about to ask may sound very unprofessional warning :) so, we have a task to simulate a G/G/1 queueing system for particular parameters ...
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56 views

Estimating means of correlated distributions with long tails

Suppose I have a relatively large number of samples (~1k) drawn from a series (~40) of increasingly long-tailed distributions (going from approximately normal to approximately log-normal). I want to ...
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67 views

Estimating Uniform distribution endpoints using data with errors

Suppose I have a random variable $X$ ~ $Unif(0,\theta)$ where I want to estimate $\theta$. I draw a sample $X_1,...,X_n$.One way is to get a point estimate using e.g. maximum likelihood estimation ...
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1answer
34 views

Estimate median from mean, std dev, and/or range

I have easy access to the the mean, standard deviation and min/max values for a variable. I also have the number of elements used to compute those values. The data is real numbers with an absolute ...
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1answer
98 views

Computing inverse probability weights — conditional (multivariate) density estimation?

The general version: I need to estimate $f(A | X)$ where $A$ and $X$ are continuous and multivariate. I'd rather do it nonparametrically because I don't have a good functional form in mind and ...
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Estimator for vectors(matrices) with increasing length

I'm now preparing exams for mathematical statistics. Our teacher told us that there will be problems concerning the estimator for vectors(or matrices) that increases length when the number of samples ...
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Estimating distribution of traffic across all Web pages

The web is estimated to have approx 5 billion web pages ( http://www.worldwidewebsize.com/ ). How would you go about estimating a CDF to know how many pages are required that make up, say, 90% of ...
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27 views

Help in Maximum likelihood etimation in presence of colored noise

I am trying to test system identification in presence of measurement noise (1) A white Gaussian noise (2) Colored noise - pink, violet. When we are estimating parameters we do so in presence of iid, ...
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27 views

System identification in the presence of noise

In some scenarios, a signal may be corrupted by chaotic noise (radar application) as $y = x + \text{chaotic noise} + \text{AWGN}$ Chaotic signal is deterministic, so in my opinion it will not have a ...
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17 views

Mutual information, entropy and parameter estimation

The papers here estimate unknown parameters of a system by selecting those parameters as the true estimates which minimize the entropy of the error. Error = desired - model output. The reason is that ...
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53 views

Relationship between entropy and information gain

Based on papers :1. Deniz Erdogmus, Member, IEEE, and Jose C. Principe, An Error-Entropy Minimization Algorithm for Supervised Training of Nonlinear Adaptive Systems J. Principe, D. Xu, and J. ...
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25 views

What is uncorrelated noise and its significance

In many applications such as estimation theory, when we need to estimate a parameter then we usually consider in presence of white gaussian noise of zero mean and some standard deviation. During ...
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16 views

Finding the right parameter for a student's $t$-distribution

Suppose I have a homogeneous time series $x_n$, where the values arrive each second. For $n\ge 60$, let $\sigma_n$ be the standard deviation of the values $x_{n-59},\ldots,x_n$. Under the assumption ...
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1answer
61 views

Find the UMVUE for $\Phi(\mu)$

Question: Suppose $X_1, \cdots, X_n$ are $iid$ normal random variables with unknown mean $\mu$ and known variance $\sigma^2$. Find the UMVUE for $\Phi(\mu)$, where $\Phi(\cdot)$ is the cdf of a ...
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Variance of plugin estimator

This question related to my previous question. Let $$X_1,\dots,X_n$$ are i.i.d. with distribution function $F$ and $$Y_1,\dots,Y_n$$ are i.i.d. with distribution function $G$. Suppose that there ...
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24 views

Trend of Cramer Rao Lower bound with signal-to-noise ratio?

Intuitively, CRLB should decrease with increase of signal-to-noise ratio (SNR). A plot of CRLB (Y axis) and SNR on X axis should be somewhat a decreasing exponential curve. Thus, when the signal has ...
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In CFA, when should ML estimation preferable and when is GLS preferable?

To a lesser extent I am also interested in when one should use Unweighted Least Squares, and other less common methods. I have been taught ML as a default but have just done a CFA and model fit was ...
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32 views

what if I know my time series are cointegrated over a long period but not over a short period?

I am regressing time series on time series. I have tested for cointegration on the entire time sample (3 years) and the series are cointegrated. I need to make a rolling window of regressions (to ...