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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16 views

Kalman Filter to correct model simulation bias

I am working with a large scale deterministic model, which attempts to simulate CO2 emissions in different regions. When compared to historic data, the model output suffers from systematic biases. ...
3
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1answer
117 views

Doubts in linear regression

If a linear regression model has a constant term say 1 or 0.2, for example if the original model is $y(t) = 0.2 + ay(t-1) $, then what does this constant term imply? Will it hamper the estimates if ...
5
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1answer
77 views

Estimating $n$ and $p$ for Binomial distribution, repeated counting of partly hidden population

A brief motivation: $n$ critters live in an aquarium, where sadly they often hide in, under or behind things. When the aquarium is observed, each critter is only seen with probability $p$ ...
2
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1answer
32 views

Unbiased estimator for $P(X_1=1)$

If $ X_1, ... ,X_n$ are IID binomial with parameters $ n$ and $p, $ find an unbiased estimator for $$G(p)=P(X_1=1)=np(1-p)^{n-1}\, .$$ I need to find this estimator so I can apply Lehmann-Scheffé ...
3
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1answer
106 views

What location parameter is modelled by robust regression?

There is quite some number of ways how to robustly fit a linear regression model, e.g. using M-estimation based on Tukey's biweight loss or on Huber's loss, see e.g. Wikipedia. I got two questions ...
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1answer
30 views

Run Many Small or a Few Big Simulations to Estimate the Mean?

I was just running some simulations on tossing a coin given certain conditions, to test out some ideas I had. I was trying to find the ratio $\frac{\mathtt{successful\ tosses}}{\mathtt{total\ ...
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21 views
+50

Conceptual questions on state and parameter estimation

Parameter estimation of nonlinear systems unscented kalman filter ( paper and many others are categorized under semi-blind identification technique because the Authors say that the dynamics of the ...
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19 views

How do I determine the innovation term in an ARIMA equation?

I am not a statistics specialist : I had to take over the internship subject of another student to include it in mine. He was working with $SARIMAX$ models and I would like to import them in an ...
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2answers
178 views

Why is the geometric median called the $L_1$ estimator?

My question is simply, why is the geometric median called the $L_1$ estimator? This always reminds of $L_p$ spaces but the distance being minimized in the geometric median's definition isn't $L_1$ but ...
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16 views

Untransforming unbiased estimates

Suppose I have some measured experimental data and I want to fit it to a power law of the form $y=ax^b$. Suppose I transform the data to log-log space and then I fit a straight line of the form ...
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23 views

General theoretical properties of empirical Bayes estimates

I was wondering if someone could provide reference (if such exists) for the theoretical properties of empirical Bayes(EB) point estimates, in the sense of what can we say about their risk under ...
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20 views

Numerical estimation of MLE in Python — normal distribution and gradient is close to zero away from the mean

I am exploring how to model a data set using normal distributions with both mean and variance defined as linear functions of independent variables. Something like $\mathcal{N} \sim \left (f(x), ...
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1answer
43 views

Gaussian Mixture Model parameters from density

How do I estimate parameters of subpopulations in a 1D gaussian mixture model when I already have density (measured on a grid) of the mixture? All the algorithms I can find (like the well-known EM ...
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0answers
17 views

Can you combined two sources with difference variance to reduce error? [duplicate]

I have two samples of data each estimates of a position x, y with Gaussian noise. One source has a larger variance than the other. Is this source in any way useful ...
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1answer
33 views

Issues in estimation and plot

I am learning adaptive filters and testing the performance of using Least Squares and Kalman filter for parameter estimation for $y = X + \text{noise}$. The model is autoregressive AR(2) model $$y(t) ...
5
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1answer
65 views

Why are Winsorized random variables independent?

While studying trimmed mean I understood that if I have some random variables $X_1, X_2, .., X_n$ by ordering them and trimming, the variables are no longer independent. However it is said that "by ...
2
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14 views

how do you estimate the parameters of a system~(alpha,beta) in R?

