Any statistical process which seeks to approximate an unknown value, such as a distribution, a point estimate (e.g. mean), or confidence interval.
0
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36 views
Linear mixed model estimated means
I am trying to determine how to get SPSS (19.0) to give out estimated means for my interaction. To preface, my analysis has 3 groups (group a, b and c) and each group was measured at 5 time points. We ...
0
votes
0answers
62 views
A special case of GMM estimation in R
I want to estimate the forward looking version of the Taylor rule equation using the iterative nonlinear GMM:
I have the data for all the variables in the model, namely (inflation rate), ...
0
votes
2answers
43 views
difference in training and testing procedure of model
Can anyone please tell me the difference in training and testing of a model. I have developed 5/6 different single pass online learning algorithm (ets, ets+, evolving fuzzy modelling, SOFNN, ...
0
votes
2answers
269 views
Lewandowski algorithm demand forecasting
I came across the Lewandowski method of demand forecasting in JDA Demand. Please help me understand at a high level the methodology it uses. I found a paper by Robert Hyndman titled
"A state space ...
1
vote
0answers
37 views
ARMA MLE - matrix setup
I am trying to estimate ARMA(2,1) series parameters via ML, but unfortunatelly I am confused of setting up Matrix "Gamma" . I have seen plenty of articles regarding this, but it seems like this an ...
1
vote
0answers
64 views
Restricted least squares: condition is that the parameter vector is greater or equal zero
I only found a example in which the constraind on $\beta_i, \ i=1,...k$ would make them sum up to one as well introduces a constraind such that all $\beta_i$ are all greater or equal zero. Since I ...
0
votes
0answers
17 views
Can the kernel-smoothed hazard rate be defined for times greater than the largest death time?
I am trying to follow the book "Survival Analysis", and here's a summary of the concepts on hazard rate estimation from sas.com
For the ALL group, the largest observed time was $t_D=662$, while an ...
-1
votes
2answers
92 views
Estimation of Density Function from a Transformed CDF [closed]
Suppose I can observe $x_1,...,x_n$ as the realization of the random variables $X_1,..,X_n$. Using $x_1,...,x_n$, I can estimate the empirical cumulative distribution function (CDF), ...
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0answers
39 views
How to estimate a distribution?
Suppose I have estimated the discrete income distribution for Maryland, and the average distribution for the U.S. What is the algorithm or method to estimate the income distribution for Pennsylvania, ...
0
votes
1answer
39 views
Estimating the number of Twitter users that drive to work
How would I go about estimating the number of active Twitter users that drive to work each morning worldwide?
What data would I need to know, and how would I approach this problem using those data ...
0
votes
1answer
58 views
How to check the distribution of the given data
I am working on time series. I have a set of data which I would like to use for estimation. Can some one tell me how to find under what distribution the data I have goes in. I tried plotting using
...
2
votes
2answers
155 views
Bayesian parameter estimation of a Poisson process with change/no-change observations at irregular intervals
Consider a Poisson process with unknown parameter $\lambda$.
We perform a sequence of $n$ observations at intervals $\overline{t}=t_1,\,t_2,\,\dots,\,t_n$. Each observation is a binary variable $x_i$ ...
3
votes
1answer
86 views
Size of a test and level of significance
What is the difference between the two and why must the level of significance be always higher than or equal to the size of the test?
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0answers
105 views
Bootstrapping Methodology
I have this bootstrap setting:
Given $n$ vector-valued statistics (each statistic is a vector) of dimension $r \times 1$, I generated $1000$ bootstrap samples and then generated an estimate of each ...
4
votes
2answers
75 views
Changing sign estimate manually
validated readers,
Is someone allowed to manually change sign of an estimate (obtained through a OLS), if this is supported by an underlying theory?
My first idea was that this is basically a ...
1
vote
1answer
101 views
Estimated error variance $\sigma^2$ for MCMC estimation in a high-dimensional space
Let $f$ be a function such that:
$$f~:~(x,~\theta)\in\mathbb{R}^{3}\times\mathbb{R}^{12} \rightarrow f(x,~\theta)\in\mathbb{R}^3$$
My observations $y$ are noisy values taken by the function $f(\cdot ...
1
vote
0answers
81 views
Likelihood estimation using iid normal samples
Given an i.i.d. sample $X = (x_{1}, \dots, x_{n}) \sim N(\mu, 1)$. I have been asked to show that the likelihood of $\mu$ based on the whole sample is proportional to the likelihood based on $\bar{x}$ ...
