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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2
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5 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 ...
1
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1answer
18 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
6 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
11 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 ...
1
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1answer
14 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 ...
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4 views

Modern Introduction to Orthogonal Density Estimators [on hold]

I've found an abundance of papers about the subject, but most of them are rather dated, Most Notably [1]. There's a good review from 1991 [2], but it is very brief and insufficient for research level ...
2
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2answers
62 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
34 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
8 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
45 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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9 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
13 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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0answers
18 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
17 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 ...
3
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0answers
32 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 ...
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0answers
18 views

Can we use cross validation and bootstrapping together?

I would like to estimate the model parameters from n data samples in a training data set. I want to know if I can use bootstrap and cross validation jointly. For instance, I have n data samples. ...
0
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0answers
27 views

Best estimate for random variable given samples and range

$X_1 ... X_{10} \sim \mathcal{N}, I.I.D$, with some parameters, that are unknown. $w_1...w_{10}$ are known weights. These 10 random variables have 10 realizations, call them $x_1 ... x_{10}$. And for ...
0
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1answer
11 views

Bayesian estimation for the distribution of the results of an experiment when the cardinality of the result set is unknown

Suppose I have an experiment X with mutually exclusive outcomes from a set S. My goal is to determine the probability distribution for S. The problem is that I do not know how many elements are in S ...
0
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0answers
11 views

Multivariate Linear Regression with Linear Constraints

Consider random samples $z_1,\ldots, z_N\in \mathbb{R}^n$ distributed according to $z_i\sim\mathcal{N}(T\cdot q_i, \Sigma)$ with $T,\Sigma\in\mathbb{R}^{n\times n}$ and $q_i\in\mathbb{R}^n$. If the ...
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7 views

Estimating parameter of a distribution for some generate random number [migrated]

I just new in R for solving my statistical problem. Currently I'm working to estimate the parameters of a distribution using 200 random numbers (RN) that I generate using R. I generate 200 RN in 100 ...
2
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1answer
40 views

Is the Jackknife estimation better than Maximum Likelihood Estimator?

I'm trying to estimate distribution parameters with Maximum Likelihood Estimator (MLE) and Jackknife estimator based on it. The estimation statistic is mean. Jackknife estimator is considered to be ...
0
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0answers
4 views

parameter estimation of fractional factorial design

I've been asked to estimate the parameters of fractional factorial design model which is normally estimated using least square method in R (code is lm). I want to know that, is it possible if I change ...
3
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0answers
30 views

Is M-estimation valid only for regression models?

Is M-estimation valid only for regression models or does it's working hold good for robust estimation of parameters in other statistical models? I understand that M-estimators are asymptotically ...
0
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16 views

Are there situations in which we want to model/estimate the *independent* variable?

Parametric regression approaches can be characterized in the following way: Assume our dependent-variable comes from a particular distribution (e.g., the normal distribution). Estimate the effect(s) ...
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0answers
7 views

How to combine statistical moments at different orders?

I am performing a number of simulations involving the estimation of statistical moments at different orders (lets say, from the 1st till the 3rd order). For certain case studies, I have useful ...
2
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0answers
11 views

a question on sequential estimation

I am reading Chris Bishop's Pattern Recognition and Machine Learning. In Section 2.3.5 he introduces some ideas on the contribution of the $n$th observation in a data set to the maximum likelihood ...
4
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3answers
57 views

How to interpret my coefficients?

I have the following model: $$ Gini_{it} = \alpha_i + \beta_1\ln(BNP_{it}) + \beta_2trade_{it} + \epsilon_{it}, $$ where $Gini_{it}$ is the Gini-index from 0 to 100, $\ln(BNP_{it})$ is $\ln$ of the ...
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0answers
14 views

Variance estimation for Levy process

Let $(X_t)$ be a Levy process. It then holds that $$ E(X_{t+\Delta} - X_t) = \Delta \nu, \\ V(X_{t+\Delta} - X_t) = \Delta \mu, $$ under sufficient regularity conditions in terms of moments. For ...
0
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0answers
16 views

how to predict mean and variance of a variable using GMM

I identified a set of variables that are related to a variable X. I want to verify empirically if those state variables can predict and capture the first and second ...
2
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0answers
26 views

Estimator of true probability — understanding margin of error for very small probability

I have a coin whose probability of landing on heads when flipped is unknown, but could be anywhere between 0 and 100%. I want to flip the coin some number of times and estimate the true probability ...
0
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22 views

