"A rule, method, or criterion for arriving at an estimate of the value of a parameter."

learn more… | top users | synonyms

0
votes
0answers
16 views

Conceptual doubt in prediction intervals in time series forecasts

Background: In the second chapter of Dr. Hyndmans book on Forecasting, he mentions the use of prediction intervals to define a range of possible values demand can take in a future interval. The ...
0
votes
0answers
22 views

Does removing variables decreases the variance of the random error estimator?

Lets say if have a regression of $y= f(x_1,x_2,x_3)$; if I remove $x_2$,$x_3$, I'll get regression of $y=f(x_1)$ By removing these variables, did I decrease variance of the random error estimator? Or ...
0
votes
1answer
45 views

constant $times$ distribution

I know that if $U\sim\chi^2(k)$ then $aU\sim \Gamma(k/2,2a)$ for $a>0$. But i read about the estimator and its distribution $$\hat{\sigma}_k^2=\frac{1}{2k}\sum_{i=1}^k ...
0
votes
0answers
20 views

M-Estimation with Biases

I am currently trying to solve an m-estimation problem with a bias component. To illustrate, I will use a quick example. Let's say you have a laser range finder at position $x$ and a wall at position ...
0
votes
0answers
15 views

In which languages can I estimate a VMA model?

In which languages/environments are there tools to estimate a VMA model of a given order? That is, given $q\in\mathbb{N}$ and a multivariate time series $y_t\in\mathbb{R}^d$, $t=1,\dots,T$, a function ...
0
votes
0answers
25 views

What is the requirement for Kalman filters

I have few conceptual Questions about Kalman filters and their role. When classical estimation techniques like Maximum Likelihood estimation exists which assumes some information such as the states ...
0
votes
2answers
42 views

How can maximum likelihood be used to estimate parameters for a Weibull distribution? [duplicate]

Consider the following survival data (cumulative): Month 0 - 100% Month 1 - 50% Month 2 - 33% Month 3 - 25% Month 4 - 20% (meaning 20% of all initial units have survived by the end of Month 4) ...
1
vote
1answer
69 views

What is the difference between bias and residuals?

I'm aware of the bias variance trade off. Intuitively I understand how as the model becomes more complex the variance decreases and the bias increases, after a certain point. But I don't really ...
1
vote
0answers
10 views

Need help understanding this algorithm for a robust estimator for Geom. dist

I am trying to figure out a way to estimate the parameter for a Geometric distribution, using a random sample that is influenced by outliers. Searching through previous questions/answers, I saw this: ...
0
votes
0answers
31 views

Establishing consistency

I need to establish the (weak) consistency of an estimator of the mean, $T=a+b\bar{X}$. I tried to apply Chebyshev's inequality, but I couldn't do much because the parameter that subtract in the ...
0
votes
0answers
9 views

Empirical Density of Model Parameters

Given a parametric model, what are some methods to determine the distribution of (uncertainty in) its parameters? It seems like the naive way is as follows. Let's say we have not just one random ...
0
votes
1answer
33 views

estimators with singular covariance matrix

Suppose I have 2 vectors of random variables $\boldsymbol\theta_1 \in \mathbb{R^n}$ and $\boldsymbol\theta_2 \in \mathbb{R^m}$ with asymptotic covariance $\Sigma_1$ and $\Sigma_2$ respectively. I want ...
1
vote
0answers
29 views

How to derive an estimator for the parameter of a continuous uniform distribution

$X_1, X_2,\dots.,X_n$ are i.i.d. random variates drawn from a continuous uniform distribution over $[0,\theta].$ The sufficient statistic is denoted $\max$. I want an estimator $e$ of $\theta$ that ...
19
votes
1answer
277 views

Shrunken $r$ vs unbiased $r$: estimators of $\rho$

There has been some confusion in my head about two types of estimators of the population value of Pearson correlation coefficient. A. Fisher (1915) showed that for bivariate normal population ...
0
votes
0answers
14 views

formal tests for ordinal probit model

What are the basic post estimation tests for an ordinal probit model? How do we check parallel line assumption for ordinal probit model? the omodel comand of stat only works for probit model, i have ...
0
votes
0answers
48 views

Estimator of The Mean of the Ratio of Uniformly Distributed Variables

Given two random variables, $ X \sim U \left[ {\mu}_{x} - \frac{{l}_{x}}{2} > 0, {\mu}_{x} + \frac{{l}_{x}}{2} \right] $ and $ Y \sim U \left[ {\mu}_{y} - \frac{{l}_{y}}{2} > 0, {\mu}_{y} + ...
0
votes
0answers
6 views

Worried about hidden costs of using this loss function to fit weights

I have the following model: $$\frac{Y}{T} = f(X \beta)$$ where beta is a vector of weights, and Y and T - Y are greater than 0. I want to fit the $\beta$ vector using the loss function $$ ...
1
vote
0answers
152 views

Summary of estimator properties (consistency, bias, sufficiency, etc.)

