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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5 views

Confidence interval for known non-normal estimation?

Assuming I know the density of my random sample - for example: $$ f_\Theta(x) = \frac{e^{-x/\Theta^2}}{\Theta^2} $$ (but I care about general single parameter case) How can I obtain $1-\alpha$ ...
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8 views

How to estimate Markov chain transition probabilities with partially observed data?

Suppose that we have a time-homogeneous discrete-time Markov chain $(X_n)$. We want to estimate the transition probabilities $p_{ij} = \mathbb{P}[X_{n+1} = j \mid X_n = i]$. In the case when we have ...
3
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63 views

Comparison between regression of $a = bc^t$ and $\log a = \log b +t \log c$

This question is more qualitative then about the maths behind the equation. Variables: a = month (1, 2, 3, ) t = shipments of a product in that month You wish to derive the relationship between $a$ ...
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1answer
19 views

Finding vectors with an extreme component

I'm looking for a function that measures if a vector component dominates all the rest. Let $$ \mathbf{v} = [v_1, v_2, \ldots, v_n] $$ and assume that it is L2 normalized, $|\mathbf{v}|_2 = ...
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19 views

variance and sample confused

When solving (b), is the variance $$ V\bigg(\frac 1 2 (x_1+x_2)\bigg) = \frac 1 4 V(x_1+x_2) = \frac 1 4 \big(v(x_1)+v(x_2)\big)= \frac 1 2 \sigma^2 $$ or should I divide the variance by the sample ...
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0answers
7 views

How to fix a scale of latent variable measured by dichotomous indicators in SEM

How can I fix a scale of latent variable measured by dichotomous indicators in a structural equation model to estimate the mean of that latent variable? I know the mean of that variable (because I ...
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29 views

Combining the Standard Deviation for Multiple Populations; Small Data Sets

I have been presented with a very small dataset which describes a material property for a particular cast of stainless steel, in this case fracture toughness. The data is: ...
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30 views

Rao-Blackwell exponential distribution

Let $X_1,..,X_n$ random sample of $X\sim\text{Exp}(\lambda)$ with $f(x;\lambda)=\frac{1}{\lambda}e^{-\frac{1}{\lambda}x}I_{[0,\infty]}(x)$ i) Find a unbiased estimator of $\lambda$ based ...
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2answers
32 views

Measuring the change of an increment in time series

Assume that two series ($x_1,\dotso,x_n$) and ($y_1,\dotso,y_n$) are linearly correlated. What is the connection between $y_j-y_i$ and $x_j-x_i$ in terms of Pearson's $r$ and the variance of $x$ ...
2
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1answer
28 views

UMVUE for a function

Let $X_1,...,X_n$ random sample $X$~$Bernoulli(p)$. For $n\geq 4$ show that the product $X_1X_2X_3X_4$ is a unbiased estimator for $p^4$, and use this fact for find the best unbiased estimator of ...
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2answers
43 views

What does “special case of GMM” mean?

I was researching purchasing this text book: http://www.amazon.com/dp/0691010188/ref=wl_it_dp_o_pd_nS_ttl?_encoding=UTF8&colid=2QTISO1Y8TYVW&coliid=I3FUEFWL47AC4L In its description it talks ...
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0answers
34 views

Which estimation technique should I use?

I have time series of six variables from 1973 to 2012, where poverty head count ratio (HCR) is taken as dependent variable. Consumer price index, GDP growth rate, population growth rate, revenue ...
0
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0answers
29 views

Confidence interval, lower and upper bound

I am studying on confidence intervals, but I'm still with some doubts Let a random sample $X_1,..,X_n$ with density $f(x;\theta)=\theta e^{-\theta x}I_{[0,\infty]}(x)$. Find a confidence interval for ...
2
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0answers
71 views

Confidence interval and probability

Suppose that $T_1$ is $100\gamma$ percent lower confidence limit for $\tau(\theta)$ and $T_2$ is $100\gamma$ percent uper confidence limit for $\tau(\theta)$. Further assume that ...
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0answers
34 views

Need help identifying which stat test to use

I have raw data. Without diving into the details, I'll try to explain the principles of what is represents; It's collected from 2 different regions. Raw data is a bunch of random time length amounts ...
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1answer
28 views

UMVUE explanations

Let $X_1,...,X_n$ a random sample where $X$~Poisson$(\theta)$. i)Find UMVUE for $\theta$ ii)Exists UMVUE for $\frac{1}{\theta}$ For i) I found that $T=\overline{X}$ is UMVUE for ...
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22 views

Is there any alternative to the EM algorithm?

