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

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Proportion and Quantile from a Normal Distribution

A company pays its employees an average wage of \$15.90 an hour with a standard deviation of $1.50 per hour. Assume the wages are approximately normally distributed. What proportion of ...
1
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1answer
34 views

Should a Poisson regression be carried out with only 3 data points?

I'm trying to test the relationship between the number of adults counted and the percentage heather cover over 3 areas. The data looks like this: ...
0
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22 views

How to represent bayesian loss function in binary classification

I am studying classification using linear regression . Now, I want to map it in Bayesian regression. Let talk about binary classification using linear regression again. Assume that I have a set ...
3
votes
1answer
114 views

Is it possible to statistically test relationships between counts and percentages?

I have counted adult butterfly numbers over 3 areas and would like to compare these counts with the percentage heather cover on each of the 3 areas. Is this possible? My data looks like this (the ...
6
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2answers
146 views

Deriving the bivariate Poisson distribution

I've recently encountered the bivariate Poisson distribution, but I'm a little confused as to how it can be derived. The distribution is given by: $P(X = x, Y = y) = ...
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14 views

Using a one-way chi-square, determine if the null hypothesis is true, that the parks actually have the same attendance [on hold]

Public Park Families Washington Park 98 Observatory Park 106 City Park 92 Cheesman Park 97 Crestmoor Park ...
2
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115 views

Question about Dynkin Lehmann Scheffe Theorem

I'm self-studying for an examination, and I would like to understand how to use the Dynkin Lehmann Scheffe theorem for an applied question. I am using Bickel and Doksum's "Mathematical Statistics" ...
2
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1answer
45 views

Bounded expectation implied bounded conditional or vice versa?

If $\mathrm{E}\left(X\right)<\infty$ does that imply $\mathrm{E}\left(X|Y\right)<\infty$? How about vice versa? I'm thinking if we condition on an event (say $Y>2$) then if we have ...
3
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20 views

The distribution of a sufficient statistic

If I understand correctly, a distribution in the exponential family... $$\underline X\sim f_{\underline\theta}(\underline x) = exp\{\sum\limits_{i}\eta_i(\underline\theta)T_i(\underline ...
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12 views

Draw a possible realization [on hold]

Consider a postoffice with only one server and a random arrival process of single arriving customers. Every customer requires a random service time and the queueing discipline is fist-come first-served. ...
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1answer
45 views

Hyper-volume of the $\alpha$ contour of a multivariate Gaussian

I'm looking for the assymptotic ($n\rightarrow \infty$) value of (the log of the determinant of) the covariance of the $\alpha$% of observations with smallest Eucledian distance to the origin in a ...
5
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2answers
67 views

Convergence in distribution of sum implies marginal convergence?

Let $X_n, X, Y$ be random variables such that $X_n + cY \stackrel{d}{\rightarrow} X + cY $ for every positive constant $c$. Prove that $X_n \stackrel{d}{\rightarrow} X$. I know if only we have joint ...
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38 views

How can i show mathematically Partial Least Square Regression is better than other Ordinary Least Square Regression?

I want to develop techniques for attribute selection (important independent variable X) using Partial least square 2 regression(PLS2R) for a large data sets .Initially i tried using multivariate ...
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0answers
17 views

How to calculate the standard deviation from a normalised value?

I have 2 data sets (I have more but for simplicity lets say I have 2). Data 1 0.15239652 0.145848036 0.175981261 Data 2 0.417902092 0.342696648 0.354871141 I ...
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0answers
11 views

How to treat “Missing Value Analysis” test results (problems)

I have a problem with Missing Value Analysis. I am using SPSS version 20. I am trying to test whether missing values are at complete random. As I know in order to ensure missing values are completely ...
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0answers
6 views

regarding generating a unique value for a set of numbers [closed]

I need to write a function (logic) so that for a set say A{1,2,3,4,5} i generate a unique value . and when i pass back the same value back to the function it should return me the set of values present ...
0
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0answers
18 views

MPE and MAPE averages

I am a computer science graduate with a minor in mathematics, however it has been a long while since taking any statistical courses. I am looking at calculating the Mean Percent Error and Mean ...
2
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1answer
98 views

What loss function can I use for linear classification?

