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3
votes
2answers
40 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
37 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 ...
1
vote
1answer
50 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
24 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
83 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
67 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
37 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
46 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
0answers
37 views

Building models with unequal intervals between time series observations

I'm trying to get into econometric/trading modeling and the universe of variables out there is immense. There are practically continuously updated variables (currency exchange rates, interest rates, ...
0
votes
7answers
560 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
136 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
71 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
30 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
125 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
38 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
46 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
82 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
134 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
30 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
31 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 ...
1
vote
1answer
796 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
99 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
68 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
45 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
180 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
150 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
82 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
40 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
122 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
428 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
99 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
141 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
335 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?
9
votes
2answers
195 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
392 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
512 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 ...
1
vote
0answers
55 views

Equivalence of with and without replacement sampling

After some heavy reordering and canceling of factorials, I discovered that the following experiment is approximately equivalent for $m \ll n < N$ if conducted with or without replacement: In ...
5
votes
1answer
68 views

Average case analysis of learning algorithms

Typically analysis of learning algorithms is in the worst-case setting, for example regret bounds in online learning, or generalisation error bounds in classification. Whilst worst case performance is ...
11
votes
2answers
671 views

Best bandit algorithm?

The most well-known bandit algorithm is upper confidence bound (UCB) which popularized this class of algorithms. Since then I presume there are now better algorithms. What is the current best ...
11
votes
2answers
1k views

In boosting, why are the learners “weak”?

See also a similar question on stats.SE. In boosting algorithms such as AdaBoost and LPBoost it is known that the "weak" learners to be combined only have to perform better than chance to be useful, ...
15
votes
7answers
2k views

What theories should every statistician know?

I'm thinking of this from a very basic, minimal requirements perspective. What are the key theories an industry (not academic) statistician should know, understand and utilize on a regular basis? A ...
9
votes
1answer
185 views

What are alternatives to VC-dimension for measuring the complexity of neural networks?

I have come across some basic ways to measure the complexity of neural networks: Naive and informal: count the number of neurons, hidden neurons, layers, or hidden layers VC-dimension (Eduardo D. ...
19
votes
3answers
3k views

Variables are often adjusted (e.g. standardised) before making a model - when is this a good idea, and when is it a bad one?

In what circumstances would you want to, or not want to scale or standardize a variable prior to model fitting? And what are the advantages / disadvantages of scaling a variable?
6
votes
1answer
174 views

Why efficiency matters?

Suppose we are trying to estimate the quantity $\theta$ and we have that the estimator $\hat\theta_n$. Suppose it is efficient, i.e. is variance is the smallest among certain class of other possible ...
7
votes
2answers
933 views

Difference between bias-variance dilemma and overfitting

I'm wondering what difference it makes whether we talk about bias-variance dilemma where fitting a regression line to the given dataset reduces bias and increases variance or whether we talk about ...
4
votes
5answers
3k views

What exactly does 'representative sample' refer to?

When reading passages like the following: Based on a representative sample of 88 recent raids, we show that the Turkana sustain costly cooperation in combat at a remarkably large scale, at ...
8
votes
4answers
397 views

Can one leave out data from research because it is not significant?

I've encountered this sentence while reading an article on sciencemag.org. In the end, responses from just 7600 researchers in 12 countries were included because the remaining data were not ...
12
votes
3answers
2k views

What does “unbiasedness” mean?

What does it mean to say that "the variance is a biased estimator". What does it mean to convert a biased estimate to an unbiased estimate through a simple formula. What does this conversion do ...
18
votes
4answers
2k views

What is the curse of dimensionality?

Specifically, I'm looking for references (papers, books) which will rigorously show and explain the curse of dimensionality. This question arose after I began reading this white paper by Lafferty and ...
7
votes
4answers
1k views

Probability theory books for self-study

Are there any good books that explain important concepts of probability theory like probability distribution functions and cumulative distribution functions? Please avoid referring books like ...