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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11 views

Can multiple imputation be used to estimate confidence intervals for population aggregates?

While still being a novice in the area of multiple imputation estimation, I have explored extensively this topic and I do understand the key concepts behind M.I. estimation and aggregation via Rubin's ...
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1answer
30 views

Estimating population variance through simulation in R

I want to estimate the variance of the exponential distribution with a rate of $\lambda=0.2$. I'm drawing a sample of 5 exponentials 1000 times, and know that the theoretical variance of my ...
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2answers
36 views

How can maximum likelihood be used to estimate parameters for a Weibull distribution? [duplicate]

Consider the following survival data (cumulative): Month 0 - 100% Month 1 - 50% Month 2 - 33% Month 3 - 25% Month 4 - 20% (meaning 20% of all initial units have survived by the end of Month 4) ...
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1answer
32 views

Maximum likelihood estimation for Cauchy noise

What is the maximum likelihood estimator of the covariance matrix for a given vector in the presence of Cauchy noise? How can we calculate it given that the Cauchy distribution has infinite variance? ...
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22 views

Estimation of variance: How to bring Bessel's correction together with degrees of freedom?

I have been considering multiple textbooks to find out the reason that the denominator of the estimation of the population variance is n-1 rather than n. Depending on the book, two reasons are given: ...
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1answer
37 views

Variance of the $\hat{\sigma^2}$ of a Maximum Likelihood estimator

Given some normally distributed observations $x_1,x_2,...,x_n$ $\forall i\ x_i\sim\mathcal{N}(\mu, \sigma^2)$ the ML estimator decides that the variance that maximizes the likelihood function is ...
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2answers
50 views

How to predict property value using lat/lon?

I have lat/lon and property values for households in a particular region. Format: Lat Lon value 32.2 -98.22 120000 .... Now I have new data of the ...
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1answer
20 views

Covariance Estimation for cauchy noise

Apart from Ledoit wolf shrinkage technique which can be better shrinkage covariance estimators for data with cauchy distribution? How to calculate optimum shrinkage intensity for data containing ...
5
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2answers
228 views

Just “take the average” they say. It's not that straightforward, right?

I have an acquaintance who does not study statistics and doesn't understand that summing data and dividing by the number of data is a summary statistic, i.e. that information is lost. For example, ...
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7 views

Finding a joint distribution of a large dimension

This is a rather soft question. I have data samples that are definitely pairwise correlated, and possibly correlated in higher order. It is of dimension $50$, and I am looking to describe it via some ...
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0answers
7 views

R examples and code for estimating temporal discounting functions with maximum likelihood?

Does anyone know of any examples that show and teach how to estimate temporal discounting functions using maximum likelihood in R? I really appreciate any help/suggestions anyone can provide. Thanks!
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120 views

Fastest way to solve Bayes estimator problem

The below problem is from an old PhD qualifying exam in our department. My own solution below is time-consuming and quite possibly wrong. It also relies on recognizing a less common distribution, so I ...
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0answers
10 views

Correct formula for unbiased estimate of population covariance [duplicate]

Is this formula a correct way to estimate population covariance from a sample? $$s_{xy} = \frac{1}{n-1}\sum\limits_{i=1}^{n}(x_i-\bar{x})(y_i-\bar{y})$$
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11 views

multiple, related, time-series applied to Statistical Process Control

I tried looking online (google), searching in stack-overflow and cross-validated, and just looking through "R" documentation for the answer, but either I am not seeing it, or I don't know how to tell ...
3
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1answer
38 views

How to prove the properties of penalized likelihood estimator in Fan and Li (2001) paper

I'm reading through Fan and Li's paper "Variable Selection via Nonconcave Penalized Likelihood and its Oracle Properties". In Page 2 near bottom right corner, they proposed three properties that a ...
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0answers
20 views

Capture recapture model validation

In the absence of an actual population to test on, what are the best practices for validating capture recapture models?
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1answer
21 views

How to estimate which distribution a new observation belongs to, when the distributions are given by a set of obervations

The question is that I have several probability distributions. For each distribution $P_i$, I don't know what it is. Instead, I have a set of observations $\{x_i^j\}_{j=1}^{n_i}$ drawn from each of ...
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0answers
36 views

“True values” of beta regression coefficients

After simulating survival time, status and covariates for a Cox model, I would like to calculate the bias of regression coefficient estimates. But for this, i need the "true values" of beta regression ...
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0answers
31 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 ...
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0answers
30 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 ...
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26 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
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1answer
206 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 ...
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65 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, ...
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2answers
46 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 ...
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0answers
20 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 ...
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1answer
54 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 ...
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0answers
50 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 ...
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0answers
10 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 ...
2
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0answers
56 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 ...
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2answers
39 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, ...
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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
41 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 ...
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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 ...
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0answers
16 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
79 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 ...
0
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1answer
27 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
65 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
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2answers
105 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 ...
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1answer
38 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 ...
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0answers
19 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 $CRB(dB) = 20 \log\left(1/|h|| \sqrt{\operatorname{tr}(\mathbf{F^{-1}}})\right)$ ...
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1answer
19 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 ...
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2answers
47 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 $k$). ...
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1answer
24 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
44 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 ...
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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
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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 ...
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1answer
73 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
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1answer
29 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 ...