I have a question about loss function in bayes classification. Let see similar case of loss function in linear classification: Given data $(x,y)=${$(x_1,y1)....(x_n,y_n)$} is map to label $T=${-1,1}. ...
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0answers
6 views

Problem with calculating the avarage power of a vector? [migrated]

I am calculating the average power of a vector. I would like to compare it the final expression with the simulation. However, they are not equal. Please help me to point out which steps are wrong. ...
0
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1answer
47 views

How to compare models from different but related datasets?

I'm building regression models on four the different but related data set and at the end, I want to test the significance of models. Since my models are built in a different data set, it's not ...
0
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0answers
36 views

Chi-square test for one group

I'm struggling with this problem. For the analysis of my test, I was instructed to use chi-square test for one group. I use Statistica and everywhere I try to do this I need the expected values​​, ...
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1answer
28 views

What are the assumptions of linear regression (both simple and multiple)

I know this is a basic question, but I get slightly different answers everywhere I look, a quick example is that I learnt at Uni that the errors of the dependent variable have to be normally ...
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4answers
397 views

Calculating PDF given CDF

I know that the PDF is the first derivative of the CDF for a continuous random variable, and the difference for a discrete random variable. However, I would like to know why this is, why are there ...
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1answer
45 views

Anomaly detection using exponential weighted moving average

I would like to detect anomaly using exponential weighted moving average. I don't have series of data points. All I have is EMA(t-1) and the data point of the current time(t) DP(t). From these data, ...
0
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1answer
22 views

Alternatives to absolute error?

Let me explain my scenario in which I need to calculate absolute error. Lets say the X is the actual value. And X' is the value of X with some error 'e'. So X' = X + e'. Lets say i = 1 to 10000. I ...
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35 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 ...
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14 views

Let $f(x)$ be the density of $X$. What is $\lim_{n\rightarrow \infty}\mathrm{E}_X[nf(X+n)]$?

The expectation can be written as $\mathrm{E}_X[nf(X+n)] = \int_{-\infty}^\infty nf(x+n)f(x)\,\mathrm{d}x$. The expectation relies on the speed of tail $f(x+n)$ goes to $0$. I posted a related ...
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16 views

Regression line fit for linearly increasing data with manual reset

I've a linearly increasing time series dataset of a sensor with value ranges between 50 to 150 on which I've implemented a simple linear regression algorithm to fit a regression line, and I'm ...
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2answers
178 views

Estimate ARMA coefficients through ACF and PACF inspection

I know that this is probably a question that's been asked plenty of times, but i haven't seen an answer that's both accurate and simple. How do you estimate the appropriate forecast model for a time ...
2
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1answer
33 views

How to combine distributions

If I have two continuous distributions $f(x)$ and $g(x)$, there are several mathematical ways to combine $f$ and $g$ to get new distributions. Which correspond to what statistical interpretation? For ...
0
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0answers
7 views

What kind of statistical method is recommended to compare ratio in pre-test and post-test

I want to compare two different ratios. When this ratio is close to 1 it shows the better stability in the body. Would you please guide me that which statistical test is better for this situation? ...
5
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2answers
58 views

How would one formally prove that the OOB error in random forest is unbiased?

I have read this statement many times but have never come across a proof. I would like to try to produce one myself but I'm not even sure on what notation to use. Can anyone help me with this?
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2 views

Which test to find out whether EC50s in my three dose-response relationships are different or not?

I injected three different cRNAs constructs (construct A,B and C) into oocytes and the oocytes expressed the respective cRNAs as respective ion channels (ion channel A,B and C). My aim was to test ...
3
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3answers
48 views

Bias of estimating a Ratio?

