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

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 ...
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3answers
44 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 BNP ...
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0answers
9 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 ...
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9 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
19 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 ...
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0answers
21 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
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1answer
33 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 ...
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6 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 ...
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0answers
24 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}) ...
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0answers
11 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 ...
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2answers
31 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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17 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 ...
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1answer
13 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
117 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
51 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
52 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), ...
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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 ...
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0answers
14 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 ...
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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 ...
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0answers
16 views

estimate the probability of randomly clicking answers in a survey [duplicate]

People are asked to choose their favorite color among 4 colors (e.g. red, green, blue, yellow) in a survey. Among m responses, x1 are red. If we know the proportion of people who choose answer ...
0
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1answer
36 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
46 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 ...
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0answers
31 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": ...
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1answer
17 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 ...
3
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0answers
24 views

Problem in estimating parameters by moments methods

I am working on one of the discrete probability distribution having pmf as $P(x)=\{p^{\log(1+x^c)}\}-\{p^{\log(1+(x+1)^c)}\},\quad 0<p<1; c>0; \,x=0,1,2,...$ The moments of the distribution ...
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1answer
39 views

Implementing Minimum distance estimation

Let $\mu$ and $\sigma$ be two parameters of interest characterising a normal distribution. From a theoretical model, I know that these two parameters are related to each-other according to ...
1
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0answers
37 views

observed data log likelihood and complete data log likelihood estimation

I have the following model. $p(z_{n}) = Categorical(\pi)$ $p(\pi) = Dir(\alpha)$ $p(x_{n}| z_{n}=k,\mu) = \prod_{d=1}^{D} {Bernouli(\mu_{kd})} $ $p(\mu_{kd}) = uniform(0,1)$ How can I find ...
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0answers
23 views

Marginal likelhood for Bayesian model estimation [closed]

When using marginal likelihood for Bayesian model assessment, is it natural to get a positive values or it should be only negative? what does it mean to get a positive values for the marginal ...
0
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0answers
10 views

How to select the thresold in Generalized Pareto distribution

I'm using generalized Pareto distribution to fit the tail data, I want to know is there any computational way to estimate the threshold parameter as we do in estimating the sigma et shape using MLE? ...
3
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1answer
48 views

How to down-weight older data in time series regression

In a regression fit of vectors varying with time $t$ $\qquad y \sim [x_t\ x_{t-1}\ x_{t-2}\ ...] \cdot [c_t\ c_{t-1}\ c_{t-2} \ ...] $ , how can one down-weight the older $x_t$ to model "older is less ...
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0answers
7 views

The estimator of variance of linear regression targets

In Section 3.2 of the book The elements of Statistical Learning (2ed), I read the text: Typically one estimates the variance $\sigma^2$ by $$ \hat{\sigma}^2 = ...
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0answers
10 views

The principle of getting the error bar of the MLE of the mean of some univariate Gaussian

I'm reading the book Information Theory, Inference and Learning Algorithms. In Section 22.1, the author gives an example of finding the MLE of the mean of an univariate Gaussian, and then obtaining ...
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0answers
19 views

Survival estimation goes crazy when I move all censored times to t=0

I have a simulated dataset with 1000 observations and Weibull-distributed survival time as outcome. A certain percentage $p_1$ of these guys belong to a risk group ($Z_i=1$ for risk group, $Z_i=0$ for ...
0
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0answers
14 views

Sample Size correction for Times Series

I have weekly time series data time Jan1-Jan7 Jan8-Jan14 Jan15-Jan22 . . . Dec17-Dec23 Dec24-Dec30 Each week there is sample of the total number of people who ...
3
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0answers
33 views

Comparing the performance of two classifiers using cross-validation

Consider the following excerpt (paraphrased, see sec. 4.6.3 for original wording) from Introduction to Data Mining (free chapter) by Pang-Ning Tan, Michael Steinbach, and Vipin Kumar. Suppose we ...
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0answers
15 views

Gaussian QMLE in estimating GARCH model

I am having some troubles understanding the estimation of a CCC-GARCH model (where the univariate GARCH models are GJR-GARCH(1,1)) by the means of Gaussian QMLE with the likelihood function of ...
1
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0answers
17 views

Under which assumptions is $\hat{x}_{MMSE}=E[x|y]$?

I've allways used MMSE estimators starting from the expected value of the conditional distribution $E[x|y]$ and I saw in Wikipedia that there were some weak regularity assumptions for this ...
0
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2answers
58 views

Why is smaller the p-value, larger is the significance? [duplicate]

I am trying to understand the concept of p-value. Wikipedia mentions: The p-value is defined as the probability, under the assumption of hypothesis $H$, of obtaining a result equal to or more ...
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0answers
19 views

Procedure for calculating a sampling distribution

I'm still trying to understand the basics of understanding the intuition of sampling distributions and calculating the sampling distributions of common estimators. For example, I understand the ...
2
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1answer
34 views

GMM Estimator of an Exponential Distribution

Suppose you have to calculate the GMM Estimator for $\lambda$ of a random variable with an exponential distribution. $$f(x) = \lambda \cdot \exp(-\lambda\cdot x)$$ with $E(X) = 1/\lambda$ and $E(X^2) ...
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0answers
26 views

Consistency and Unbiasedness Proof Examples [closed]

I was wondering if you have any suggestion on where to find done proofs of consistency and unbiasedness for estimators (apart from sample mean and variance which is trivial). If you have some it ...
1
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0answers
23 views

Problem with initial guess in Newton-Raphson iteration method

I'm working on estimating the four parameters of Exponentiated Modified Weibull Extension Distribution introduced by Sarhan and Apaloo (2013) with the Maximum Likelihood Estimation (MLE). Because the ...
3
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0answers
56 views

How to estimate single event probablitity based on data of aggregate event outcomes?

At a recruiting company, we have cases with $n$ applicants each, and each case may result in a successful recruitment or not. We'd like to be able to determine the expected value of a single ...
1
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1answer
26 views

change points/break points in nonlinear regression

I have a problem in which I am trying to estimate change/break points where the data has a linear portion (or semi-linear at least)and a nonlinear (actually an exponential) portion. Does anyone know ...
1
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1answer
23 views

Determine bias of estimator?

If I have a unbiased estimator, I may obtain another estimator through a reparametrisation. Say, if I have $\lambda$ for a sequences of iid exponentials, I have the unbiased estimator $\sum X/n$, and ...
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27 views

Is the sample mean a better point estimate of the population median than the sample median?

A beginner's question to check I've understood correctly. A basic stats textbook says: "The variance of the sampling distribution of the median is greater than that of the sampling distribution of ...
1
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1answer
25 views

Estimating a “true” value with a noisy number of additive noises

I want to recover an estimate of the "true" value of a variable from a small set of noisy observations (5–20). I have an a priori model describing the physical process that generates the ...
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0answers
17 views

Which likelihood function for ML estimate of continuous variable?

Let's say my data consists of the counts of the following words in a text. I can then estimate the probabilities of occurrences of these words using MLE: ...
8
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2answers
184 views

Comparison between Bayes estimators

Consider the quadratic loss $L(\theta,\delta)=(\theta-\delta)^2$, with prior given $\pi(\theta)$ where $\pi(\theta)\sim U(0,1/2)$. Let $f(x|\theta)=\theta x^{\theta-1}\mathbb{I}_{[0,1]}(x), ...