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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0
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6 views

“True values” of beta regression coefficients [on hold]

I simulated survival times, status and covariates for a Cox model. Now I would like to calculate the bias of regression coefficient estimates. But for this, i need the "true values" of beta regression ...
0
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0answers
22 views

Establishing consistency

I need to establish the (weak) consistency of an estimator of the mean, $T=a+b\bar{X}$. I tried to apply Chebyshev's inequality, but I couldn't do much because the parameter that subtract in the ...
0
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0answers
11 views

Difference between clipped time series, PRBS, PN sequence and their application in signal processing

A real valued time series can be converted into binary series through the process of clipping. Clipping, or hard limiting, a time series is transforming a real valued time series Y into a binary ...
1
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0answers
23 views

Sampling Distribution of Sample Correlation Coefficient

For a linear process $X_t=\mu+\sum_j\varphi_jW_{t-j}$ where $W_t$ is white noise and $\mathbb E(W_t^4)<\infty$ , $$ \begin{pmatrix} \hat\rho(1) \\ \hat\rho(2) \\ \vdots \\ ...
2
votes
1answer
191 views

Interpretation of a 95% confidence interval calculated via bootstrapping?

I've been thinking about what exactly a 95% confidence interval means when it is calculated via bootstrapping. The formal definition of a 95% confidence interval is something like this: "if the ...
0
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0answers
9 views

Clarification in CRLB for linear model

Paper : CRAMER-RA0 BOUNDS FOR SEMI-BLIND, BLIND AND TRAINING SEQUENCE BASED CHANNEL ESTIMATION? Download link presents the CRLB expression for non-blind ...
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0answers
60 views

Can anybody help with this state space model for filtering with random matrix connecting observation and state

I need an urgent help in an issue with a state space model for filtering. My state model is like: $\mathbf{d}_k = \mathbf{d}_{k-1} + \boldsymbol{\eta}_k$ with $\boldsymbol{\eta}_k \sim \mathcal{N}(0, ...
0
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2answers
39 views

I am running a logistic regression model and get very low predicted probabilities

I am running a logistic model for catastrophic health expenditure (CHE) in Argentina. The sample size is 22500. I followed Xu et al. methodology to define CHE and adjusted for 8 socioeconomic ...
1
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0answers
19 views

MLE of CTMC parameters

Let the data set be $$D = \{(s_0, t_0), (s_1, t_1), ..., (s_{N-1}, t_{N-1})\}$$ where $N=|D|$. Each $s_i$ is a state from the state space $S$ and during the time $[t_i,t_{i+1}]$ the chain is in state ...
2
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1answer
52 views

Estimating frequencies of a population

I have a sample of size 1121 from a population of size 2171 and I don't have access to any additional samples. The counts are ...
1
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0answers
42 views

How to combine normal distributions to have a mixture with specified kurtosis

I want to generate random samples from Normal Distributions $N(\mu_i,\sigma_i)$ by fixing kurtosis parameters ($\beta$s), as I need to simulate data by varying $\beta$ for my problem. I am trying to ...
4
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0answers
42 views
+50

Help in the expression for log-likelihood and maximization for PRBS signal

I am trying to do blind system identification of a univariate linear FIR model : $$y(n)=\mathbf{h^Tz(n)} + w(n)$$ Where the input $z(n)$ is a PRBS sequence of $\pm1$. Assuming, the input to be from ...
2
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0answers
29 views
+50

Help in CRLB for PRBS input

I am trying to do blind system identification of a univariate linear FIR model : $$y(n)=\mathbf{h^Tz(n)} + w(n)$$ Where the input $z(n)$ is a PRBS sequence of $\pm1$. Assuming, the input to be from ...
0
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0answers
9 views

Statistical distance in R with samples of different lengths

I have it really hard to find R functions that estimate various statistical distances (e.g. the Hellinger distance between two samples that have different lengths. I have gone through the R package ...
0
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0answers
10 views

Bayes minimax estimator [closed]

I am having trouble finding bayes minimax estimator using least squares method. Can anyone clearly elaborate on this
5
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0answers
91 views
+50

Parameter estimation using bayesian estimates in $R^k$ Euclidean space?

I am facing difficulty in identifying how the formula given by Eq(2) in the paper ...
2
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0answers
55 views

what is 1/0 in this article?

