Mathematical theory of statistics, concerned with formal definitions and general results.

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21 views

Is it possible to reduce Fisher's non-central hypergeometric distribution from a multivariate to a univariate equivalent?

Is it possible to combine the odds for two or more groups of balls in a multivariate version of Fisher's non-central hypergeometric distribution to give a univariate equivalent? For example, this ...
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17 views

Prob Question-Winning a Game

A and B have a game. There are 7 games in total, who wins 4 games first will succeed the whole game and then the game ends. Given that A has a probability P to win one game, and A already lost the ...
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1answer
15 views

Resource request : Relationship between chaotic dynamics and $i.i.d$ random variables

The article Statistics of chaotic binary sequences presents the spectral properties of chaotic systems such that they can be candidates for generating pseudo random binary sequences. Another article, ...
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1answer
48 views

Handle random orthogonal matrix determinant

I've got probably a silly question about which, I must confess, I'm confused. Imagine repeated generating of uniformly distributed random orthogonal (orthonormal) matrix of some size $p$. Sometimes ...
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1answer
31 views

Are $\hat{\beta}_{\text{ls}}$ and $S^2$ independent if errors are not normally distributed?

When estimating a linear model $$ Y_i = X_i\beta + \varepsilon_i \quad \quad 1\leq i\leq n$$ We have $\hat{\beta}$ the least squares estimation of the slope and the estimation of the variance, $S^2 = ...
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1answer
32 views

Closed form solution for t-stats and p-values in multiple regression

I am trying to build a spreadsheet that will perform multiple linear regressions on a number of data series using the closed-form solution. It was fairly straightforward to write the solution for the ...
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16 views

Why do we take the absolute value of weight of evidence when computing the information value?

I was looking at the explanation for Information Value calculation in STATISTICA and I find it a bit confusing: ...
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0answers
15 views

Does THE discordance test for outliers exist? [on hold]

I have looked but can't find 'the discordance test for outliers'. Does this specific test even exist? And if it doesn't, which test would you suggest to measure discordance for outliers?
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1answer
39 views

More than one unbiased estimator for a single unknown parameter?

Is it possible to have more than one unbiased estimator for a single unknown parameter?If "Yes" then how and if "No" the why?
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1answer
86 views

Distribution of the quotient of two gamma random variables with different rate parameters?

I have a question about how to derive the distribution of the quotient of two random gamma variables drawn from two different Gamma distributions with the same shape, but different rates. For example, ...
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14 views

Standardization (z-score) across the “Samples” or across the “variables”?

I found in literature that one of the most common way of standardization data is to compute z-scores (mean subtraction and division by standard deviation). Can anybody tell me if it is ok to compute ...
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0answers
19 views

Deducing an approximation to the Gini coefficient

Assuming we do not know the Lorenz curve function, If $(X_k, Y_k)$ are the known points on the Lorenz curve, with the $X_k$ indexed in increasing order $(X_{k – 1} < X_k)$, so that: $X_k$ is the ...
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11 views

Class of semimartingales for which all characteristics can be estimated?

I'm going to ask the question for Ito semimartingales rather than semimartingales in general, but more general answers would be great. An Ito semimartingale is a martingale for which the ...
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1answer
40 views

Finding $Cov(2X+7, X^2 +3X - 12)$

So I have this pdf, $f(x)=3x^2$ for $x\in (0,1)$ and I need to find $Cov(2X+7, X^2+3X-12)$. My main concern about how I answer this is, what is the joint pdf for these two distributions? I guess ...
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1answer
145 views

How can I compute $\int_{-\infty}^{\infty}\Phi\left(az+b\right)^{2}\phi(z)\,dz$ in closed form?

How can one evaluate the expectation of the squared normal CDF in closed-form? $$\mathbb{E}\left[\Phi\left(aZ+b\right)^{2}\right] = \int_{-\infty}^{\infty}\Phi\left(az+b\right)^{2}\phi(z)\,dz$$ ...
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1answer
35 views

Mean vs. Standard deviation for data ranging between 0 and 1

If e.g. 100 people can rate a subject between 0 and 1 than the dispersion (e.g. standard deviation) among the 100 raters is potentially largest for a mean of 0.5 (50 people rate 0, 50 people rate 1) ...
4
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1answer
87 views

Is a spike-and-slab prior a proper prior?

