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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6 views

Estimating the mean of a random variable from greater than/less than answers

Let $X_1,\dots,X_n$ be $n$ samples from a certain probability distribution (e.g, a normal distribution). Your goal is to estimate the mean of the distribution. However, you are not allowed to see ...
2
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23 views

Some logical questions about parameter estimation in the situations when the model is misspecified

When we have a parametric model, we can use many procedure to estimate the parameters in the model, i.e., obtain many different estimators. We usually focus on the set of consistent estimators. For ...
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1answer
16 views

Should the underlying logic of the model evaluation criterion match with the estimation procedure?

Assume we have a parametric model with parameter $\beta$. We want to use this model to make predictions, e.g., credit card firm using some attributes $X$ of the customer to predict the default rate $Y$...
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6 views
0
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35 views

Prove consistency of estimator

Let $X$ be a random variable with density $f(x;\theta)=\frac{1}{2\theta}I_{(-\theta,\theta)}(x), \ \theta>0$. Is $\hat \theta = \dfrac{1}{n}\sum_{i=1}^nX_i$ a consistent estimator for $\theta$...
3
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1answer
27 views

Uncertainty in parameter estimates when fitting distributions

I used the fitdist function from the "fitdistrplus" package in R to estimate the parameters of my data. Once I get the parameters, I must get the confidence ...
2
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1answer
25 views

estimating variance using only data at the tails without resorting to Gibbs sampling

Suppose we know that the population size is $n=1,000$ but for whatever reason, we only have the bottom $n_1=100$ observations and the top $n_2 = 200$ observations. Furthermore, suppose we know the ...
4
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1answer
62 views

Variance computed using Taylor series does not agree with numerical experiment

I would like to estimate an angle $\theta\in\left(-\frac{\pi}{2},\frac{\pi}{2}\right)$ given the noisy observations of its sine and cosine (this is related to my earlier question). My estimator is ...
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29 views

Equivalent of standard error for variance?

I would like to know if there is an equivalent formula of standard error for variance or standard deviation, that is, I would like to know how far the variance of my sample is from the real variance ...
3
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1answer
79 views

What is the proper way to measure error for an estimation algorithm?

Our algorithm is about estimating the true statistic values from a data set. The data set is a table in relational database, we are going to estimate the statistic value for filtered records, like <...
3
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1answer
24 views

methods to estimate 2 sinusoids in noise

Are there some strategies to estimate a function which has the form $y=A\sin(f_1x+O_1)+B\sin(f_2x+O_2)+\epsilon$ (where $\epsilon$ is small-variance Gaussian noise) I have initial estimates of of ...
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2answers
98 views

Estimate of parameter of exponential distribution with binned data

I have the following data, which can be modeled by exponential distribution ...
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0answers
53 views

Variance of Maximum Entropy solution [closed]

Background: Assume we are interested in solving the Maximum Entropy solution for a six sided dice with expected value of 4. $$H= - \sum_{i=1}^6 p_i \log(p_i) $$ $$\sum_{i=1}^6 p_i = 1$$ $$\sum_{i=...
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1answer
34 views

Likelihood between two functions

I have a function $f(x)$ describing a physical process, and a function $g(x)$ that tries to approximate it. I can clearly see by eye when the two functions are close enough, but I would like a ...
0
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0answers
27 views

Maximum likelihood estimation for non-stationary time series

I want to estimate how the taxes influence the retail price of alcoholic beverages. The price function is tricky because in EU countries there is excise duty and also VAT. The non-linearity (which is ...
0
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0answers
13 views

simulation and model comparison

I created a simulation to compare a number of regression type models/estimators, lets call them M1, ...,Mn. for each iteration of the simulation run: I generate randomly data set X I generare ...
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0answers
12 views

How to make a covariance matrix from multiple observations of different objects?

I have $N$ objects. From each object, I sample $M$ values $(x,y)$ like so: ...
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20 views

How can I decompose the error after an ARIMA estimation, and how do I store the estimated values?