I am reading the article with title "metric learning by collapsing classes" lately http://papers.nips.cc/paper/2947-metric-learning-by-collapsing-classes.pdf . Everything goes well until the equation ...
1
vote
2answers
38 views

New to the field of stats, trying to apply it to my day job (cost estimating)

So to preface, I am very new to the world of Stats / quantitative analysis (I have recently gone back to uni and the paper I just completed is QA, specifically Regression, Estimation, Hyp. testing, ...
1
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0answers
12 views

Parameter estimation from unknown noise pdf

I have a noisy time series assumed to be the output of a linear process. My problem is that I do not know the pdf and hence I cannot estimate the parameters of the process model. I apply density ...
0
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1answer
34 views

Real time example: Estimation for incomplete data

Following is from Csiszar and Shields' FnT monograph "Information Theory and Statistics": The expectation–maximization or EM algorithm is an iterative method frequently used in statistics to ...
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0answers
45 views

Estimating posterior probability using kernel frequency estimation

given a dataset containing a numeric random variable $X$ and a class label $Y=\{+,-\}$ , the posterior probability $P(y|x)$ should be estimated using kernel frequency estimation. I can't seem to ...
0
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1answer
12 views

Coefficient of determination applied to difference in means?

Assume we have one random variable X, and two groups A and B have different mean X values. Let's say we have another variable Y that has a correlation with X of 0.5. If I wanted to estimate a Y ...
0
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0answers
14 views

How to estimate survey data at cluster level in a stratified clustering survey design?

While estimating from the survey data involving stratification & clustering survey design and using survey package of r, is it possible to estimate at the cluster level? For eg; for following ...
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0answers
52 views

Finding the optimal threshold parameter

Assume we are penalizing the least squares by the hard thresholding penalty: $argmin_\theta 2^{-1}(z_2-\theta)^2 + p_\lambda(|\theta|)$ where $p_\lambda(|\theta|)$ is the hard thresholding penalty ...
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1answer
26 views

Estimate population mean from sample

Population contains two independent parts: Group A & Group B with size $N_A$ nad $N_B$. $N = N_A + N_B$ Now sample from Group A and Group B separately. Sample size $n_A$, $n_B$. $n = n_A + ...
2
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1answer
58 views

What are the general methods for parameter estimation in statistics?

I have a task to estimate the probability of evolution selection of a given node. The only parameter estimation method I can think of is using the law of large numbers, i.e., use the proportion to ...
2
votes
2answers
93 views

modeling prices with the Hedonic regression

I'm using the concept of Hedonic regression in order to model the prices for real estates. I'm having some trouble with my approach. What I have and what I do my data consists out of real estates ...
1
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1answer
21 views

Estimating median survival times from Kaplan-Meier plot inspection

I've gone through the various questions relating to Kaplan-Meier plots and survival estimates, but I haven't really been able to find anything to help with this specific scenario. Sometimes, when ...
2
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0answers
13 views

How to derive the CRB for FIR blind equalization

Fast Maximum Likelihood for blind identification of multiple FIR channels presents the CRB expression on Pg 10 which is $CRB(dB) = 20 \log\left(1/|h|| \sqrt{\operatorname{tr}(\mathbf{F^{-1}}})\right)$ ...
0
votes
1answer
16 views

Probability two predictions (from linear model) are different from each other

Suppose I fit a linear model to a bunch of training data and make two out of sample predictions: $P_1 = .5$ with standard error $SE_1 = .08$ and $P_2 = .7$ with standard error $SE_2=.09$. What is ...
0
votes
2answers
45 views

Sample covariance matrix and its inverse

Assume we have the sample covariance matrix $S_1 = XX'/k$ which is not positive definite (in fact it is positive semi-definite) and not well conditioned in very large dimension (large $p$, small $k$). ...
0
votes
1answer
23 views

Least square estimation with quadratic fit. Any simple solution?

We consider the least square problem in the case where we got only one independant variable $x_i$ and only one dependant variable $y_i$. The number of observations is $n$. In the case of the linear ...
1
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1answer
41 views

Maximum Likelihood, normal distribution

Let $Z$~$N(\mu,\sigma^2+1)$, find the maximum likelihood estimator for $\mu$ and $\sigma^2$. I did but I want to check that this right actually ...
1
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1answer
34 views

Estimation of a process

I have this process to estimate: $x_t - x_{t-1} = \lambda(\gamma-x_{t-1}+\varepsilon_{t-1})+\varepsilon_t-\varepsilon_{t-1}$ but as far I can see it is unidentified. Any suggestions how to estimate ...
1
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0answers
11 views

Estimation Error when neglecting $\mu$ while computing Covariance-Matrix

Error when neglecting $\mu$ while computing Covariance-Matrix I would like to quantify the estimation error I have to accept when estimating the Covariance matrix based on $T$ observations of ...
3
votes
0answers
33 views

How do I find the center and radius of my circularly distributed data?

