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2
votes
1answer
23 views

Control limits in $\bar{x}$ and R chart

I am learning a Quality Control course and in theory part I don't understand calculating the control limits for $\bar{x}$ and R chart.I want to know, say when I calculate the R chart control limits no ...
1
vote
1answer
39 views

Definition of Scale median

Lehmann, in Theory of Point Estimation p.212 (and also on p.169), defines scale median as the solution to: $${E(X)I(X\le c)} = {E(X)I(X\ge c)}$$ given $X$ is a positive random variable, and ...
0
votes
0answers
15 views

Regression using a priori knowledge

I am sorry if the title (and probably the question) is not very clear but I have a regression problem which might be a bit over my head if I want to do it well. I am only interested in getting some ...
3
votes
2answers
68 views

Why are econometric analyses valid when the subject of study is inherently different?

I am reading numerous articles pertaining to unemployment as references for my own work. Yet I've encountered many where they use long time series in countries which have had some sort of pertinent ...
0
votes
1answer
16 views

Ensemble in stochastic process

I am learning a time series and forecasting course.In the book "The Analysis of Time Series by Chris Chatfield" it says that We only have single outcome of the process and a single observation on ...
0
votes
0answers
22 views

Statistical learning theory

I am looking for some good books for statistical learning theory. For an introduction I went through "An elementary introduction statistical learning theory Kulakrani" It was a good read with less ...
0
votes
1answer
20 views

Requirements for a valid neural network activation function?

What rules define a valid neural network activation function, excluding biological plausibility? What set of principles do softmax, rectified linear units, hyperbolic tangent, sigmoid, etc. follow? ...
4
votes
0answers
22 views

Polling vs averaging in Random Forest models

Why is it that for Random Forest we take the average vote from each classifier in the ensemble rather than the average probability from each classifier in the ensemble? Is there theory behind why ...
0
votes
0answers
9 views

Linear-time approximation to kernel SVM?

Scaling kernel support vector machines to large datasets is a very challenging problem. For linear SVMs, PEGASOS is able to learn efficiently online, so training time scales linearly with the size of ...
0
votes
0answers
8 views

Intuition for uniform integrability as asymptotic light tails

I am trying to get an intuition to the concept of uniform integrability: $$ \lim_m \sup\lim_n \mathbb{E}[|X_n| I_{\{X_n \geq m \}}] \to 0 $$ Can this be seen as a form of "asymptotic light tails"? ...
2
votes
1answer
74 views

Logistic regression & categorical explanatory variables

I'd like to perform logistic regression with some categorical explanatory variables with more categories than just binary 0/1. Is this possible and why? I am inclined to think that this would give ...
3
votes
0answers
41 views

Formalizing pdf using both discrete and continuous densities

I'm trying to formalize the probability density function for a rather simple process, but I'm having difficulty writing it precisely. Specifically, consider simulating a 1-D Gaussian random walk ...
0
votes
0answers
39 views

Most Important Stat Theory Concepts — Interview [duplicate]

I have an interview with a top company for a data scientist position. I was made aware that they will be testing probability/statistical theory concepts. So the question: If you had 1 hour tops ...
1
vote
2answers
43 views

Mixed variable, joint distribution, How do we know which one is continuous distribution, which one is discrete

If we have one continuous r.v. $x$ and a discrete r.v. $y$ which takes one of the two values $y_1$ and $y_2$. Let's say we know the prior probabilities $P(y_1)$ and $P(y_2)$. From Bayes theorem we ...
8
votes
1answer
125 views

Why is variability measured relative to a point?

Why are measures of dispersion calculated relative to some central point? Why wouldn't, for instance, all possible non-repeated, pairwise differences in the dataset be a valid measure of spread?
3
votes
2answers
71 views

Combining models for prediction based on residual performance

I have never read or seen someone do this before, so I wanted to pose the question here. Suppose I fit a basic linear model, $\text{price of house} = \beta_0 + \beta_1*\text{taxes} + ...
1
vote
2answers
57 views

Can a nuisance multi-class classifier do better than binary classifier?

This is rather a theoretical question in order to save the trouble in trying to do empirical testing and is part of a bet, so I hope I am right... Say there are M classes in the data BUT you want to ...
2
votes
1answer
74 views

How can you derive the sample size to obtain a particular type II error rate?