EDIT (in response to Stephan's comments): I was able to read a paper by Bessembinder & Seguin (1992) on futures trading and stock price volatility, wherein they used the ARIMA model to decompose ...
1
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1answer
42 views

How to show the least square estimator of $b$ has the minimum variance in the class $\sum a_iy_i$

Consider the regression model: $$ y_i=bx_i+e_i,1\leq i\leq n.$$ where $x_i$'s are fixed non-zero real numbers and $e_i$'s are independent random variables with mean zero and equal variance. $(a)$...
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0answers
6 views

Theoretical/intuitive question about time-varying Generalized Pareto Distribution

I fitted the GPD to the right tail of nine log return series (I multiplied log returns by -1, so modeling the right tail equals modeling the losses) with a threshold equal to the 95% quantile. Some of ...
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0answers
17 views

Why are standard errors downward biased when considering weak instruments

I was wondering why standard errors are (severely) downward biased when you are using the (general) instrumental variable - estimator or the generalized method of moments (gmm) estimator.
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12 views

Sparsity estimators

I've recently started to read about sparsity estimation. Let's recall that the sparsity function is defined as $s(\tau)=f(Q(\tau))$, where $f$ is the population density and $Q$ is its quantile ...
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0answers
10 views

Comparison of Stahel-Donoho and Minimum Covariance Determinant estimation

I am interested in detecting multivariate outliers in a low dimensional data set ($n<p$). Various high-breakdown robust methods for multivariate settings such as Stahel-Donoho and Minimum ...
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43 views

On randomized estimators

I been looking at this for a few days; I cant understand how the pseudo-random generator comes into play, why do we need it? Is it just in order to have an actual $X^{'}=X \mid t$ in a real life ...
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0answers
4 views

Simulation Model Performance for Flood Quantile Estimation at Ungauged Site

I have proposed a model that is the modified ANN to estimate flood at ungauged site. In order to test the performance of the model, i want to design the simulation for ungauged estimation problem. Did ...
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0answers
30 views

Estimation of regression model with error terms having a Pareto distribution

I am trying to estimate the regression model, say standard linear model, with the error term having a Pareto distribution instead of normal. Although it is fairly straightforward to construct the ...
1
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1answer
75 views

Likelihood of observations for HMM with continuous state and observation distributions

I have a "real" and estimated HMM model given as $(\pi,\mu, \nu)$ and $(\pi^{\text{est}},\mu^{\text{est}}, \nu^{\text{est}})$, where $\pi$ is initial state distribution of Markov chain, $\mu$ is state ...
3
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1answer
44 views

On theorem on characterization of MRE estimaters

I have some trouble with understand the second equality in the proof of theorem 6; Using the lemma we can just plug in $\delta_{0}-v$ and minimize over that w.r.t $v$, but howcome we have the ...
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0answers
25 views

Normal distribution analog for HSV colour space

[This question inspired by work by Jason Thornton et al (see https://cryptome.org/2012/05/person-large-area-spy.pdf , Equation (4))] I am interested in modelling a distribution over the HSV color ...
1
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1answer
29 views

Finding unbiased estimator of function of p from a geometric distribution

Let $X_1$ and $X_2$ be a random sample from the geometric distribution with $Pr(X_i=j)=p(1-p)^{j-1}$ for $i = 1, 2$, $j = 1, 2, \ldots$ and $0<p<1$. Which statistics $T(X)$ could be an unbiased ...
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0answers
30 views

How many observations to estimate a parameter of an Archimedean copula?

Let's consider for example the bivariate Gumbel copula. $$C(u_1, u_2)=exp \left[-\left((-ln(u_1))^{\theta}+(-ln(u_2))^{\theta}\right)^{\frac{1}{\theta}}\right]$$ In R there are some functions (such as ...
1
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1answer
41 views

Which of the followings can be regarded as sufficient statistics?

The probability of heads showing up upon tossing a certain coin is $p$, this coin is tossed $3$ times, let $X_i,i=1,2,3$ be $1$ or $-1$ depending on the outcome of the $i^{th}$ toss being head or ...
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2answers
193 views

Unbiased estimator of poisson parameter

The number of accidents per day is a Poisson random variable with parameter $\lambda$, on 10 randomly chosen days the number of accidents were observed as 1,0,1,1,2,0,2,0,0,1, what will be an unbiased ...
19
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2answers
421 views

Bias of moment estimator of lognormal distribution

I am doing some numerical experiment that consists in sampling a lognormal distribution $X\sim\mathcal{LN}(\mu, \sigma)$, and trying to estimate the moments $\mathbb{E}[X^n]$ by two methods: Looking ...
1
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0answers
16 views

