Mathematical statistics is the study of statistics from a mathematical standpoint, using probability theory as well as other branches of mathematics such as linear algebra and analysis.

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Statistical Estimation Book Request

I am seeking a clear book for parameter estimation, estimation methods, properties of estimators, minimum variance estimators, asymptotic properties of estimators and interval estimation reducution.
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1answer
17 views

Units of vaiance when variable is in %.

I have some confusion here. If some random variable is measured in some units, say $kg$ then clearly it's variance is measured in $kg^2$. But if the variable is dimensionless and measured say in ...
3
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2answers
27 views

Determinant of Fisher information

In information geometry, the determinant of the Fisher information matrix is a natural volume form on a statistical manifold, so it has a nice geometrical interpretation. But what is it in ...
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2answers
25 views

Errors and Residual

Why are errors independent but residuals dependent? As far i know the sum of the residuals within a random sample is necessarily zero, and thus the residuals are necessarily not independent. But also ...
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1answer
42 views

History of Mathematical Formulas

I just wondered why in calculating something for example Variance we square the difference of the value and its Arithmetic Mean and do not take the absolute value of the difference? Are there books or ...
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1answer
21 views

Find joint distribution function in region

I can't for the life of me figure this one out, I am stuck on part (c) ... I have this as my starting point ? $$ \frac{45}{304}\int_0^x\int_{2-x}^2 u^2v^2\,\mathrm{du} \mathrm{dv} $$ Here is my ...
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1answer
23 views

Risk function of binomial random variable

Suppose $X\sim Binomial(100,\theta)$, True estimator($\delta$) $= X/100$; $$R(\theta ,\delta) = E_{\theta}\left[\left(\theta - \frac{X}{100}\right)^2\right] = \theta(1-\theta)/100$$ I am ...
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0answers
16 views

SBC score clarification

For the SBC test, it says that this is more favourable as compared to the Anderson darling, kolomogorov Smirnoff test and the chi-squared tests because it doesn't have the fault that, when n increases ...
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16 views

What does a presentation on block design and Latin squares consist of?

I read the wikipedia pages of both and I just cannot understand these two concepts. I have a presentation on both of these topics next week and I need some headway on both of these topics.
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1answer
21 views

Prove that mean square error equals expected conditional variance

I'm a first year grad student in Statistics. The book I'm using mentioned conditional variance, and I wanted to read up more about it. I dove down the google rabbit hole and found this website. I read ...
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14 views

A question regarding 90 ball bingo [on hold]

What is the average number of calls necessary to daub a number on a ninety ball bingo ticket?
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2answers
19 views

Variance of the sum of sample means

Let $X$ be a random variable with normal distribution with mean $ \theta$ and variance $ a>0$. Let $ Y $ be a random, variable with normal distribution with mean $\theta$ and variance $b>0$. ...
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2answers
68 views

Log normal distribution - Where am I wrong?

Let $X$ be a R.V whose pdf is given by $$f(x)=p\frac{1}{\sqrt{2\pi\sigma_1^2}}\exp\left(-\frac{(x-\mu_1)^2}{2\sigma_1^2}\right)+ ...
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16 views

Hypercontractivity of Markov Operator

I have been reading a paper by Ahlswede and Gacs on hypercontractivity of Markov operator (see here 1) and its application to information theory. To be honest, I could not fully understand the ...
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1answer
15 views

What are the chances of a sample distribution, given that I know the larger population's distribution?

I know that the larger population, of size m, follows a normal distribution. I have some sample that is size n, and follows its own particular distribution, which is not normal. Given my sample sizes, ...
3
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3answers
77 views

How many ways can $10$ digits be written down so that no even digit is in its original position

If I have the numbers $0,1,2,3,4,5,6,7,8,9$ written down in that order, how many ways can the $10$ digits be written down so that no even digit is in its original position? It would seem that I can ...
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0answers
28 views

Economics, Statistics

Now suppose I am trying to forecast using historical data and using random walk method, In the formula $ y_t = y_{t-1} + u_t $, how can I find the $u_t$ form the model ?
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1answer
103 views

How to convert a problem to a stars and bars problem?