0
votes
1answer
69 views
Parameter learning of Markov random field
Given a Markov random field $\mathcal{G} = (\mathcal{V},\mathcal{E})$, the corresponding density function to which is expressed by
$f(x) \propto \prod_{x\in\mathcal{V}} \psi_u(x) ...
3
votes
2answers
163 views
Estimating the covariance posterior distribution of a multivariate gaussian
I need to "learn" the distribution of a bivariate gaussian with few samples, but a good hypothesis on the prior distribution, so I would like to use the bayesian approach.
I defined my prior:
$$ ...
3
votes
0answers
150 views
Statistics for machine learning, papers to start?
I have a background in computer programming and elementary number theory, but no real statistics training, and have recently "discovered" that the amazing world of a whole range of techniques is ...
1
vote
0answers
129 views
Finding the UMVUE of the variance of a gaussian with mean zero
Given $Z_1, ..., Z_n, \sim\mathcal{N}(0, θ^2), θ>0$. Define $X_i=|Z_i|$ and consider estimation of $\theta$ and $θ^2$ on the basis of the random sample $X_1,...X_n$. Find the uniformly minimum ...
4
votes
1answer
93 views
What's the difference between Maximizing Conditional (Log) Likelihood or Joint (Log) Likelihood while estimating parameters of a model?
Consider a response y and data matrix X. Suppose I'm creating a model of the form -
y ~ g(X,$\theta$)
(g() could be any function of X and $\theta$)
Now, for estimating $\theta$ using Maximum ...
0
votes
0answers
143 views
proving sample covariance is unbiased with matrix algebra [closed]
Given an i.i.d. sample $(x_i,y_i)$ of size $n$ from a bivariate distribution $(x,y)$, I'm trying to prove that the sample covariance $$\frac{1}{n-1}\sum_{i=1}^n(x_i-\bar{x})(y_i-\bar{y})$$ is an ...
3
votes
1answer
98 views
Estimating parameters of a normal distribution from noisy observation of samples
Suppose I have a number of samples drawn from a normal distribution $x_i \sim \mathcal{N}(\mu,C)$ with $i = 1 \dots n$. I can make observations $z_i = x_i + e_i$ for those samples which are perturbed ...
0
votes
0answers
54 views
Estimation of max likelihood sample mean and sample covariance
How do I estimate the maximum likelihood sample mean and sample covariance of the data set consisting of
N = 100 2-dimensional samples x = (x1 , x2 )T ∈ R2 drawn from a 2-dimensional Gaussian ...
1
vote
1answer
51 views
Calculate boundary for MAE given RMSE
E.g. from the Netflix prize I know that the best RMSE = 0.8563 where the test dataset has a size of n=1,408,789.
Can I calculate a boundary for the MAE. If not, why can't I calculate a boundary?
I ...
3
votes
1answer
115 views
What is the name of the estimator that takes the mean of likelihood?
Let $X,Y$ be input and output (observed) continuous variables in $\mathbb{R}$. Let $\{y_1,...,y_n\}$ be the set of $n$ observations. Is there a name for the estimator $\hat x = \int_{x \in X} x ...
3
votes
2answers
152 views
Bayesian estimation of Dirichlet distribution parameters
I want to estimate parameters of Dirichlet mixture models using Gibbs sampling and I have some questions about that:
Is a mixture of Dirichlet distributions equivalent to a Dirichlet process? What ...
0
votes
0answers
26 views
How to estimate a stochastic time delay
Say I have irregular samples of two random processes that are both based on an unobserved process, $Z(t)$. Their SDEs are
$\mathrm{d}X(t) = \mathrm{d}Z(t-u(t)) + \epsilon(t)$
$\mathrm{d}Y(t) = ...
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votes
0answers
27 views
Maximum Likelihood for Mixed-type Variables
I have samples generated according from a distribution which has jumps in its cumulative distribution function. How can we write and maximize the likelihood function for these samples?
The problem ...
0
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0answers
32 views
Estimable function of OLS parameters can be shown by inner product with Null space?
I am in a advanced linear models class, and we are currently covering estimable functions. The criterion that we have for an estimable function is that for any $a^T\beta$ there exists an unbiased ...
4
votes
0answers
161 views
Robust parameter estimation for shifted log normal distribution
I have a data set which fits a logNormal distribution quite well. (From a theoretical point of view, it is some hard-to-tackle quotient distribution).
However, the data is quite dirty, so parameter ...
2
votes
1answer
77 views
Parameter estimate for linear regression with regularization
For given cost function $S(\beta) = (Y - X \beta)^T(Y - X \beta) + \lambda \beta^T \beta$, where $\lambda$ is regularization parameter, the $\beta$ that minimizes the given cost function is $\beta = ...