Is a spike and slab prior a proper prior? (I am talking about a (product of Bernoulli) spike and Normal slab) If not, does it still lead to a proper posterior?
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1answer
39 views

Computational complexity for linear discriminant analysis

The linear discriminant analysis algorithm is as follows: I want to conduct a computational complexity for it. For each step, the complexity is as follows: For each $c$, there are $N_cd$ ...
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0answers
18 views

Z-score across the “Samples” or across the “variables”?

I found in literature that one of the most common way of standardization data is to compute z-scores (mean subtraction and division by standard deviation). Can anybody tell me if it is ok to compute ...
0
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1answer
40 views

Weibull distribution

I need to find a distribution that fail regularity condition.Maybe weibull distribution can be but I did not find why, please help me.
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2answers
96 views

Likelihood Ratio for the Bivariate Normal distribution

For a random sample from a Bivariate Normal distribution with $\rho=\frac{1}{2}$ and equal variances, i.e. $\sigma^2_x=\sigma^2_y=\sigma^2$, I would like to derive the Likelihood Ratio Test for the ...
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1answer
58 views

A Simple Regression Model for Our Experiment? [closed]

We know, In statistics, simple linear regression is the least squares estimator of a linear regression model with a single explanatory variable. In other words, simple linear regression fits a ...
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1answer
69 views

uniform distribution with density function? [closed]

If $0.3,0.2,0.8,0.3,0.4$‌ are found from one random instance with uniform distribution with following density function, We need to find $\theta $ estimate with Method of moments. how should we do ...
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1answer
57 views

Connection between MLE (Maximum Likelihood Estimation) and introductory Inferential Statistics?

The first thing that one learns in statistics is to use the sample mean, $\hat{X}$, as an unbiased estimate of the population mean, $\mu$; and pretty much the same would be true for the variance, ...
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26 views

Complete statistic for uniform distribution

$X_{(1)}, X_{(2)}, \ldots, X_{(n)}$ are i.i.d uniform where $f(x; \theta1, \theta2) = 1/(\theta2 - \theta1);\qquad \theta1 < x < \theta2$. Let $X^{(1)} = \min(X_{(1)}, X_{(2)}, \ldots, ...
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24 views

Book recommendation of Time series analysis [duplicate]

I am doing research in data mining, i am not sure if this course (time series analysis) gonna help me in my research. I am almost new to statistics and i know a little about this field, so do you ...
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94 views

A question on the paper by Littell and Folks (1971)

I have been reading this very interesting paper but have come across something that I do not quite understand, namely how the asymptotic limit of the quantity $-\frac{1}{n} \log \left(1-F_n^{F} ...
4
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1answer
84 views

Null distribution of subspaces similarity, or what is the distribution of $\mathrm{tr}(AA'BB')$?

What is the distribution of $\mathrm{tr}(AA'BB')$ where $A$ and $B$ are two random matrices of $d \times k$ size with orthonormal columns? Maybe the expected value is easier to compute? A fallback ...
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11 views

Computation of likelihood of a simulated mean value being a part of population of observed mean value?

0 down vote favorite Would you please help me to clarify this question: I use a model to simulate milk yield of a population of animal (200 individuals), in each simulation I calculate the mean milk ...
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1answer
51 views

calculating $\mathrm{Var} (e^{-X})$

suppose $X$ has probability density function $f_\theta(x)=\exp(-(x-\theta)-\exp(-(x-\theta)))$. how can I calculate $\mathrm{Var} (e^{-X})$
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29 views

calculating UMVUE of parameter $ e^{2\theta}$

suppose $X_1,X_2,\ldots, X_n$ be random sample with $f_\theta(x)=\exp(-(x-\theta)-\exp(-(x-\theta)))$. how can I calculate UMVUE of parameter $ e^{2\theta}$. I suppose $T=\sum_{i=1}^n e^ {-x_i}$. ...
3
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1answer
42 views

Predict the weekday of a recurring event and its probability

Suppose, we have 100 observations of variable X. X is the day of the week (Sunday – Saturday) when a specific event occurs on regular basis. E.g. when a postman delivers a package every week for 100 ...
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12 views

How to show ancillary statisitc of normal random sample?