I'm analysing data that was collected in an optics experiment. The measurements are roughly in the form of a ring. In an ideal world the center of this ring would coincide with the origin, but due to ...
1
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1answer
68 views

When the sample covariance matrix becomes singular

Assume a data set $X$ which contains $k$ iid random vectors of size $p$. Denote by $S$ the sample covariance matrix. Really I have some questions and I need your very appreciated opinions: 1) Ledoit ...
3
votes
1answer
28 views

Confidence interval for exponential distribution

Let $X_1,...,X_n$ random sample of $X$~$exp(\theta)$. i) Find a exact confidence interval for $\theta$ with coefficient of confidence equal to $\gamma$ ii)Find a asymptotic confidence ...
1
vote
2answers
57 views

Find the confidence interval, uniform distribution

Let $X_1,..,X_n$ a random sample of $X$~$U[-\theta,\theta]$, $\theta>0$. Find the confidence interval for $\theta$. I'm trying to find a pivotal quantity with the maximum and minimum, but I ...
1
vote
0answers
23 views

Maximum likelihood estimator for minimum from a vector of random variables

Let $X_i, i =1,\ldots,N$ be vectors of random varaibles. Each of them has $m$ components representing dimension, $X_{ij}, j=1,2,\ldots,m$. Specific values $x_{ij}$ are observations or data. From, ...
1
vote
0answers
27 views

How to derive an estimator for the parameter of a continuous uniform distribution

$X_1, X_2,\dots.,X_n$ are i.i.d. random variates drawn from a continuous uniform distribution over $[0,\theta].$ The sufficient statistic is denoted $\max$. I want an estimator $e$ of $\theta$ that ...
2
votes
0answers
22 views

Estimating multiple populations

I have a set of sequential data of unknown size randomly spread across $n$ locations. I am trying to estimate the population size of all $n$ locations and provide a confidence interval as well. This ...
1
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0answers
19 views

Bias and variance of amplitude estimator [closed]

I'd like to estimate the amplitude $a[n]$ of the following measured signal, $$ s[n] = a[n] \sin(\omega_0 T n + \phi ) + w[n] $$ where $w[n]$ is assumed to be unbiased Gaussian white noise with ...
-1
votes
1answer
43 views

Interpretation of Monte Carlo results - R

I have a question regarding the interpretation of Monte Carlo results. I am applying the Monte Carlo simulations to an estimate process about development team size. The input distribution of the ...
6
votes
1answer
92 views

Shrinkage of the eigenvalues

Assume we have $n$ samples $X_1,..., X_n$ which are independent and identically distributed with mean = 0 and unknown non-singular covariance matrix $M$. Each sample $X_i$ is a vector of size $p\times ...
6
votes
1answer
64 views

A question about the effective sample size in life tables

I am currently studying basic methods of survival analysis and I came across this strange estimator of the effective sample size at a given interval. For the jth interval say, the estimator ...
0
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0answers
4 views

Can all parameters be cast as risk minimizers?

Can any population parameter can be cast as a risk minimizer? Thus estimable with an M-estimator (i.e., empirical risk minimizer)?
0
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0answers
39 views

Discrete sinusoidal to state space

I'm looking to apply an optimal LQR filter to a discrete signal of the form $x[n]=A \sin(\omega_0n + \phi)+ v[n]$ The amplitude $A$ and the phase $\phi$ are unknown variables I want to estimate ...
5
votes
1answer
97 views

On the sample complexity of mean estimation in $\ell_p$-norm

Let $1\leq p\leq \infty$, let ${\cal D}$ be a distribution over $\mathbb{R}^d$, and assume its support is contained in the unit $p$-ball. What is the minimum number $n$ of i.i.d. samples $W_i\sim ...
13
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3answers
1k views

Why do we need Bootstrapping?

I'm currently reading Larry Wasserman's "All of Statistics" and puzzled by something he wrote in the chapter about estimating statistical functions of nonparametric models. He wrote "Sometimes ...