Any statistical process which seeks to approximate an unknown value, such as a distribution, a point estimate (e.g. mean), or confidence interval.
9
votes
2answers
3k views
Why is sample standard deviation a biased estimator of $\sigma$?
According to the Wikipedia article on unbiased estimation of standard deviation the sample SD
$$s = \sqrt{\frac{1}{n-1} \sum_{i=1}^n (x_i - \overline{x})^2}$$
is a biased estimator of the SD of the ...
15
votes
0answers
627 views
Practical thoughts on explanatory vs predictive modeling [duplicate]
Possible Duplicate:
Practical thoughts on explanatory vs. predictive modeling
This question has been bugging me for some time, and I was going to write a blog post about it. However, I ...
8
votes
3answers
2k views
Calculating required sample size, precision of variance estimate?
Background
I have a variable with an unknown distribution.
I have 500 samples, but I would like demonstrate the precision with which I can calculate variance, e.g. to argue that a sample size of 500 ...
16
votes
2answers
905 views
How to find confidence intervals for ratings?
Evan Miller's "How Not to Sort by Average Rating" proposes using the lower bound of a confidence interval to get a sensible aggregate "score" for rated items. However, it's working with a Bernoulli ...
10
votes
3answers
485 views
Can the empirical Hessian of an M-estimator be indefinite?
Jeffrey Wooldridge in his Econometric Analysis of Cross Section and Panel Data (page 357) says that the empirical Hessian "is not guaranteed to be positive definite, or even positive semidefinite, for ...
3
votes
1answer
924 views
Variance of the reciprocal II
Background
I've recently read the paper
Leo A. Goodman, On the Exact Variance of Products
Journal of the American Statistical Association
Vol. 55, No. 292 (Dec., 1960), pp. 708-713
from where I ...
10
votes
2answers
3k views
How to calculate Zipf's law coefficient from a set of top frequencies?
I have several query frequencies, and I need to estimate the coefficient of Zipf's law. These are the top frequencies:
...
9
votes
4answers
2k views
What is the difference between estimation and prediction?
For example, I have historical loss data and I am calculating extreme quantiles (Value-at-Risk or Probable Maximum Loss). The results obtained is for estimating the loss or predicting them? Where can ...
3
votes
2answers
194 views
Sorting answers, given overvotes and undervotes
At many question-and-answer sites, like StackExchange, people can upvote or downvote each answer. These sites also typically try to use the votes to sort answers, so the answers that are most likely ...
2
votes
1answer
451 views
What is complete sufficient statistics?
I have some trouble understanding complete sufficient statistics?
Let $T=\Sigma x_i$ be a sufficient statistic.
If $E[g(T)]=0$ with probability 1, for some function $g$, then it is a complete ...
7
votes
2answers
346 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 ...
13
votes
3answers
729 views
Unbiased estimation of covariance matrix for multiply censored data
Chemical analyses of environmental samples are often censored below at reporting limits or various detection/quantitation limits. The latter can vary, usually in proportion to the values of other ...
8
votes
4answers
631 views
Why squared residuals instead of absolute residuals in OLS estimation?
Why are we using the squared residuals instead of the absolute residuals in OLS estimation?
My idea was that we use the square of the error values, so that residuals below the fitted line (which are ...
3
votes
1answer
220 views
How to interpret the divergence of Fisher information expectation?
Consider translated Weibull distribution with probability density function:
$$
f(x ; k, \lambda, \theta) = \frac{k}{\lambda} \left( \frac{x-\theta}{\lambda} \right)^{k-1} \exp\left( - ...
2
votes
3answers
814 views
How to compute significant interaction estimates when main effect is not significant?
I have a linear model of a dependent variable, $y$, with two predictor variables, year and site, and their interaction, with year being numeric and site categorical.
The main effect of year is not ...
8
votes
2answers
350 views
Reference for $\mathrm{Var}[s^2]=\sigma^4 \left(\frac{2}{n-1} + \frac{\kappa}{n}\right)$?
In his answer to my previous question, @Erik P. gives the expression
$$
\mathrm{Var}[s^2]=\sigma^4 \left(\frac{2}{n-1} + \frac{\kappa}{n}\right) \>,
$$
where $\kappa$ is the excess kurtosis of the ...