I've read about various properties of estimators, but I'm wondering if there's some source with a summary (maybe a list, table, or graphic) of the properties for different kinds of estimators. ...
1
vote
0answers
36 views

Derivation of Variance for formula of Cohen's d statistic

Cohen’s d is one of the most common ways we measure the size of an effecthttp://en.wikiversity.org/wiki/Cohen%27s_d. Cohen’s d simply a measures the distance ...
2
votes
1answer
62 views

Maximum likelihood of constrained distribution

A random variable $X$ is represented by the following CDF: $F(x)=(1+\frac{1}{x^2})^{-\beta}$ , $x\in(0, \infty), \beta>0$ Question: How do you get the MLE of $P(X>1)$ for the distribution? I ...
2
votes
1answer
61 views

Density estimation and histograms

This is an excerpt from BW Silverman's Density Estimation for Statistics and Data Analysis: The oldest and most widely used density estimator is the histogram. Given an origin $x_0$ and a bin ...
0
votes
0answers
80 views

Practical application of Cramer-Rao lower bound to calculate the variance of estimator

I would like to use the Cramer-Rao lower bound to help me estimate the variance of my maximum likelihood estimator, across a range of different samples of data. My question is, how do I do this ...
1
vote
1answer
41 views

Confidence interval for a function of the MLE

I am studying an old assignment in which I have calculated the MLE for a sample from an exponential distribution. It then gives the formula for the median of an exponential distribution ...
2
votes
1answer
80 views

Why are inf and sup used in the definition of minimax estimators?

An estimator $\hat{\delta}$ is minimax iff $$\sup_\theta R(\theta,\hat{\delta})=\inf_\delta\sup_\theta R(\theta,\delta)$$ or in english iff out of all estimators it has the least maximum risk. For ...
1
vote
1answer
69 views

Going from derived estimators to their implementation in software

Estimation and Inference in Econometrics by Davidson and MacKinnon (1993 edition, the older one) on page 552, ch 16.3 'Covariance Matrix Estimation' states: "Consequently, the matrix \begin{eqnarray} ...
0
votes
0answers
22 views

Efficient implementation of this estimator when software runs out of memory

Further to the excellent discussion and answers on projection matrices here, I am wondering if there are perhaps more gains to be made when implementing this estimator \begin{eqnarray} (X' P X - ...
4
votes
2answers
147 views

Speeding up hat matrices like $X(X'X)^{-1}X'$ (projection matrices) and other aspects of custom-built estimator when software runs out of memory

Is there a way to speed up $Z(Z'Z)^{-1}Z'$ type matrices? I am implementing the expression below directly using a matrix language and my program frequently crashes while if I run OLS on them using a ...
0
votes
1answer
89 views

Normal method of moments derivation explanation of Algebra step

In deriving normal estimators using method of moments, why does the below equality hold? $$ \frac{1}{n} \sum X_i^2 - \bar{X}^2 = \frac{1}{n} \sum (X_i - \bar{X})^2 $$ This is from Example 7.2.1 from ...
-2
votes
1answer
47 views

What is the Mean Squared Error for this estimator?

I understand that to find the MSE, i must find the variance and bias and add them together. I've had trouble calculating either of these so a breakdown would be immensely helpful. The estimator is: ...
0
votes
0answers
30 views

Dependence of PDF of LLR of symbols

I have a system model with $y=hs+\sum_i^n gx+n$ where h is rayleigh fading desired channel, g is interfering channel x is interfering symbols. $\hat{s}=w*y$ where w is MMSE filter. On what factor pdf ...
0
votes
0answers
19 views

Finding a consistent estimator mathematically

This is my first post on this website so hopefully everything will go smoothly. Let me first ask the question, then go over my problem. Q: Suppose that we are given $({X_{1i},X_{2i}})$ which is a ...
-1
votes
1answer
30 views

Estimator $\gamma = \sum a_i\times x_i$ , where $X_i \sim \exp(t_i \theta )$ Show $\gamma$ is unbiased if $\sum a_i/t_i = 1$

I'm getting really confused with the estimators in this question! $X_i \sim \exp(t_i \theta x)$ where $t_i$ are positive constants. The MLE for $\theta = \frac n{\sum t_i x_i}$ And $\phi = ...
3
votes
1answer
71 views

Does MCD estimator suffers from swamping effect?