2
votes
0answers
38 views
Random walk with restricted graph knowledge
I have a very large graph and a function of its vertices, and want to estimate mean value of this function.
It's not possible to sample vertices uniformly in this problem, so a reasonable choice for ...
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votes
1answer
64 views
How to show what is going on if we drop significiant variable in logit model?
How to show what is going on if we drop significant variable in logit model ? Bias and heteroskedasticity should emerge. But what is the framework for showing such behaviours in econometric models ?
2
votes
2answers
62 views
What's this called? A small Gaussian at every data point to estimate probability
Say I have a dataset $X \subset{\mathbb R}^d$ (assumed to be iid samples) and I want to estimate the probability density of some unseen point y under that (unknown distribution). One way of doing that ...
2
votes
1answer
115 views
Estimate the second moment of a latent variable using a conditionally unbiased proxy
The Setup: Let $X_t$ denote an unobservable stochastic sequence where the first two unconditional moments are finite constants; ie $\mathbb{E} X_t = \mu < \infty$ and $\mathbb{E} X_t^2 = \gamma ...
1
vote
2answers
81 views
What is the name of (and alternatives to) this Bayesian point-estimate?
Assume that we have a Markovian environment that generates at every time step an event $A$ with probability $p^*$ and an event $B$ otherwise. Now suppose you are a Bayesian agent that wants to learn ...
3
votes
0answers
118 views
Robust parameter estimation for Exponentially modified Gaussian distribution
I'd like to test how well my data can be modeled by an Exponentially modified Gaussian distribution (Wikipedia) or Normal-exponential-gamma (NEG) Distribution. However, the parameter estimation (which ...
10
votes
1answer
468 views
Maximum likelihood estimators for a truncated distribution
Consider $N$ independent samples $S$ obtained from a random variable $X$ that is assumed to follow a truncated distribution (e.g. a truncated normal distribution) of known (finite) minimum and maximum ...
7
votes
2answers
337 views
Estimating parameters of a normal distribution: median instead of mean?
The common approach for estimating the parameters of a normal distribution is to use the mean and the sample standard deviation / variance.
However, if there are some outliers, the median and the ...
1
vote
0answers
29 views
Possible outcomes of approximate profile-likelihood estimator (APLE) for spatial autocorrelation
I've been working with spatial autocorrelation for a while and now I'm trying to move from more traditional estimators such as Moran's I or Geary's C to the new APLE estimator. I read Li's papers on ...
0
votes
0answers
31 views
How to estimate parameters for a nonlinear model with parameters both inside and outside of trigonometric functions?
For the given set of data $y(t)$ I have a model $y(t) = c_1 cos(\omega t) + c_2 sin(\omega t) + c_3$
How can I estimate parameters $c_1,c_2,c_3$ and $\omega$?
1
vote
1answer
41 views
What is most appropriate test?
I have conducted a survey using 5-Point Likert scale (Strong Agree; Agree etc.) in which a panel of experts indicated their Agreement with suggested statements.
There are three sub-Groups within the ...
1
vote
1answer
54 views
Any suggestion for a good introductory to optimization for parameter estimation?
I was reading about parameter estimation techniques such as Maximum Likelihood Estimation(MLE) and Expectation Maximization(EM). I tried to derive the Maximum Likelihood Estimation formula for Markov ...
0
votes
0answers
36 views
Show that the slope estimate can be written as a sum
I am stuck on a homework question for a graduate level linear models class. The question is to show that for simple linear regression the slope estimate $ \hat{\beta_1} = ...
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votes
0answers
43 views
Confidence intervals based on asymptotic normality
I wrote a report about confidence intervals based on asymptotic normality. However, my supervisor said that the definition in the second paragraph is wrong, but I ...
3
votes
2answers
192 views
Standard errors for covariance estimate in R
This is a very simple question: how does one get the standard error for the covariance estimate in R? I estimate the covariance using the cov function but there ...
0
votes
0answers
47 views
density estimation when only mean and variance are known
I want to estimate the distribution function of the random variable. Due to the complicate nature of this function, I can be calculated only the first and second order moments(mean and variance) of ...
3
votes
2answers
69 views
Estimating covariance of the difference of directional distributions derived from Gaussian mixtures
Given Gaussian mixtures $X_1, X_2 \in \mathbb{R}^p$ defined as $$P(X_i = x) = \sum_s \omega^{(s)}_i \mathcal{N}(x; \mu^{(s)}_i, \Sigma_i)$$ where the superscript $(s)$ indexes the $s$-th component of ...