8
votes
4answers
708 views
How large should a sample be for a given estimation technique and parameters?
Is there a rule-of thumb or even any way at all to tell how large a sample should be in order to estimate a model with a given number of parameters?
So, for example, if I want to estimate a ...
6
votes
2answers
180 views
Estimating the parameters of a sum of a Gaussian and an $\alpha$-stable random variable
Let's assume I have a set of samples of a random variable
$$
X = Y + Z \>,
$$
where $Y$ is Gaussian (with a mean of zero and variance $\sigma^2$) and $Z$ has a symmetric $\alpha$-stable ...
5
votes
1answer
162 views
Estimating speed from position updates with uncertain time intervals
I have 2 alternative methods to solve a problem, and I was just wondering what people who know the math better than I think, and if there is a better method to use for this type of problem.
The ...
3
votes
0answers
125 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 ...
3
votes
1answer
275 views
Posterior distribution for multinomial parameter
(topic moved from maths.stackexchange.com)
I'm currently developing an application integrating a probabilistic inference engine for Bayesian Networks. The Bayesian Network integrates some form of ...
3
votes
2answers
179 views
Bayesian updating using $n$ noisy observations of Brownian motion
I am very new to Bayesian inference and can't figure out what may be an elementary problem. Also, please forgive me if I am screwing up the notation -- this is my first foray into Bayesian ...
2
votes
1answer
277 views
Parameters’ uncertainty for small sample size
Suppose we have a small set of numbers (5 to 10 observations), and we’re trying to fit a distribution to this set. Also, we know that all numbers are positive. I tried to fit lognormal, but I’m not ...
2
votes
0answers
93 views
Generating likely populations given a subsample and control totals
Context
In transportation planning, agent-based microsimulation is a method to deal with the complexity of the problem. Instead of computing aggregate flows (as in the classical four-step model), ...
2
votes
2answers
707 views
Parameter estimation for normal distribution in Java
Given a set of data (~5000 values) I'd like to draw random samples from the same distribution as the original data. The problem is there is no way to know for sure what distribution the original data ...
0
votes
1answer
456 views
Controlling for variables in pooled OLS estimation in EViews
I am working on the Chinese economy and my topic of research is how external political instability can affect Chinese exports. So I want to estimate the Chinese export demand function for 1988-2011 ...
-1
votes
1answer
405 views
Question regarding sampling, estimation and accuracy [closed]
Let's say there are N chunks of metal, each are 4 inches thick. They are to be hammered and reduced to following best possible sizes: 1, 2, 3 or 4 inches. If we were to use sampling to get an estimate ...
7
votes
4answers
6k views
Calculating the parameters of a Beta distribution using the mean and variance
How can I calculate the $\alpha$ and $\beta$ parameters for a Beta distribution if I know the mean and variance that I want the distribution to have? Examples of an R command to do this would be most ...
10
votes
4answers
375 views
Is the mean squared error used to assess relative superiority of one estimator over another?
Suppose we have two estimators $\alpha_1$ and $\alpha_2$ for some parameter $x$. To determine which estimator is "better" do we look at the MSE (mean squared error)? In other words we look at $$MSE = ...
7
votes
3answers
309 views
References on numerical optimization for statisticians
I'm looking for a solid reference (or references) on numerical optimization techniques aimed at statisticians, that is, it would apply these methods to some standard inferential problems (eg MAP/MLE ...
9
votes
2answers
235 views
Dynamic calculation of number of samples required to estimate the mean
I am trying to estimate the mean of a more-or-less Gaussian distribution via sampling. I have no prior knowledge about its mean or its variance. Each sample is expensive to obtain. How do I ...
6
votes
3answers
624 views
Estimation of exponential model
An exponential model is a model described by following equation:
$$\hat{y_{i}}=\beta_{0}\cdot e^{\beta_{1}x_{1i}+\ldots+\beta_{k}x_{ki}}$$
The most common approach used to estimate such model is ...
2
votes
1answer
452 views
Delta method and correlated variables
I have been reading about the delta method in regards to auto regressive distributed lag models. This is very new to me, so excuse any beginner mistakes.