Continued question from here. With certain questions I have $x_i$ being constrained by various different inequalities, I want to know how to remove these from the problem, to bring me back to a ...
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2answers
37 views

Integration by parts

Integrate using integration by parts: $F(y) = (y+1)e^{-y}$ Find: Evaluate the $\int_{a=0}^{b=\infty}F(y)\;dy$ using integration by parts. Thus far, I've distributed the $e^y$ term and split ...
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Math issue implementing an invoice API [on hold]

Okay, so, I have $2$ separate systems: An invoice record database on an external site, I do not have access to the code here. An prestashop e-commerce installation, where i am developing a plugin. ...
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1answer
11 views

discrete variables in fraction

I am looking for examples of discrete variable whose value is in fraction ONLY. I am told there are very few such examples. I am not looking for variables with mixture of both whole numbers and ...
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0answers
18 views

Jeffrey's Prior for Bivariate Lognormal

Exactly what the question says, I'm working on code for an MCMC simulation and need to set some uninformative or weakly informative priors. I haven't been able to find the prior for the sigma ...
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0answers
12 views

Limiting distribution of loss random variable?

I'm going to try to make the notation not actuarial-specific, but for those with a background in actuarial science, this relates to exam MLC. Suppose I have random variables $X_{i} \geq 0$ such that ...
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4answers
35 views

Probability: Linear Seating Arrangement

Okay, I'm new at probability and statistics, so please try to answer this as thoroughly as possible and explain why you did everything, from using a specific number to why using factorials and ...
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1answer
21 views

Expected length of a random vector

I meet a basic definition about the expected length of a random vector when reading a paper: What is "expected length" How to roughly derive both equations (yellow part) (Is that Gamma ...
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3answers
93 views

How to use stars and bars(combinatorics)

How to use the stars and bars method? Say I want to find number of combinations I can get with $x_1+x_2+x_3+x_4=22$ Where $x_i\in\mathbb{N}$ Is this the correct time to apply the method?
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31 views

Determining the Cramer-Rao lower bound

Let $X = (X_1,\dots,X_n)$ be a vector of iid variables from the smooth density $f(x,\theta_0), \theta_0 \in \Theta \subset \mathbb{R}$. Let $L(\theta)$ be the likelihood and $I(\theta)$ the ...
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1answer
19 views

Compound Interest - Initial Amount Borrowed [on hold]

Could someone explain how to calculate this question? Two loans of an equal amount were taken out at $10\%$ interest per annum for $3$ years and $4$ years respectively. The difference in the ...
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1answer
14 views

Avg # of Rectangle Intersections in 2D Field

So imagine I have a large 2D field. Thousands of small rectangles overlay the field. The field is much larger than the rectangles. The rectangles are placed randomly in the field such that they may or ...
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30 views

Estimators of the binomial distribution

This is a follow-up of this previous question and elaborates on the answer I received there. $\def\b{\begin{pmatrix}}\def\e{\end{pmatrix}}\def\a{\alpha}X_1,X_2,\dots, X_n$ are a random sample from ...
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1answer
26 views

How to predict next number from a given set of measurement data?

I have to do some experiment and measure it on a specific time 0, 3, 6, 9, 12, 18, 24, 36 months $$ \begin{array}{l|c|c|c|c|c|c} \text{Month} &ID1 & ID2 & ID3 & ID4 & ...
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1answer
30 views

Need my data to fit ANOVA…

I am doing some research on constructed wetlands. I have four wetland as follows. Wetland A - Gravels Wetland B - Gravels + Plant Wetland C - Biochar + Plant Wetland D - Biochar + Gravels + Plants ...
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1answer
27 views

How to estimate the standard deviation in this normal distribution?