Given a system made up of n different components who follow a Weibull distribution. we can easily estimate both the shape and scale parameters for each component. if the components forms a parralel ...
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1answer
71 views

Estimator (preferably unbiased) of $\ln (\text{E}[X])$

Given the distribution function of random variable $X$ I know how to estimate its mean. What would be an estimator (preferably unbiased) of $\ln(\text{E}[X])$ ?
3
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2answers
91 views

Normalization to non-degenerate distribution

I am reading de Haan's Extreme Value Theory (2006). In the discussion of distribution of sample maximum, he said "in order to obtain a non-degenerate limit distribution, a normalization is necessary". ...
6
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1answer
113 views

Comparison between MAD and SD

I am reading Huber's Robust Statistics (2nd). On page 2 and 3 he gave an example. The basic facts are summarized here. Let $(X_n)$ be a sequence of random variables and define two measures of spread ...
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1answer
43 views

Help with MLE regression

I have a data set containing two variables x and y. I want to estimate the parameters for a regression model. The regression ...
0
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1answer
38 views

A Kalman Filter for estimating z-scores?

I have been struggling to fit the following problem into a linear state space model for a Kalman Filter (KF). I'm having a hard time seeing what I'm doing wrong. I suspect I'm violating some law of KF ...
2
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0answers
23 views

Maximum Rank Correlation for panel data

Let $Z=(Y, X)$ be an observation from a distribution $P$ where $Y$ is a response variable and $X$ is a vector of regressors. Assuming the following model: $Y = F(X'\beta, u)$ where $X'\beta$ is a ...
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1answer
18 views

Estimating costs with extreme values

I am trying to estimate health care costs and I was wondering what the standard practice is for extreme values? By extreme values I mean I have a large portion of my costs being zero and a small ...
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17 views

Name for a problem where the unknown is a vector of integers and the data points are proportional to it?

I've got an unknown vector of integers I, an unknown constant c, and my data are cI + noise. The noise has mean 0. The problem is to estimate I. I know that it's possible, because if you had an ...
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18 views

Estimating number of intersections between point and polygons

I have a 2D plane (a large rectangle) with a finite size in the x and y direction, which is the field of my problem. The field is covered by $n$ smaller rectangles that are located randomly within ...
2
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1answer
42 views

MAP estimate of posterior parameters

I have a setup where the joint posterior is written as: $$ P(w, \lambda, \phi \vert y) = P(\phi) \times P(w \vert \lambda) \times P(\lambda) \times \prod_{i=1}^{N}P(y_i \vert w_i, \phi, \lambda) $$ ...
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11 views

How to do and interpret a generalized estimating equation

My study is looking at the effects of enclosure type (1 IV (penned v not penned)) on the stereotypical behaviours and interactions (2 DV's (counts)) of elephants, however using rain (yes/no) and high ...
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1answer
25 views

Consistency of unbiased estimator of error term variance in Multiple regression

Let $Y=X\beta+\epsilon$. We know that $\frac{e'e}{n-k}$ is an unbiased estimator of $Var(\epsilon)$, where $e$ is the vector of residuals, and $\epsilon$ is multivariate normal distributed in this ...
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0answers
16 views

Asymmetric Dynamic Conditional Correlation in Matlab

I need to interpret the results of the estimation of the A-DCC model by Cappiello, Engle and Sheppard, 2006, Journal of Financial Econometrics. I used the Matlab routines of the MFE Toolboox ...
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26 views

Robust estimation in SPSS generalized mixed models

I'm using mixed models in SPSS 19 to analyse dietary data. The mixed procedure is used because we have more than one measurement from many of the participants. My problem is that many of my dependent ...
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40 views

How to validate goodness of fit and forecasting quality of a model?

