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

Estimating errors for parameters from a nonlinear fitting procedure

I'm examining a code in C++ for a nonlinear fit. It is basically a Levenberg Marquardt routine you can find on Netlib or elsewhere. The last step is estimating the errors of the parameters that are ...
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9 views

Ordinal probit model tests

I have been reading ordinal probit model however one thing that i am not getting clear is that what standardized tests should be used pre and post estimation of ordinal probit model in STATA? Thanks ...
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22 views

Does the order of variables in a Markov Regime Switching model matter?

since Ive received feedback that my previous question was not well-recieved Ill just have to give it another shot. I am estimating Markov Regime Switching Models, and I am getting different results ...
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45 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} + ...
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11 views

Minimization of Lp-Norm based functional

Given some vectors $p_k$ I want to find a single vector $p_0$ and scalars $s_k$ such that $$ \sum \|p_k - s_k p_0 \|_p^p \to \min $$ I think for $p=2$ first one computes $p_0$ as the average of the ...
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1answer
31 views

How to estimate weights

I have a $y$ variable and 2 $x$'s ($x_0$ and $x_1$). I am told that the $y$ is a function of the 2 $x$'s. I know the functional form of this relationship, but want to calculate the weights/values of ...
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2answers
31 views

Distribution of p(x) in empirical model

I am having a hard time to exactly name what I am looking for (I am quite sure it already exists out there...) so I'll start with a concrete example: I have a population of discrete colours (red, ...
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5 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 $$ ...
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17 views

standard error of slope and intercept estimate

In the linear model $\mathbf{Y} = \mathbf{X}\beta + \epsilon$, where $\epsilon \sim N(0, \sigma^2 \mathbb{I})$, it is known the the standard error of the estimator $\hat{\beta}$ is given by ...
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1answer
18 views

Standard error for slope/intercept estimate in linear regression

Given a linear model $\mathbf{y} = \beta \mathbf{X} + \epsilon$, it is well known that the estimate for $\beta$ that gives the minimum residual sum of squares (RSS) is given by $\hat{\beta} = ...
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23 views

Why is estimating the standard error of an estimate that is itself the product of several estimates so difficult?

Singer and Willett (2003) write the following about estimating the standard errors of estimated survival probabilities within the context of discrete time event history models (e.g. logit hazard ...
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11 views

Estimating the number of units bought at a certain price in a stock

I need a way to know the value of my stock. Let $(x_1, \dots, x_n)$ be the quantity of the products $1$ to $n$ I have in stock, such that, for example, if I have $8$ units of the product $2$, $x_2 = ...
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1answer
27 views

Why are $M$-estimators NOT scale equivariant?

Consider the following location model. $$ x_i = \mu + u_i, (i = 1,\dots, n), $$ where $u_i$ are $i.i.d.$ with density function $f_0$. Hence, $x_i$ are $i.i.d.$ with density function $f_0(x-\mu)$. It ...
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8 views

Estimate parameters of two geometric Brownian motion processes over the time

Consider we have two geometric Brownian motion processes with given $\mu$, $\sigma$, and $\rho$ (one of the theses process starts at time zero and second one start at time equal $t$. I am wondering ...
2
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1answer
49 views

Estimator of moments

If $X_1,..,X_n$ is a random sample with density $f(x;\theta)=e^{-(x-\theta)}e^{-e^{-(x-\theta)}}$ ($x \in\mathbb{R}$) and $-\infty<\theta<\infty$, $\quad$i) Find the estimator of $\theta$ ...
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8 views

Significance of m parameter in m-estimate

To assign a probability to events that have not occurred yet(for a fixed set of events), one of the simplest methods is to use the m-estimator, which is defined as the following: $$Pr(A) = ...
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83 views

What is the name of the density estimation method where all possible pairs are used to create a Normal mixture distribution?

I just thought of a neat (not necessarily good) way of creating one dimensional density estimates and my question is: Does this density estimation method have a name? If not, is it a special case of ...
7
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1answer
72 views

How do you find the population size N based on the highest n values?

For example assume $N$ people performed a selection test like GMAT. Assume the distribution of the scores is a normal distribution (but parameters are not known). If you have a list of the $n$ highest ...
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20 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 ...
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0answers
64 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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17 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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2answers
24 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 ...
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1answer
43 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?
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22 views

How do I compute the CRLB for a linear model for system identification

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 ...
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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 ...
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1answer
61 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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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
23 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 ...
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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 ...
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62 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 & ...
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2answers
115 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 ...
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13 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 ...
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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 ...
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1answer
61 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 ...
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1answer
70 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 ...
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0answers
23 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 ...
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0answers
30 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
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1answer
121 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
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1answer
57 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 ...
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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 ...
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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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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
152 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 ...
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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 - ...
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2answers
123 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 ...
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2answers
45 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
27 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 ...
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14 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 $\mu\in\{0,1\}^d$ ...
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1answer
51 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 ...