Binary outcome estimation from n “measurements”

Assume you have a binary parameter $y$ which is either $0$ or $1$, and have $n$ measurements $\tilde{y_k}$ of it, each with a different probability $p_k$ of being correct (equal to $y$). With $k=1,..,...
6
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1answer
50 views

Estimating a variable from its cosine corrupted by additive Gaussian noise

I observe $y_i=\cos(\theta)+z_i$, $i=1,\ldots,n$, where each $z_i\sim\mathcal{N}(0,\sigma^2)$ is an i.i.d. zero-mean Gaussian random variable. I am interested in estimating $\theta\in[0,\pi]$ with ...
3
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1answer
38 views

How to prove that $Cov(\hat{\beta},\bar{Y}) = 0 $ using given covarience properties

To quote: It is well known that, if $W_1, ..., W_n, Z_1, ..., Z_m$ are random variables and $a_1, ..., a_n, b_1, ..., b_m$ are constants, then $Cov ( \sum_{i=1}^n a_iW_i, \sum_{j=1}^m b_jZ_j) = \...
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0answers
11 views

Estimating days of usage for a limited time frame

I would like to estimate how many individual days of a week user have been using a feature in my app, but I'm kinda lost as to do that? Basically the set up is an A/B test, where some users get one ...
0
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0answers
16 views

Random right cenoring

I observe a series of values from different trials ($Y_1, ... Y_N$). All values come from the same distribution ($F(\cdot)$). Trials do not have the same number of values ($N$ differs across trials)....
1
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1answer
17 views

Minimizing MMSE over positive random variables

Let X be a random variable with a finite second moment. We know that: Argmin E(X-Y)^2 = E(X|g), Where the minimum is taken over all g-measurable random variables Y. How can I find argmin E(X-Y)^2 ...
2
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2answers
68 views

Student t-distribution parameter/s and MLE

So I always thought of the Student t-distribution as having only 1 parameter, v, the degrees of freedom (as described by wikipedia). When I searched however on how to find the MLE of v I keep coming ...
1
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1answer
35 views

Variance Estimation of MA(1) with known autocovariance function

I haven't worked with time-series in a while now and stumbled upon them in a different setting. Given $X_t\sim\mathcal{N}(0,\sigma^2)$ for $t=1,\ldots,n$ and the process $Y_t$ for $t=1,\ldots,n-1$ ...
0
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0answers
10 views

Goodness of fit for complex valued curves (i.e. frequency responses in frequency domain)

I'm not a hero at statistics, som my apologies for perhaps the stupidity of this question. Presume that one has the frequency response $Y_{data}(k)$ and also has the synthesized response $Y_{syn}(k)$. ...
1
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2answers
50 views

Voting: probability of outcome flip

Assume you have a set of $N$ persons who should vote in a poll "for" or "against" an issue. The outcome of the poll is taken with simple majority. Each person's vote is independent of the rest and ...
3
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0answers
11 views

Technique for predicting ratios given earlier observations

Say I have the following situation: A realtor has previously estimated the values of n properties to be x1, ..., xn. They sold ...
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0answers
15 views

Complex valued design matrix

In statistics design matrix is fundamental concept. It includes set of explanatory variables, for example in case of MRI data we use dc component, drift,physiological noise and so on. What will ...
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22 views

Distinguishing between Poisson distribution and a similar distribution w/ small mean

I have an experiment where if all is going well the measured distribution should be Poisson (to very good approximation) with mean $\lambda \sim .1$, but if something goes wrong the distribution will ...
3
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0answers
21 views

Confidence interval for odds ratio with differents results

Find the confidence interval for the odds ratio, where $OR=e^{\hat{B_1}}=3.5701$, $\hat{B_1}=1.2726$, $\sigma(\hat{B_1})=0.5016$ with 95% confidence. First I followed the idea from notes that I ...
3
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0answers
38 views

Most efficient estimator of mean

Let's say we want to estimate a mean $E[F]$ for some unknown distribution $F$. If we only care about the MSE (and don't mind using biased and non-linear estimator), what theory is available to help us ...
0
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0answers
5 views

What's the relationship between detection and estimation?

I'm a bit confused by the relationship between detection (hypothesis testing) and estimation. For example, in sparse PCA setting, we may want to estimate the leading eigenvectors of the covariance ...