I am working on biomedical signal analysis and the most used method for parameters estimation is the EM algorithm. My question is : what are the most powerful alternatives to this algorithm?
2
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1answer
32 views

Cramer-Rao Lower Bound

Let $X_1,..,X_n$ be an iid sample of $N(0,\sigma^2)$. Find an unbiased estimator of $\sigma^2$ and its lower bound. I found that $$\hat{\sigma}^2 = \sum_{i=1}^{n} X_i^2$$ is an unbiased ...
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0answers
13 views

Location parameter estimation in $\alpha-$stable distributions

Let $x$ be a $\alpha-$stable distributed random variable of parameters $\alpha,\beta,c,\mu$. When $\alpha \gt 1$ I can estimate the location parameter $\mu$ of the distribution as $\mu=E[x]$ But how ...
2
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1answer
21 views

Identifiability of a particular Independent Component Analysis model

I am considering the model : $$ \mathbf{x} = \mathbf{A}\mathbf{s} $$ where $\mathbf A \in \mathcal{M}_{n,p}(\mathbb{R})$ and $\mathbf s \in \mathbb{R}^{p}$ such that the entries of $\mathbf s$ are ...
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1answer
57 views

Using Neural Networks to predict stock values

How are neural networks usually used to predict market evolution? My data consists of a set of pairs (time, value), taken at an interval of 15 minutes. My ideas so far are: I.Take 40 values (or ...
2
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0answers
51 views

Show that MLE of $\lambda = \frac{n-T_n}{S_n+cT_n}$

$X_i$ are i.i.d exponential, mean $\lambda^{-1}$ for $1 \leq i \leq n$ and, the values are measured such that $X_i = c$ if $X_i \geq c$ and $X_i$ otherwise. Show that MLE of $\lambda = ...
2
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1answer
55 views

Unbiased estimator and sufficient statistics

Let $X_1,..,X_n$ be a random sample of $f(x;\theta)=\theta x^{\theta-1}I_{[0,1]}(x)$ Find a sufficient statistic for $\theta$ and construct a unbiased estimator for $\theta$ as a function ...
4
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1answer
36 views

How to find maximum likelihood of multiple exponential distributions with different parameter values

Let's say that I have a bunch of independent samples, $X_1, X_2, \dots, X_n$ and that they all follow Exponential($\theta_i$) distributions. (So they all have pdf $f(x_i)=\theta_i\exp(-\theta_iy_i)$.) ...
0
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1answer
65 views

Find a complete sufficient statistic,

Let $X_1,...,X_n$ be iid observations.Find a complete sufficient statistics for i)$f(x|\theta)=\frac{\theta}{(1+x)^{1+\theta}}I_{[0\infty)}(x), \theta>0$ What I did ...
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1answer
31 views

How to calculate $\phi$ (phi) - a first order autocorrelation coefficient

I have a dataset of historical quarterly earnings per share for 8 years. I am trying to use the following formula for the purpose of estimating earnings: $E(Q_t) =Q_{t-4} + \phi_1(Q_{t-1} - Q_{t-5}) ...
0
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1answer
29 views

Minimal sufficiency and UMVUE in a pseudo-Normal distribution

I already asked a (stupid) question about this problem here thinking I wouldn't have problems to continue it but I was pretty wrong. I'm finding several more problems trying to solve it. I'll try to ...
0
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0answers
31 views

Book suggestions - robust regression

I'm start to study M estimator - Robust Statistics. Can you suggest sound books for this topic? Note that I have Huber's books. Thank you.
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13 views

Estimating affluence of a commercial area

Ok, i hope this time i won't be off-topic, but i have been told to ask here : ) I am trying to estimate the average affluence of a commercial area.. I know how many people are leaving nearby, how ...
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0answers
24 views

Estimate the population variance from a set of weighted means

Proviso: I do not have a lot of experience with statistical theory, so please forgive my occasionally poor choice of notation.$$\\$$ My problem is as follows: I have a set of measurements $X_i, ...
1
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1answer
34 views

Restricted Maximum Likelihood

Why don't we use restricted maximum likelihood to estimate parameters in non-mixed models?
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0answers
27 views

Unsmoothing of returns [migrated]

The following problem arises in the context of private equity, which typically report "smoothed" returns (think of it as a moving average). As you can imagine, "smoothed" returns would have a much ...
0
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0answers
12 views

Given an N-sided die, an error and a Z-value, how many throws do I need?

I have a random variable with an almost-but-not-quite iid distribution mapping to N different values. I wish to use the empirical distribution from k samples as the "true" distribution, and have ...
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0answers
27 views

Estimate density dependent on another variable

I have an (unknown) random function $y=f(x)$, i.e. for each value of $x \in [0,1]$ it is a random variable with some distribution. Also I can sample this function, and got values of $y$ for many ...
0
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1answer
15 views

Testing if variables have a non-linear relationships with the dependent variable

How can I find evidence that a independent variable has a non-linear relationship with the dependent variable? Can I possibly achieve this by squaring all the independent variables and estimate a ...
2
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1answer
34 views

Estimate probability mass function from observed samples?

This question is related to but is distinct from Estimation of probability mass function using finite samples. As in the related question, suppose we have a discrete random variable $X$ with known ...
4
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2answers
63 views

What is a Highest Density Region (HDR)?

In statistical inference, problem 9.6b, a "Highest Density Region (HDR)" is mentioned. However, I didn't find the definition of this term in the book. One similar term is the Highest Posterior ...
1
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1answer
23 views

Estimating Markov Switching Probit

I attempt to fit the following probit model to a time series where we observe the binary variable $R_{t}$ and another variable $X_{t}$, a latent unobserved variable $y^{*}_{t}$ and a state variable ...
0
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2answers
44 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 ...
0
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1answer
173 views

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 ...
6
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2answers
76 views

Estimating bias in surveys

Say a company runs a survey across random N cities independently in some country estimating the fraction of males and females on each city. E.g.: Males = $X_1$% ...
2
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1answer
20 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 ...
0
votes
1answer
19 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
29 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 ...
0
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1answer
26 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
46 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 ...
0
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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 ...