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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9 views

Describing Differences between Two Inferred Populations

I am interested in the size of an animal in two populations, and found reliable estimates of the population provided by NOAA. The data was in the form of estimated total population within discrete ...
0
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0answers
42 views

Maximum likelihood method vs. least squares method

What is the main difference between maximum likelihood estimation (MLE) vs. least squares estimaton (LSE) ? Why can't we use MLE for predicting $y$ values in linear regression and vice versa? Any ...
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13 views

Using the terms significance, probability or likelihood, in connection with estimators

Imagine a number of variates $x_i$, and a number of processes $P_k$ which depend on these variables, in an unknown way (ie no clear cut formulas to work with). Now consider the scenario where you ...
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19 views

What are the odds of having the same Lawyer make a mistake in two wills involving the same person? [on hold]

A lawyer made mistakes in my will and were caught while I was alive to have it fixed and then a loved one died and it turns out the very same lawyer made a mistake in his will that the deceased can't ...
0
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0answers
23 views

What are the odds of having 2 windows shot- one facing the west one year and another structure window the following? [on hold]

It is a small rural community with fields between our house and a hedgerow between us and the neighbors to the north, and different neighbors across the street with a field. It was always assumed ...
2
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2answers
17 views

Piecewise-constant density estimation

I came across the term "piecewise-constant density estimation" in a paper and haven't been able to find a definition for it online or in my textbook resources. No example was given in the paper ...
3
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1answer
37 views

More than one unbiased estimator for a single unknown parameter?

Is it possible to have more than one unbiased estimator for a single unknown parameter?If "Yes" then how and if "No" the why?
2
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0answers
19 views

How do I compute the CRLB to show if the estimator is indeed MVU

In system identification or parameter estimation, various input signals are used for exciting the process models. I am interested in parameter estimation of time series model using pseudo random ...
0
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0answers
12 views

What is the effective kernel for smoothing methods?

I'm learning different smoothing methods and the term "effective kernel" came up and I don't really understand it. By definition, for a smoothing method, the vector of estimates ...
6
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1answer
53 views

Gaussian Mixture and Method of Moments

Given solely the first $n$ moments $m_1,\dots,m_n$ of a random variables $X\in\mathbb{R}$, I was wondering whether there exists a direct methodology to approximate $X$ with a Gaussian Mixture ?
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20 views

arima-garch firstly arima part failed lm test but still couldcontinue the garch estimation [closed]

I saw a paper which said even if it fails the lm-test, it still could continue to do the garch estimation, and it said it was according to the book "GARCH Models structures, statistical inference and ...
0
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0answers
19 views

estimating the probability density function of a random variable

I have a random variable $X$ that is a sum of two non-independent random variables $X_1$ and $X_2$. Since $X_1$ and $X_2$ are non-independent, then convolution theorem cannot be used to find the pdf ...
2
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1answer
22 views

On FIML assumptions

In Hayashi's Econometrics, page 529, he states one of the assumptions we need for the FIML estimator. My doubt is in the third line of point 1). He says that the vector ...
0
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0answers
9 views

The sample variance is an inefficient estimator of the conditional variance in a t-GARCH model?

Harvey states in this paper (2008) at the end of the second page that: "The possible inappropriateness of letting $\sigma^2_{t|t-1}$ be a linear function of past squared observations when $v$ is ...
0
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0answers
59 views

How can the R-matrix in a mixed model be estimated?

In Henderson's Mixed Model equation: $y = X\beta + Zv + \epsilon$ where the joint variance of v and the error term is: $Var\begin{bmatrix} v \\ \epsilon \end{bmatrix} = \begin{bmatrix} G & ...
2
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2answers
109 views

Ax = b. How can I estimate A, given multiple data vectors of x and b?