I often see that the sample size for a $z$-test to achieve a particular type II error rate $\beta$ (at a given significance level, $\alpha$) is: $$n = ...
0
votes
0answers
27 views

Mixed model weight matrix

Consider Henderson’s classic mixed model equations: What is the nature of the weight matrix, S-1? I believe that this is composed of the covariance matrix, but at the same time it is diagonal. ...
1
vote
1answer
91 views

Is it valid to apply large scale statistics to a single case?

I have a small black box that displays a 0 or a 1 every time I press its button. I can tell you, truthfully, that over the past 20,000,000,000 times it has been pressed, 19,999,999,990 times it has ...
0
votes
1answer
85 views

When Monte Carlo simulation can't be used to simulate a statistical system?

My question is simple. Which are the general conditions for which a Monte Carlo simulation can be used to represent a statistical system? Or conversely, which are the statistical system that cannot be ...
0
votes
0answers
50 views

Approximating a binomial distribution with a mixture normal

This is purely a theoretical question (I legitimately can't think of a real application), but if you wanted to approximate a binomial distributed variable with a two-component mixture normal, is there ...
0
votes
1answer
85 views

Non significant Pearson correlations included in hierarchical regression?

I would like to perform hierarchical regression in which all variables are based on previous research/theory. But when I perform Pearson correlations, I found that some variables did not correlate to ...
0
votes
8answers
588 views

Does the presence of an outlier increase the probability that another outlier will also be present on the same observation?

**Edit: (10/26/13) More clear (hopefully) mini-rewrites added at the bottom** I'm asking this from a theoretical/general standpoint - not one that applies to a specific use case. I was thinking ...
11
votes
1answer
149 views

Is there a statistical application that requires strong consistency?

I was wondering if someone knows or if there exists an application in statistics in which strong consistency of an estimator is required instead of weak consistency. That is, strong consistency is ...
0
votes
1answer
157 views

Theoretical expected value and variance

Let $X$ be a random variable having expected value $\mu$ and variance $\sigma^2$. Find the Expected Value and Variance of $Y = \frac{X−\mu}{\sigma}$. I would like to show some progress I've made so ...
1
vote
0answers
33 views

Modelling with multiple-valued variables

I am about to start out analysis of a microbiological data set (ETEC: enterotoxic echerichia coli in children with diarrhea). The variables refer to the ETEC, not to the children. Some of the ...
2
votes
2answers
138 views

How do we understand the relationship between independent probabilities and real-world independence?

From what I have come to understand, the events A and B are considered independent for purposes of probability theory when $$ p(A \cap B) = p(A) \cdot p(B) $$ Now, supposing I flip two coins. I ...
0
votes
0answers
39 views

Frequency of data: is quarterly data better than half-year data? Why?

Hi have a dataset which I constructed using quarterly observations (from bank accounts). I could have also used half-year or yearly data, but I chose quarterly because I thought that higher frequency ...
4
votes
1answer
48 views

What is the name/relevant details of this exponential-family related structure?

Suppose that $X$ comes from an exponential family $$ p_\theta(x) = h(x)\exp(\theta x - A(\theta)), $$ and that, conditional on $X$, $Y$ also comes from an exponential family of the form $$ ...
3
votes
2answers
112 views

Similarity theory: Testing whether dimensions are separable or integral

Note: I'm not referring to linear separability. I've found the interesting comment in Edelman, Shahbazi: "Renewing the respect for similarity" that for integral dimensions, Euclidean distance is ...
2
votes
0answers
184 views

Improving an unbiased estimator using the Rao-Blackwell theorem [closed]

Given data following a Bernoulli distribution $Y_1,...Y_n \sim B(1,p)$, we want to measure $\theta = \text{Var}(Y_1)$ I found this unbiased estimator $S^2 = \frac{\sum{(y_i-\bar{y}})^2}{n-1}$ I need ...
1
vote
1answer
32 views

How to analyse data from the same group where some people have opted out and data is anonymous?

I have a peculiar situation, I am conducting research and had a group of students participate in it. I had them scored on (property) $X$ and say $n_1$ people participated. After an intervention, I ...
1
vote
0answers
35 views

Partials of PDF with no closed form solution

I need to estimate partial derivatives for all N parameters denoted $\theta_{N}$ of a probability density function(PDF) $\mathcal{f}$. This PDF $\mathcal{f}$ has no closed form solution and is ...
2
votes
2answers
1k views

How do you Interpret RMSLE (Root Mean Squared Logarithmic Error)?