The problem is as follows:
We have a model ...
11
votes
3answers
467 views
How to do estimation, when only summary statistics are available?
This is in part motivated by the following question and the discussion following it.
Suppose the iid sample is observed, $X_i\sim F(x,\theta)$. The goal is to estimate $\theta$. But original sample ...
6
votes
2answers
282 views
How can I estimate unique occurrence counts from a random sampling of data?
Let's say I have a large set of $S$ values which sometimes repeat. I wish to estimate the total number of unique values in the large set.
If I take a random sample of $T$ values, and determine that ...
5
votes
4answers
232 views
How to evaluate quality of probability estimator for Bernoulli experiments?
Given that I have a set of bernoulli experiments, each with a different and unkown probability $p_i$ and an outcome $x_i$, and an estimator that for each experiment gives a prediction of the ...
5
votes
3answers
842 views
Estimating beta-binomial distribution
Suppose that I culture cancer cells in n different dishes g₁, g₂, … , gn and observe the number of cells ni in each dish that look different than normal. The total number of cells in dish gi is ti. ...
4
votes
0answers
166 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
2answers
442 views
How do I sort an ordinal list of user-generated ratings data?
The Ubuntu Software Center uses a 1 to 5 star rating system for its App Reviews. However, it's current ratings sorting algorithm looks very fishy. I believe this is a different question from this ...
2
votes
0answers
127 views
About kernel based estimates
Kernel based operations are common in a variety of applications, such as image processing (e.g., blurring), generating smoothed estimation maps, and so on. A common approach is to select four ...
2
votes
2answers
416 views
Estimating distribution parameters from few data points
Say I'm doing stats on the height of adults from various countries.
I assume the heights of adults from one country are normally distributed, and ignore sex differences (I also ignore the fact that ...
0
votes
1answer
143 views
Timeseries regression
I'm following an undergraduate course on timeseries using OxMetrics and wanted to reproduce som results in R
Estimating an ARMA(3,3) model:
...
9
votes
2answers
224 views
Computationally efficient estimation of multivariate mode
Short version: What's the most computationally efficient method of estimating the mode of a multidimensional data set, sampled from a continuous distribution?
Long version: I've got a data set that I ...
6
votes
2answers
149 views
How to find MLE when samples depend on the estimated parameter
Can you show me what I'm doing wrong here? This is the homework problem:
Consider a random sample $Y_1, \ldots , Y_n$ from the pdf $f_Y(y;\theta) = 2y\theta^2$ where $0\le y \le \frac{1}{\theta}$. ...
6
votes
1answer
2k views
Mean squared error vs. mean squared prediction error
What is the semantic difference between Mean Squared Error (MSE) and Mean Squared Prediction Error (MSPE)?
5
votes
1answer
185 views
Expectation of an estimator?
When evaluating an estimator in a frequentist setting, using MSE and let say to compute the Bias of the estimator we compute the expectation of this estimator, are we supposing that the estimator has ...
5
votes
1answer
3k views
How to show that an estimator is consistent?
Is it to show that MSE = 0 as $n\rightarrow\infty$? I also read in my notes something about plim. How do I find plim and use it to show that the estimator is consistent?
4
votes
3answers
326 views
Can I use Kolmogorov-Smirnov test and estimate distribution parameters?
I've read that Kolmogorov-Smirnov test should not be used to test the goodness of fit of a distribution whose parameters have been estimated from the sample.
Does make sense to split my sample in two ...
4
votes
1answer
391 views
How to check that a sample suits multi-dimensional uniform distribution?
I have a 3-dimensional sample $(X_k,Y_k,Z_k), k=1, \ldots, N$ which I suspect to be uniform on some parallelepiped in $R^3$ (i.e. a set of the form [a;b]X[c;d]X[e;f], where numbers a,b,c,d,e,f are ...
3
votes
0answers
80 views
Time series modeling the number of users of a mobile app
I want to model the number of users of an mobile app. This app has two kinds of users: free and paid. I thought of this autoregressive model:
$x_t = Ax_{t-1}$
with $x_t$ being a 4-dimensional ...