I have a problem and I believe there must be a machine learning technique to solve it, but I am new to machine learning and I have no idea where to start. So, I have multiple multivariate parameter ...
0
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0answers
12 views

Parameter estimation in generalized linear models

I have a bunch of questions on parameter estimation in GLM. They are all inter-related. I have tried to maintain a logical sequence of questions in the following. Bear with me, if the order doesn't ...
0
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1answer
62 views

Maximum a posteriori estimation with one single training example?

I am doing maximum a posteriori (MAP) to estimate $\mu$ and $\sigma$ with $N$ samples drawn from $\mathcal{N}(5, 1)$. The priors that I place are $\mu\sim\mathcal{N}(5, 1)$ and ...
0
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1answer
58 views

A Simple Regression Model for Our Experiment? [closed]

We know, In statistics, simple linear regression is the least squares estimator of a linear regression model with a single explanatory variable. In other words, simple linear regression fits a ...
0
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1answer
69 views

uniform distribution with density function? [closed]

If $0.3,0.2,0.8,0.3,0.4$‌ are found from one random instance with uniform distribution with following density function, We need to find $\theta $ estimate with Method of moments. how should we do ...
0
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0answers
21 views

Showing a variance estimator is unbiased

I am trying to show that the variance estimator $ \hat{\sigma}^2 = \sum_{i=1}^{N}(X_{i}^{2}+ X_{i}X_{i-1} + X_{i+1}X_{i})$ is unbiased. $E(\hat{\sigma}^2) = \sigma^2$. I know that ...
0
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0answers
27 views

Estimating parameters of Dirichlet distribution

This is a very basic question but after reading few documents I found online I am a bit confused about Dirichlet parameter estimation. My data is multinomial. I have my Dirichlet prior and I would ...
2
votes
1answer
119 views

Conceptual question on log-likelihood value

I am trying to implement the log-likelihood expression Eq(7) from the paper, Parameter Estimation for Linear Dynamical Systems (1996). Re-writing, For the model, $h(t) = \mathbf{A^T} h(t-1) + ...
3
votes
1answer
51 views

Ranking batters by average when number of observations (innings) vary

This is my first post here and I'm new to this area so please forgive me if I'm asking a naive question. I want to rank a number of batsmen (e.g., in cricket) by their skill. I'm planning to use ...
0
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0answers
16 views

hedonic model: estimating coefficients for variables not used in the regression

I'm trying to estimate the value of a real estate upon its characteristics. To do so, I'm using the Hedonic Model and I'm doing the regression using ...
2
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0answers
61 views

How many people initially had apples?

Story problem: Assume 10 apples are distributed across $X$ unknown people, where each person has at least one apple. For each apple a biased coin is flipped to see if that apple should be kept or ...
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0answers
8 views

Determining a scaling parameter for estimating integer measure form continous data

I need to scale continuous data before rounding it. The measures are a continuous estimate of count. And I want to minimize the error in rounding. Essentially I'd like to be able to determine x from ...
6
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1answer
151 views

What is shrinkage?

The word shrinkage gets thrown around a lot in certain circles. But what is shrinkage, there does not seem to be a clear definition. If I have a time series (or any collection of observations of some ...
1
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1answer
67 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} ...
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21 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
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2answers
120 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
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2answers
40 views

Computationally efficient Gaussian MAP estimation algorithm in MATLAB

I have a MAP estimation model for a Gaussian prior and i.i.d Gaussian noise: $$y=x+n$$ where $x\sim\mathcal{N}(0,\Sigma)$ and $n\sim \mathcal{N}(0,\sigma^2I)$. The MAP estimate is given by $$ ...
2
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1answer
21 views

Suggested method for estimating door counter stats when data is lost

I'm wondering if you have any advice about a methodology to use to estimate "door counter" stats (i.e., an automated count of visitors to our organisation, based on "break beam" door counters ...
2
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106 views

Help in formulating the log-likelihood expression for AR model

An IIR system is excited by a signal $z_n$ described as follows: $z_n$ is the binary input to the system. The state vector $\mathbf{z_n} = [z_n,z_{n-1},\ldots,z_{n-p+1}]$ and $\mathbf{z_n}$ are the ...
0
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0answers
12 views