There is this simple looking basic statistics question that asks to estimate its mean and standard deviation. I have some doubts and just want to make sure whether my working is correct. For part ...
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1answer
18 views

Standard deviation in normal distribution

A manufacturer uses a machine to make metal rods.The diameter of the rods follow a normal distribution with a mean of 1cm and a standard deviation of 0.02cm If the standard deviation of the diameters ...
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10 views

find the mean of a collection of the solutions of given linear systems

Suppose one has a group of $k\times k$ square matrices $A_i, i = 1,2..n$, another $k$-vector $b$ is also given. I want to exam the mean of the group of vectors $x_i$ over $i = 1,2...n$ where $A_i * ...
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1answer
19 views

Simplify $\dfrac {\partial }{\partial b}\left( \sigma ^{2}\right) =0$ and $\dfrac {\partial }{\partial m}\left( \sigma ^{2}\right) =0$

Given $\sigma ^{2}=\sum ^{N}_{i=1}\left[ y_{i}-\left( mx_{i}+b\right) \right] ^{2}$ How to simplify $\dfrac {\partial }{\partial b}\left( \sigma ^{2}\right) =0$ and $\dfrac {\partial }{\partial ...
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0answers
19 views

Negative integer factorial in Koziol's combinatorial approach

I' m trying implement Unbiased split selection from this document: http://www.stat.uni-muenchen.de/sfb386/papers/dsp/paper464.pdf I have problem on 14 page. I have list of $$ \binom{i_k}{j_k} $$ $$ ...
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1answer
12 views

Finding the percentile of a value given other percentiles

I am using someone else's research and only have part of the data. I want to find the percentile of a value, such as 350.2, based upon the data given. The following is known: mean = 308.2 The ...
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2answers
13 views

How to prove a given statistical test has the greatest power

It is very conventional in evaluating the null hypothesis to consider the distribution of the mean of a sample of some size if the null hypothesis were true and to compare the mean of your own sample ...
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12 views

Comparision between Hamming distance and cosine similarities?

I want to check the similarities between binary vectors of different length and I am using cosine similarities and hamming distances for calculations. These are of length 1000 elements(0 and 1). ...
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1answer
20 views

Median of grouped data

part (ii) Median = $Lm +(n/2-cf)/fm*h$ = $171+(20-16)/12*3$ = $172$ am i correct?
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1answer
29 views

Statistical Inference - Finite Population Correction

I am studying for an exam in Quantitative Analysis and I am looking through past exam papers (here's a link the exercise I'm referring to: http://i62.tinypic.com/2cz1nqh.jpg). I understand all of the ...
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1answer
27 views

Equivalence of two formulas for variance and covariance

I know two formulas for variance: $$\operatorname{variance}(f) = \operatorname{expectation}((f(x) - \operatorname{expectation}(f^2(x)) \\ = \operatorname{expectation}(f(x)^2) - ...
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1answer
26 views

How to derive “Pooled Sample Variance”?

Let $s_p^2 = bs_1^2 + (1-b)s_2^2$, this can be an unbiased estimator of population variance, provided we find the correct value for $b$; in particular, $s_p^2 = \frac{(n1-1)s_1^2 + ...
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1answer
39 views

Statistics Probability Density Functions with Mutliple Features (Multivariate Normal Distribution)

I'm looking for a beginner-friendly explanation on how this Probability Density function works when dealing with mutliple features and what the variables and terms mean in detail. I'm seriously ...
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1answer
30 views

A Bayesian estimate for rank

I am not sure how to put this succinctly but here is the problem. Consider a random variable $X$ which can take a finite number of non-negative values. It takes each value with the same probability. ...
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3answers
58 views

Derivation of standard error of mean

I was going through this wikipedia article on standard error. I could not understand the crucial step here. It goes like this: This formula may be derived from what we know about the variance of a ...
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2answers
60 views

Does an exponential model fit my data?

I am measuring accumulation of a fluorescent-tagged protein at a particular location within a cell over time. In previous experiments that I have performed, I see a standard exponential distribution ...
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1answer
27 views

time series similarity heuristic

What is a good heuristic for time series similarity. I'm ok with false positives bc I will then pass the results of the heuristic to an actual series similarity algo. Basically I want the heuristic to ...
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1answer
59 views

Math required for medical statistics

I have never been good with Math. I talk to many of my medical colleagues and it seems to me that most of them have a poor understanding of statistics. Many of them claim to understand it but actually ...