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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42 views

How does the following statistics work?

How come a college could had 60 percent of 6 year graduation rate and total 14000 undergraduates accept 2500 new transfer student each year while the transfer out rate is 20 percent? Also, Does it ...
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50 views
+50

Likelihood and sufficient statistics

a)Find the maximum likelihood estimador for $a$ in the density $f(x;a)=\frac{2}{a^2}(a-x)I_{(0,a)}(x)$. b)Is it a sufficient statistics? I did $$\prod f(x;a)=\prod \frac{2}{a^2}(a-x)I_{(0,a)}(x)$$ ...
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0answers
63 views
+50

Probability distribution for a proportion based on (continuous) quantities

I have a problem related with probability distributions and parameter estimation, which comes from a real case. I would be very grateful if you could help me. Let us suppose that we have a continuous ...
3
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1answer
28 views

Estimating bias in surveys

I run into the following problem on a job interview, and am still wondering what is a principled way to solve it. I think the problem is general enough that will hopefully have enough educational ...
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1answer
19 views

Why is $\sin(\theta)$ not U-estimable in this example?

For completeness I give the definition of being U-estimable: An estimator $\delta$ is called unbiased for $g(\theta)$ if $E_{\theta} \delta(X) = g(\theta) \ \forall \theta \in \Omega $. If an ...
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1answer
17 views

Log likelihood for inverse gamma

For a gamma distribution, the answer to this question shows that you can just use the log of the gamma distribution density function. Is the same true for inverse gamma? It is the same as the log of ...
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0answers
11 views

VECM+GARCH two-stage estimation

Supposed I have a system of cointegrated time series. The conditional mean model is a vector error correction model (VECM). The conditional variance model is a multivariate GARCH (MGARCH) model. For ...
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1answer
23 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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22 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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1answer
23 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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0answers
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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0answers
12 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 ...
2
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2answers
32 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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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 $$ ...
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0answers
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
22 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} = ...
2
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1answer
24 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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0answers
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 = ...
1
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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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0answers
9 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
51 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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0answers
9 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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0answers
84 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
78 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 ...
2
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0answers
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
66 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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0answers
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 ...
2
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2answers
25 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
44 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
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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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
votes
1answer
62 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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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
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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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 ...
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0answers
65 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
116 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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0answers
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 ...
0
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1answer
63 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
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
122 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 ...
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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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
155 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 ...