Any statistical process which seeks to approximate an unknown value, such as a distribution, a point estimate (e.g. mean), or confidence interval.

learn more… | top users | synonyms

2
votes
1answer
39 views

Show that the value is, indeed, the MLE

Let $ X_1, ... X_n$ i.i.d with pdf $$f(x;\theta)=\frac{x+1}{\theta(\theta+1)}\exp(-x/\theta), x>0, \theta >0$$ It is asked to find the MLE estimator for $\theta.$ The likelihood function is ...
0
votes
0answers
13 views

How to find TP,FN,FP,TN in function ROC (Epi package) [on hold]

I have a question about how I can calculate TP,FN,FP,TN using ROC function (Epi library) to cut off point library(Epi) opis<-ROC(from=stan~pokaz, data=dane)
1
vote
0answers
28 views

Distribution of sample variance for non-normal random variable [duplicate]

For a sample of size $n$ of non-normal random variables $x_1,...,x_n$. Is it possible to know which distribution the sample variance estimator follows? Details: The distribution of $x_i$'s is not ...
2
votes
1answer
22 views

Estimation probability in related binomial distribution

I have two binomial experiments with an unknown probability - But i do know that the ratio between the probability in the first experiment and the probability in the second experiment - For example I ...
2
votes
1answer
49 views

What is the name of the distribution of unbiased sample variance for a sample from Gaussian distribution?

Suppose $X_i$'s are iid Gaussian random variables with mean $\mu$ and variance $\sigma^2$. The distribution of $\sum_i (X_i - \bar{X}_i)^2 / (n-1)$ isn't Chi square. What is its distribution called? ...
0
votes
0answers
8 views

Kernels determination in Gaussian Regression multiple input features

How can i choose a proper kernel for Gaussian Regression when i have more than one feature in my inputs? I am relatively new to this and all the lectures and most literature seem to have described ...
1
vote
0answers
19 views

Follow-on to “Training with the full dataset after cross-validation” - sequential parameter estimation

Background: Here is the background for the question, both the question itself and the answer given by Dikran Marsupial. Training with the full dataset after cross-validation? It asks about after ...
1
vote
0answers
27 views

Question about Lagrangian Multiplier (Gradient) Statistic of constrained GMM

I am trying to derive the Lagrangian multiplier statistic (GMM version) under a restriction. The question is given below The quadratic form is given by $Q_n(\theta,\alpha)=[m(\theta)', ...
1
vote
1answer
28 views

Missing data analysis software

Does any standard statistical software like R, SAS or SPSS have procedures or codes to analyze log-linear models for missing data in contingency tables using maximum likelihood estimation (or EM ...
0
votes
0answers
12 views

Plotting of density estimates in matlab [migrated]

Given the biometric match scores, I am required to plot the graphs of estimated densities of matching genuine and impostor scores. Following are the graphs I got for genuine and impostor scores ...
2
votes
1answer
41 views

How is lasso an M-Estimator?

The definition of an M-estimator is an estimator (from Casella and Berger) of the form $$\hat{\theta}=\min \sum_{i=1}^n \rho(X_i-\theta),$$ where $X_1,X_2, \cdots, X_n$ is the data for some function ...
0
votes
0answers
6 views

What is the meaning of “finite sample error control”?

I encountered this phrase while reading a paper which goes like this -- "These methods lack finite sample error control due to instability". Although it might not be important, the paper deals with a ...
4
votes
2answers
56 views

How does one interpret the distribution over parameters in bayesian estimation?

I am new to Bayesian estimation. The assumption that the parameters are random variables seems a little unsettling to me. For example when considering a model for data, what physical interpretation ...
3
votes
0answers
54 views

Unbiased estimator with minimum variance for $1/\theta$

Let$ X_1, ...,X_n$ be a random sample feom a distribution $Geometric(\theta)$ for $0<\theta<1$. I.e, $$p_{\theta}(x)=\theta(1-\theta)^{x-1} I_{\{1,2,...\}}(x)$$ Find the unbiased estimator ...
0
votes
0answers
22 views

Predicting stock returns - in a panel data specification or by using portfolio formation strategies?

I'm working on an empirical analysis where I try to predict stock returns using weekly data. Ideally, I would like to use a panel data model like the following: $$ ...
3
votes
1answer
66 views

Unable to understand derivation of Expectation Maximizaton

In Paper, System Identification using Symbolic Chaotic Sequence, Authored by A. Kurian and H. Leung download link under section II B, can somebody please explain ...
3
votes
2answers
125 views

How to estimate model with both linear and exponential parameters?

I have a theoretical growth function that can be perturbed by events, and I'd like to estimate the growth parameters as well as the perturbation, and the rate of falloff after that perturbation. I'm ...
0
votes
0answers
10 views

Estimating a vector from a rank-one symmetric matrix plus scaled identity

I have a problem regarding estimating a $M\times 1$ vector from a given $M\times M$ symmetric matrix. The known matrix is a scaled identity matrix with a rank-one update. I have some idea how to ...
0
votes
0answers
23 views

How many models I need?

I am doing an estimation using a bunch of sparse data. Suppose that I have a 100x100 grid and 20 data is available on this 2D grid. One solution is to use a determiastic method and estimate the other ...
3
votes
1answer
23 views

Estimate a proportion using priority sampling (I just made that up)

I have this idea in my head that is either bunk or has a name I don't know. (I'm not naive enough to think I'm breaking new ground here!) Here's my scenario: I would like to know the proportion of a ...
3
votes
0answers
78 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
votes
1answer
120 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
votes
1answer
91 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
votes
1answer
50 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
votes
1answer
109 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 ...
2
votes
1answer
31 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\ ...
2
votes
0answers
48 views

Difference between blind and semi-blind 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 ...
0
votes
0answers
21 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 ...
6
votes
2answers
183 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 ...
0
votes
0answers
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 ...
0
votes
0answers
32 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 ...
0
votes
0answers
37 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), ...
1
vote
1answer
47 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 ...
0
votes
0answers
18 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 ...
0
votes
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
votes
1answer
67 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
votes
0answers
17 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 ...
1
vote
1answer
75 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
votes
2answers
107 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
votes
1answer
115 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 ...
1
vote
1answer
44 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
votes
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
votes
0answers
26 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 ...
1
vote
1answer
21 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 ...
1
vote
0answers
18 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 ...
2
votes
0answers
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
votes
1answer
46 views

MAP estimate of posterior parameters

I have a setup where the joint posterior is written as: $$ P(w, \lambda, \phi \vert y) = P(\phi) \times P(w \vert \lambda) \times P(\lambda) \times \prod_{i=1}^{N}P(y_i \vert w_i, \phi, \lambda) $$ ...
0
votes
0answers
12 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 ...
0
votes
1answer
26 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 ...
0
votes
0answers
25 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 ...