Let $X_i \sim N(\mu,\sigma^2)$ and $X_i$ are independent. Then how to show that: $$ T = \left(\frac{X_1-\bar{X}}{S},\frac{X_2-\bar{X}}{S},\ldots,\frac{X_n-\bar{X}}{S}\right) $$ $T$ is an ancillary ...
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2answers
87 views

Introductory multivariate statistics reference for beginners

I am from computer science department doing research in data mining and image mining. I remember the last course about stat was introductory to statistics and probability in general. Now I have this ...
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1answer
38 views

How is Gram-Schmidt procedure used in the following time series context?

I was reading the innovation algorithm in Brickel's Time Series Theory and Methods (page 171-172). Let $H$ denotes a Hilbert space, $P$ denotes the projection operator and $\bar{sp}$ denotes closed ...
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0answers
17 views

How do I find the odds ratio using the output of a loglinear model?

This was a homework problem from Agresti (7.2) that I didn't get, even after looking at my class' solutions. Help? So we are given the output of a loglinear regression ($λ_{ij}^{XY}$). The output is: ...
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1answer
422 views

What are the theoretical guarantees of bagging

I've (approximately) heard that: bagging is a technique to reduce the variance of an predictor/estimator/learning algorithm. However, I have never seen a formal mathematical proof of this ...
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1answer
63 views

What distribution is appropriate for modeling internet forum posting?

Internet message boards, such as 4chan, consist of a series of "threads" to which people post replies. One observes that most threads receive zero or one reply, a few receive 2 or more, and only the ...
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25 views

Distribution of estimator

Some help would be appreciated on this one. There is something I can't get around my head. Let's suppose we havfe $ln x$ that is following a Normal distribution of parameter $lnx\rightarrow ...
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0answers
25 views

Incremental autocorrelation coefficient lag 1

I am a developer and I am trying to compute the autocorrelation coefficient of lag 1 incrementally. The problem is I have to test the results with some certified results from NiST Datasets. The ...
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0answers
46 views

3 Class Classification based on a Bernoulli feature and gaussian feature

Consider a 3-class classification problem with mixed features, where one feature is Gaussian and another is discrete Bernoulli: Prior class probabilities: P(C1) = .5, P(C2) = P(C3) = 0.25 ...
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28 views

Bias and variance of a naive bayes classifier and KNN classifier

After reading the paper by J. Friedman, ”On bias, variance, 0/1-loss, and the curse-of-dimensionality,” Data Mining and Knowl- edge Discovery, 1997. I would like to estimate both bias and variance ...
2
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1answer
36 views

Why are inf and sup used in the definition of minimax estimators?

An estimator $\hat{\delta}$ is minimax iff $$\sup_\theta R(\theta,\hat{\delta})=\inf_\delta\sup_\theta R(\theta,\delta)$$ or in english iff out of all estimators it has the least maximum risk. For ...
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1answer
34 views

Problem with generalized likelihood ratio test from samples from beta distribution

I was trying to resolve this exercise: This exercise is from the book "Statistical Inference, Second Edition" by Casella and Berger. Checking the solutions manual, I was understanding the solution ...
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1answer
62 views

Excess Bunching - Bunching Estimator (Saez 2010)

Saez (2010) defines excess bunching at the kink as the area under the density in the dominated region: $$ B = \int^{z^*+d z^*}_{z^*} h(z)dz \approx h(z^*)dz^* $$ where income $z$ is distributed ...
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23 views

How to categorize users based on their movie views?

Apologies for cross posting. I have a dataset of size (61573, 25). The rows represent users whereas the columns represent ...
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1answer
15 views

sample from a mixture

Suppose I have two types of students, male or female. Suppose a test score of a male student follows a distribution $F_m$ and suppose a test score of a female students follows a distribution $F_f$. ...
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19 views

What is the number of sample points when a pair of dice is thrown once

What is the number of sample points when a pair of dice is thrown once. How can we calculate it using permutation?
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176 views

A practical question in simulating real world outcomes

PredictWise aggregated polling data and, for each state, estimated the probability that the Obama or Romney would win. Here is the polling data. The data frame has 51 rows(51 states). the name of this ...
5
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0answers
153 views

A tricky question about correlation [duplicate]

$X$, $Y$ and $Z$ are three random variables where their pairwise correlations are the same, i.e., $corr(X,Y)=corr(Y,Z)=corr(X,Z)=\rho$ what are the possible values of $\rho$? I was asked this in an ...