Estimating a parameter which itself is a sample from a parametric distribution

I am trying to model an engineering problem in the following way: Suppose $\theta_1$ is an unknown parameter lying in some set $A$, and let $\mathcal{P} = \{P_{\theta_1}: \theta_1 \in A \}$`be a ...
2
votes
1answer
39 views

Exact maximum likelihood estimation of MA(1)

I want to calculate the MLEs of the MA(1) model and for this purpose I have written the exact likelihood for the same. I built a programme in R for the log-likelihood, but it seems some problem in it ...
1
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0answers
7 views

How do I determining the exact percentile among a sample given the 10, 25, 50, and 90 percentiles

Background: I'm trying to provided employees or decision makers with comparative wages analysis based on national or regional wage estimates. I'm developing a tool to provide employees and clients an ...
0
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0answers
31 views

maximum likelihood for multivariate gaussian (covariance estimator)

Given the multivariate gaussian $N(\mathbf{\mu}, \mathbf{\Sigma})$, I want to get the maximum likelihood estimator for $\mathbf{\Sigma}$. I start with the log likelihood function $\ln p(\mathbf{X}) ...
0
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0answers
12 views

Nonparametric test for discovering a unimodal distribution?

I am doing a literature review. I want to count how many times a given HCI concept has been found to have some effect (strong, medium, weak or none, with negative effects that's an ordinal scale with ...
4
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2answers
32 views

What is the meaning of admissibility within a class, that every decision rule in a class is admissible in that class?

Suppose that I have that $X$ is a Poisson random variable with mean $\lambda$. Suppose a decision rule is to estimate $\lambda$ by using $\delta(Y) = aY$. Now, let $K$ be the class of all decision ...
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0answers
18 views

Estimates for a subset of observations : how to proceed

Please note that I don't know the name of what I am trying to do, so maybe there is a lot of theory on it, or questions I couldn't find. I am trying to estimate the value of a parameter in my model ...
0
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1answer
14 views

Bayesian minimum mean square error estimator

In Fundamentals of Statistical Signal Processing, Estimation Theory, by Steven M. Kay the author shows on p. 312-313 that the estimator $p(A\mid x)$ minimises the Bayesian mean square error when you ...
3
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2answers
124 views

Confusing confidence interval question from old textbook

Lets say an investigator reports a 95 percent confidence interval of 1 to 23 dollars per month in reduced utility bills for a randomly selected group of 50 customers who underwent training in ...
2
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1answer
63 views

what is bias and variance of an estimator?

I know what Variance is. But what is Bias? I just have problems to understand this what is written!
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1answer
54 views

Identification from minimum value of truncated distribution

Suppose that a given population is endowed with a pair of characteristics $T$ and $K$. Let's think of these characteristics as random variables $$(T,K) \sim \operatorname{BiNormal}((\mu_T, \mu_K), ...
0
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0answers
37 views

Estimating a normal distribution from three order statistics

I am interested in predicting a normal distribution, but not sure if this is possible. I do not have information on the mean or standard deviation. However, I know the range of values, let's say ...
0
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1answer
21 views

adjusting Kalman estimates for no data

I have a kalman filter like set up, when I get the current value of an observable process, and update my estimate of the state variable with it. However, my observations are non-uniform in time, and ...
0
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0answers
10 views

In factor analysis what is more stable sample to sample: regression coeffients or structural coefficients?

In Which matrix should be interpreted in factor analysis: pattern matrix or structure matrix? ttnphns remarks "Weak side of pattern matrix is that it is less stable from sample to sample (as usually ...
0
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1answer
37 views

Inventory Turnover Estimation

I have an inventory of real estate. Every period I am acquiring some new inventory and selling some items from the inventory. I would like to estimate the average waiting time it takes to sell an ...
1
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1answer
49 views

Panel data with country fixed effects

I am wondering about the estimation of a fixed effects model. It is just given in the paper that estimation is done via OLS with robust standard errors. Which method is meant by such explanation? Did ...
1
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0answers
32 views

unbiased estimate for household size

We have a population of N people. They live in households of varying sizes: 1, 2, 3, 4, etc. We are going to do a random telephone survey and ask them how big their household size is. What are the ...
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25 views

Parameters estimation of a normal distribution from noisy observations

Some reference links since I don't have enough reputation to post more than 2 links: "First post": Estimating parameters of a normal distribution from noisy observation of samples "Second post": ...
0
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1answer
23 views

How can I estimate a state-action matrix for q-learning when I do not have complete knowledge of all possible spaces and actions?

In this example of q-learning the "state-action" matrix R can be easily defined since there is a limited number of possible actions in each state and they are easy to identify. This example is very ...