If there are multiple outliers in the data set, the Mahalanobis distance suffers from masking and swamping effects. In order to rectify this problem, robust estimation of location and scale, such as ...
3
votes
0answers
34 views

Fixed parameter estimates of parent factors in a nested design

Summary: What is happening with parameter estimates of factors that are the 'parents' of nested factors? Data: My analysis involves testing the effect of different parameter settings for automatic ...
3
votes
2answers
144 views

Self-study: Finding the maximum likelihood estimates of the parameters of a density function

Consider a random sample $x_1,x_2,...,x_n$ from a newly-generated distribution, whose probability density function is given below \begin{equation} f(x|\alpha,\beta,\sigma)=\frac{1}{\Gamma \left( ...
3
votes
1answer
42 views

How to prove that the permutation of the points are the minimal sufficient statistics for Cauchy distribution?

I see this everywhere that the permutation of the samples $X_{(1)}, ..., X_{(n)}$ is the minimal sufficient statistic for the Cauchy distribution [1]. It is clear that it is a sufficient statistic,but ...
0
votes
1answer
114 views

Horvitz-Thompson estimator for two-stage cluster sampling

So I want to apply the Horvitz-Thompson (H-T) estimator to two-stage cluster sampling. The H-T estimator is defined as: $$\sum\frac{Y_i}{\pi_i}$$ where $\pi_i$ is the probability of including the ...
0
votes
0answers
14 views

Multivariate Generalization of (Fisher) Efficiency Ratio

Fisher defined efficiency as the ratio of variance of the most efficient estimator to the variance of the estimator in question. The Cramer-Rao bound allows easy computation of the variance of the ...
0
votes
0answers
17 views

Derivation of description length

In class, our professor posted the following: We will discretize $\theta$ (some model) into $1/\sqrt{n}$ distinct values. Intuitive argument: with $N$ data points, our estimation error for $\hat ...
2
votes
0answers
25 views

linearization of an estiamtor

Suppose we have two variables $x$ and $y$ defined in some population, with all values of $x$ known. A Poisson sample is drawn, with corresponding inclusion probabilities $\pi_k$ that are proportional ...
2
votes
0answers
41 views

Unbiased estimator of the variance [duplicate]

I am going through the book The Elements of Statistical Learning and I'm finding it extremely terse. I have a background in probability but not statistics so perhaps that is why. Anyway, in Chapter 3, ...
0
votes
1answer
60 views

Posterior mode estimator unchanged under coordinate transformation?

I'm looking at a data set where the posterior mode has noticeably less "bias" than the posterior mean and posterior median, and somewhat less error. However, the posterior mode is not invariant under ...
0
votes
0answers
24 views

Source of least square estimator of Poisson parameter

I have $X \sim \text{Poisson}(\theta)$ I need to see how least square estimator of $\theta$ is obtained. Is there anything online showing that?
1
vote
0answers
25 views

Risk in density estimation: grasping the definition

When generalizing estimators to an entire function what is the space in which we perform the integral to obtain the expected value (with respect to this function)? For example, when estimating ...
1
vote
1answer
88 views

What are the implications of estimating a covariance matrix from a correlated sample?

Given a sample of $n$ independent observations $x_1,...,x_n$ (where $x_i$ are $p$-dimensional column vectors), the $p \times p$ sample covariance matrix is defined as ...
1
vote
1answer
44 views

Pointwise probability limit

Suppose we have a joint distribution of a random sample $(y_n,x_n)\in R^2$: $$ y_n = \beta_0 x_n + \epsilon_n $$ and the estimator $$ \hat \beta = argmin_\beta \frac{1}{N} \sum_{n=1}^N(y_n - \beta ...
0
votes
0answers
58 views

Finite variance of harmonic mean estimator when samples are bounded

Harmonic mean estimator is notorious for the possibility of having infinite variance. Now I want to show that it has finite variance when samples are bounded. I am wondering whether my following ...
1
vote
1answer
96 views

Generalized minimum chi-square estimators?

I need to implement the generalized minimum chi-square estimators (alternative to L-moments method and maximum likelihood estimate (MLE)) for estimate the parameters of the gamma distribution. My ...
1
vote
1answer
44 views

Deriving the formula for the mean of a stratified sample

The formula for the mean of a stratified sample $\bar Y_s$ is: $$\bar Y_s = \frac 1 N \sum_i N_i \bar Y_i$$ where $N$ is the sample size for all strata, and $N_i$ and $Y_i$ are the sample size and ...
0
votes
0answers
38 views

Help in calculating OLS estimators under certain constraints/modifications

I am new to these forums and to econometrics as a whole. I was hoping someone would be able to give me a nudge in the right direction with this problem. I've done extensive research both online and in ...