How to apply AIC to a situation where the mean of a multivariate normal is a 0-1 d-dimensional vector with exactly k 1's

I am trying to apply AIC to estimate mean in the following case: Let us consider that I have $n$ random variables $X_1, \ldots, X_n$, drawn i.i.d. from a normal distribution of mean $\mu\in\{0,1\}^d$ ...
0
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1answer
49 views

Bootstrap and MonteCarlo Method

I am trying to make sense of the bootstrap method. I am studying on Rice, "mathematical statistics and data analysis" Here it is its explanation of the bootstrap method: Imagine for the moment ...
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0answers
6 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
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1answer
29 views

OLS parameter estimation of an expression?

During my research for a class, I came across a paper that said they estimated an equation using OLS. But the parameter they were estimating appeared to be an expression that looked like this (not the ...
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24 views

Methods of Proving that a UMVUE does not exist?

Are there efficient methods of showing when a UMVUE does not exist? I can think of the trivial case when no unbiased estimators exist at all. But that's not really interesting. I feel like this ...
2
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2answers
52 views

How might Google go about estimating and updating traffic speeds?

This is, I guess, a specific example of a wider class of problem, one to which there must be a well-established solution, but which I, as a relative layman when it comes to statistics have thus far ...
0
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1answer
25 views

Deriving the common LIML estimator from first principles

David Hendry (1976) comments that deriving the LIML estimator is hard. I tend to agree. Guido Imbens has a nice expression here which reads \begin{eqnarray} \hat{\beta}_{LIML} = (X'(I - \lambda M_Z) ...
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0answers
18 views

Loss function for rank deficient covariance matrices?

I'm trying to compare the efficiency of different estimators of the covariance matrix of a particular type of multivariate normally distributed data. This comparison, as well as the estimation process ...
0
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1answer
40 views

Difference between restricted and unrestricted parameter space in MLE

I searched on the internet but I could not find any clues about my question. Can anyone just simply tell what is the difference between restricted and unrestricted parameter space in MLE? I have used ...
0
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1answer
22 views

Confidence interval and confidence region

Could you please tell me what is the difference between confidence interval and confidence region in the following sense? For example, we have s multiple linear regression model. For individual ...
2
votes
1answer
31 views

mle estimate for standard deviation of t-distribution

For a Student-t distribution, $t_{\nu}\left(\mu,s^2\right)$, let $\hat{s}$ be mle of scale and $\hat{\nu}$ be the mle of degrees of freedom. Functional invariance of mle implies that any linear or ...
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0answers
34 views

Generalised Tobit for clustered data (type 2?)

I would like to make a Tobit estimation where my dependent variable is stadium attendance, but there are observations from 18 different stadiums (different capacities). My thoughts are it may be type ...
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0answers
37 views

Huber's M estimator for contaminated Gaussian noise

Huber discussed in this seminal paper "Robust Estimation of a Location Parameter" link that if we have some observations $x_i$ as follows: $$y_i = \theta + \nu_i, ~~i=1,\cdots,N, \tag{1}$$ where ...
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0answers
16 views

Fisher information matrix of an arbitrary statistic

I have a proof (that is a bit long) that shows that for a single parameter $\Theta$, $J_\mathbf{X} (\Theta) \geq J_\mathbf{T} (\Theta)$ where $J_\mathbf{X} (\theta)$ is the fisher information of the ...
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0answers
16 views

Fitting multiple power laws, Zipf's law in the real-world

As a preface, the following questions are related: How to calculate Zipf's law coefficient from a set of top frequencies? How to estimate parameters for Zipf truncated distribution from a data ...
0
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1answer
52 views

Time Series Unobserved Components Model

I have real price data for 55 years and want to study its trends. for this i am trying to estimate the Unobserved Components (UC) Model. Which software will be better eviews or stata? Also what are ...