I've been doing a machine learning competition where they use RMSLE (Root Mean Squared Logarithmic Error) to evaluate the performance predicting the sale price of a category of equipment. The problem ...
3
votes
1answer
105 views

Question regarding Bonferroni correction

Prove the following version of the Bonferroni inequality- $$P\left(\bigcap_{i=1}^kA_i\right)\ge1-\sum_{i=1}^kP(A_i^c)$$ When creating simultaneous confidence interval, what are $A_i$ and $A_i^c$? ...
2
votes
1answer
72 views

What is the name of the theory (if there is one) that states lottery winners are more likely to tell others about their lottery entry?

I've previously read about a theory that I remember (correctly or not) being called the "Winning Lottery Theory" which is essentially the following: An individual hears about disproportionately ...
1
vote
0answers
50 views

Confusion related to inverse problems in statistics

I am getting started with inverse problems in statistics. However, I didn't something related to it. I was reading this paper http://math.uni-heidelberg.de/studinfo/reiss/CavalierInvProb.pdf. It ...
2
votes
0answers
199 views

The formula for covariance in terms of joint cdf

I want to show that $$\newcommand{\cov}{\operatorname{cov}}\newcommand{\d}{\mathrm{d}}\cov(x,y) = \iint (F_{X,Y}(x,y) - F_X(x)F_Y(y))\,\d x\,\d y$$ However, I have no idea how to start. I know that ...
-1
votes
1answer
161 views

Random forest like procedure for regression or other statistical models

I'm wondering if there exist methods similar to one used in random forest algorithm - I mean taking simultaneously bootstrap sample and random subset of features, then building statistisal model. Have ...
0
votes
0answers
93 views

Comparing two different leagues of similar but not equal distributions around a standard deviation of error of a prediction from a rating system

This query ties a lot of my interests in rating sports teams together, because as I’ve mentioned before I do a version of the Kenneth Massey method (as per his 1997 thesis ...
2
votes
0answers
47 views

Generalization error for classification with a nonconvex loss function

I've been working my way through Vapnik's 1998 Statistical Learning Theory book and one thing that I'm still unsure of is if his risk bounds hold for nonconvex loss functions -- i.e., when we can't be ...
6
votes
2answers
138 views

Algebra for data confidence

Very often, we use data which are derived from some measurements. These measurements usually have a confidence measure associated which tells how reliable or confident we are about the measure. For ...
0
votes
1answer
523 views

For linear regression, what's the distribution of error term from Classical and Bayesian point of views?

I know that linear regression is based on the assumption that the errors are normally distributed (from both bayesian and classical views). I'm just trying to verify this assumption based on the final ...
1
vote
2answers
103 views

Independence in a sum relationship

I have a model of total reaction time T, which is a composite of a selection time S and a discrimination time D. So a person first finds something, this takes the tS. Then he discriminates and reports ...
1
vote
0answers
191 views

Is possible use HoG features to train a Neural Network?

I was wondering if it is possible use HoG features to train a Neural Network, I know that in the original paper by Dalal and Triggs they used the data generated to train a SVM. If not is possible or ...
2
votes
3answers
398 views

Is it true that in high dimensions, data is easier to separate linearly?

I have often seen the statement that linear separability is more easily achieved in high dimensions, but I don't see why. Is it an empirical fact? An heuristic? Plain nonsense?
10
votes
2answers
212 views

Does the principle of indifference apply to the Borel-Kolmogorov paradox?

Consider Jaynes' solution to the Bertrand paradox using the principle of indifference. Why doesn't a similar argument apply to the Borel-Kolmogorov paradox? Is there something wrong with arguing that ...
8
votes
1answer
491 views

Problems with a simulation study of the repeated experiments explanation of a 95% confidence interval - where am I going wrong?

I'm trying to write an R script to simulate the repeated experiments interpretation of a 95% confidence interval. I've found that it overestimates the proportion of times in which the true population ...
1
vote
1answer
818 views

Standard deviation of game results about predictions from a rating system

I'm very in to Sports analysis and am keen to look at finessing my analysis models that I have worked up (I don't have a great maths background, I've just done a little bit of reading). Standard ...