I am working on big data sets, which represent electricity consumption on power substation throughout the year. I have data every 10 minutes and multiple (and long) seasonalities. I have a daily, ...
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21 views

Estimating nested copula parameters in R

Using the R copula package, is there a built-in way to estimate the theta parameters of a nested Archimedean copula (ideally together with the marginals) based on empirical data? In the non-nested ...
5
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1answer
250 views

Name for the special estimate of the mean

During my masters studies, I heard about the following estimate of the mean: We take the minimal and the maximal value from sample and simply average them out. Does this estimate have any name? And ...
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18 views

Estimating probabilities of probability products

I have a process which generates a binary outcome from a multiplication of two independent stochastic binary inputs: Out = X1(P1) * X2(P2) . X1 and X2 generate a binary output with some probability, ...
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10 views

How many answers are needed to establish a Schelling focal point?

Consider Schelling's question about a focal meeting point for NYC in game theory (described in the second paragraph under Formulation in the Wikipedia entry). Schelling didn't say how many students ...
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2answers
99 views

Estimating the time for completing a sequence of actions

In short: suppose I have observations for times taken to do some action. I want to estimate, how long will it take to complete a sequence of actions. The estimate should minimize the mean absolute ...
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26 views

High dimensional model estimation with outliers

I have a set H of k m-dimensional hyperplanes in n dimensional space, where ...
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105 views

Least mean square algorithm – conceptual doubt

I have used the least mean square (LMS) algorithm to estimate a signal in the presence of high chaotic and random noise. MSE values in db at each SNR for the coefficients is positive even though I ...
5
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1answer
39 views

Restoring original distribution from noisy observations

There is a known set of pairs $(y_i, \sigma_i)$ such that $y_i = x_i + \sigma_i N_i$ $N_i \sim \mathbf{N}(0,1) $ for all $i$ $x_i \sim \rho$ for all $i$ where $y$ is observed value, $x$ is true ...
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1answer
43 views

Difference between estimation and learning

What is the difference between parameter estimation which includes system identification and learning in machine learning perspective? Let say the model is y= Ax. x is the input and y is the output. ...
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1answer
36 views

Geographic regression

I'm working on a project to estimate real estate and started with some classique techniques, such as linear regression etc. The obtained results are already going in the good direction, but to get ...
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1answer
44 views

Estimation of AR(1) process

Suppose the stochastic process ${X_t}$ satisfies the equation $$X_t=\phi X_{t-1} + Z_t \tag{A}$$ where $\phi>1$ and $Z_t$ is a white noise. Then iterating forward we get that the only stationary ...
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0answers
11 views

Parameter estimation of gaussian function kernel using cross-validation

I need to estimate (using cross-validation), the parameters $\sigma$ and $\lambda$ of the Gaussian kernel: $K_G(x,y) = \sigma^2 \exp{(-\frac{1}{2\lambda^2}\sum_{i,j}(x_{ij}-y_{ij})^2})$ where $x$ ...
2
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2answers
85 views

Which distribution for modelling duration of tasks?

Recently I was present with a task estimation technique. Instead of letting people rate a task for x - amount of hours, I let them discretize tasks into discrete sizes like small / medium / large / ...
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0answers
33 views

Intuition behind the Stein's paradox

I had read wiki and some sources. jmanton's blog, Wasserman's blog the background is that: You have Xi ∼ N(θi, 1), and we want to estimate the each θi. Where Xi are ...
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1answer
22 views

Covariance estimation

Suppose I want to estimate the covariance of $n$ $p$-dimensional iid random vectors $X_i$, where $n>p$. I've read in several places that if $n-p$ is small then the MLE covariance matrix estimate ...
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2answers
37 views

Why representation of AR process comes up in estimation

Let ${X_t}$, $t=...-2,-1,0,1,2...$ be a stochastic process that satisfies: $X_t=\rho X_{t-1}+\varepsilon_t$ with $|\rho|<1$ and $\varepsilon_t$ is a white noise. In that case, we also know that ...
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1answer
33 views

Why does maximum likelihood estimation not work in estimating signal in deterministic chaotic noise

I have few conceptual questions related to application of chaos in communications. In few application such as radar Chaotic signal reconstruction with application to noise radar system, cryptography, ...
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26 views

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)} & ...