I would like to know why 1/N * Summation of(y/x) is a worse estimator than average of y divided by average of x. This is in the context of constructing an estimator of a ratio where the ratio would ...
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14 views

to test the difference between 3 vaules [closed]

I measured half maximal effective concentration (EC50) of three different RNA construct and I want to test whether they are statistically significance or not. Which test should I use?
3
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1answer
56 views

Additive vs Multiplicative decomposition

My question is a really simple one but those are the ones that really get me :) I don't really know how to evaluate if a specific time series is to be decomposed using an additive or a multiplicative ...
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0answers
22 views

How to understand Demartines theorem [migrated]

Demartines theorem (page 3) explain why norm of a random vector increases with dimension, whereas its variance remains constant: Let $X \in \mathbb{R}^d$ be a random vector with i.i.d. components: ...
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0answers
22 views

Generating density function from $\phi(t)= 1-|t|$

Given: $\phi_X(t) = \left\{ \begin{array}{l l} 1-|t| & \quad \text{if |t| ≤ 1}\\ 0 & \quad \text{otherwise} \end{array} \right.$ Find the density of X. Attempt: ...
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1answer
37 views

Is $\phi(t) = \frac{1}{2}[cos(t) + cos(t\pi)] $ absolutely continuous?

X is a real-valued random variable with characteristic function: $\hspace{20mm}$$\phi(t) = \frac{1}{2}[cos(t) + cos(t\pi)$, $\hspace{10mm}-\infty<t<\infty$. Is the distribution of X ...
3
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1answer
41 views

Asymptotic distribution of sample variance of non-normal sample

This is a more general treatment of the issue posed by this question. After deriving the asymptotic distribution of the sample variance, we can apply the Delta method to arrive at the corresponding ...
5
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1answer
70 views

Simulating Convergence in Probability to a constant

Asymptotic results cannot be proven by computer simulation, because they are statements involving the concept of infinity. But we should be able to obtain a sense that things do indeed march the way ...
3
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0answers
75 views

Tail probabilities of multivariate normal distribution

I would like to compute tail probabilities of the standardized multivariate normal distribution for different dimensions. For example, in the case of bivariate normal I need to compute the gray area ...
1
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1answer
28 views

Showing characteristic function is infinitely differentiable

Suppose that X is a real-valued random variable. Suppose that there exists a constant M > 0 such that the support of X lies entirely in the interval $[-M,M]$. Let $\phi$ denote the characteristic ...
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32 views

Show X is degenerate if $|\phi(a^Tt)| = 1$

Let $X$ denote a $d$-dimensional random vector with characteristic function $\phi$. Show that $X$ has a degenerate distribution iff there exists an $a \in R^d$ so that \begin{align*} |\phi(a^Tt)| ...
2
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1answer
109 views

If a random variable V is independent of two independent random variables X and Y, how to prove that V is independent of X + Y?

This is question 3.8.4 of An Introduction to Mathematical Statistics and Its Applications, 5th Edition, by Larsen and Marx. This is not homework for a class I am taking now, but might someday be for ...
3
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1answer
57 views

Distribution from $\lim{T\to\infty}\int_{-T}^{T}\phi(t) dt = 2$

Let X denote a real-valued random variable with distribution function F and characteristic function $\phi$. Suppose that $\phi$ satisfies the following condition: ...
3
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2answers
82 views

Is $F(E[Y_n]) \approx E[F(Y_n)]$ a reasonable approximation?

Studying the asymptotic distribution of order statistics I came across this approximation: $$F \left( E \left[ Y_n^{\left(n \right)} \right] \right) \approx E \left[ F \left( (Y_n^{\left( n \right)} ...
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1answer
49 views

Prove that $E[g(X)] = \int_{-\infty}^{\infty}G(t)\phi(t) dt$

Let $X$ denote a real-valued random variable with characteristic function $\phi$. Suppose that $g$ is a real-valued function on $\mathbb{R}$ that has the representation $\hspace{25mm}g(x) = ...
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1answer
32 views

Characteristic Function proof

Let $\phi_1,\ldots,\phi_n$ denote characteristic functions for distributions on the real line. Let $a_1,\ldots,a_n$ denote nonnegative constants such that $a_1+\ldots+a_n = 1$. Show that ...