A weighted mean (or weighted average) is like an ordinary mean, but the observations don't contribute equally - more emphasis is placed on some data values than others; they are weighted by a bigger or smaller amount than 1/n.

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Weighted mean: Inverse of individual values's confidence interval as weight?

This seems to be a very basic question, however I could not find a satisfactory answer throughout the web, yet. I have, say, N values, whose I know the N respectives 95% confidence intervals (said ...
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9 views

Combining several variances, obtained from weighted mean and moving average

I have three questions 1: Can variances for different mean calculations be combined to obtain the combined variance? \begin{equation} S = \sqrt{s_1^2 +s_2^2 + s_3^2} \end{equation} 2: When using ...
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21 views

Mean of an interval censored random variable

It is likely that I am incorrect terminology here, but I am trying to compute a "mean" of an interval censored random variable. Here is an example where: 1. a random sample from the standard normal ...
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8 views

Weighted Standard Deviation [duplicate]

I got a problem calculating a weighted standard deviation for a municipality and its precipitation on various landcover types (LC). I got the mean values of precipitation for several days for each ...
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7 views

Determining overall score based on several scores in the past

I'm one of the captains of my school math club (http://lhsmath.org), and I'm looking for insight into how to determine the overall competitive math ability of a person based on a number of past tryout ...
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1answer
27 views

Representing a subset of observation using weights

I have $n$ observations for $m$ variables that are sorted by time, e.g. observation $1$ is the oldest, whereas observation $n$ is the newest. I represent this data as an $n\times m$-dimensional matrix ...
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20 views

with two EWMA means of different window sizes, can we estimate any other means? slopes? jumps?

EWMA is defined as follows(1, 2, 3, 4, 5): $$ \mu_{N} = \frac {1}{N} \Sigma_{i=1}^{N}x_i $$ $$ =\frac {1}{N} \Sigma_{i=1}^{N-1}x_i + \frac{1}{N}x_{N} $$ $$ =\frac {N-1}{N} \frac{1}{N-1} ...
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29 views

Aggregating Standard Errors for Predicted Probability Estimates

I obtain predicted values from a logistic regression for a certain outcome (e.g., mortality) at the hospital level – the data is at the patient level – and need to compute the average across ...
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47 views

Exponentially Weighing Moving Average (EWMA) for weekly data

I'm aware that the typical EWMA approach is applied over larger time periods (say for Volatility, where lambda = 94% and all weights add up to 100% for stock returns data from last 5 years). ...
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16 views

Weighted mean and covariance

I have a variable $O$, depending on two other variables $x$, $y$ as $O=\frac{x}{y}$. I have several measurement (each one with its uncertainty) of $x$ and $y$ and for both of them I have computed a ...
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13 views

Outlier detection in weighted time series

Given a set of observations $X _n = \{x_1, \dots, x_n\}$, and a new observation $x_{n+1}$, we aim to find whether $x_{n+1}$ is outlier. One approach to solve this problem is to check whether ...
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32 views

Weighted variance of the weighted variance in frequency transition matrix?

Assume I have a $m\times n$ Transition Matrix $A$ with $m$ different observations and $n$ represents a discrete state space. Each column counts the frequency that state $j\in [1...n]$ was visited from ...
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1answer
30 views

Inverse-variance weighting

I'm writing a Bachelor Thesis in engineering an a small part of it has two deal with assigning weights to independent measurements. This is from the thesis: I am pretty sure that what equations ...
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1answer
25 views

Estimating costs with extreme values

I am trying to estimate health care costs and I was wondering what the standard practice is for extreme values? By extreme values I mean I have a large portion of my costs being zero and a small ...
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60 views

Weighting on tables

I have a question about terminology. Suppose I have data categorized by three factors A, B, and C, with cell means $\bar{y}_{ijk}$ and cell frequencies $n_{ijk}$, where $i$, $j$, and $k$ index A, B, ...
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1answer
13 views

Appropriate weighting for averages

What is the appropriate (or the advantages of disadvantages for each) measure for weighting mortality rates across countries: total population or total number of deaths? For example, if you have ...
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1answer
82 views

Calculating and comparing weighted means with changing number of daily values

I have daily data where the number of values changes with each day. I would like to calculate the weighted mean of this data, where days with more values are weighted higher than days with less. ...
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1answer
118 views

Compare Log-Normal Distributions

I am looking at distributions for the fuel consumption of vehicles in the US and I have two sets of data: Data Set 1 - This is a dataset for the fuel consumption of all vehicles made available for ...
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1answer
71 views

Estimating an overall summary statistic (mean) for a value reported by ten published studies

Background I am writing a systematic review and meta-analysis of the association of exposure to X with the outcome Y. I have identified ten studies that report on this subject. This will be a ...
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1answer
103 views

How to compare subjects with different weights?

I have a collection of products that could be rated as good or bad. Every product has a grade, that is the sum of "good" votes minus the sum of "bad" votes. These products are also split into two ...
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22 views

Computationally cheap estimation of the mode from 2D samples

I say 'mode' in the title – perhaps there's something more appropriate I can find. Here's my problem: A person is in a $100\mathrm m$ by $500\mathrm m$ space. I have about 100 samples randomly ...
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21 views

How do I determine the significance of a difference in weighted averages from a Likert-type survey question?

I have multiple survey questions that give respondents 4 Likert-type options for a response to qualify their knowledge/skill in a particular area. I have calculated a weighted average (and divided by ...
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13 views

Number of occurrences gives higher weights

I have this algorithm that I'm implementing that I need to change to give it a better accuracy. To give you an idea of the problem, I have a a bunch of lists that contain items and all items in these ...
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3answers
74 views

How to calculate the weighted mean?

For example assume I have three observations as given in matrix A $A = \left[ \begin{array}{ccc} 1 & 0 & 1 \\ 1 & 1 & 0 \\ 0 & 1 & 1 \\ \end{array} \right]$ each row vector ...
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101 views

Paired test: many repetitions, few subjects

I have a situation similar to this: 9 normal-sighted subjects are each tested under two conditions: say, with and without spectacles (of a fixed power) and asked to reach towards an object many times ...
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165 views

Weighted average of measurements with unequal errors

Suppose I have the numbers below. Consider them as results of some measurement. ...
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1answer
310 views

Standard deviations and confidence intervals (weighted) running average

My question is related to this one. I am calculating averages, actually as many as I have samples because I calculate a running average, and for equal weighting I know how to calculate the $95\%$ CI, ...
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183 views

Weighted Standard Deviation vs. Weighted Regression Standard Error

This is an R question. I have $n$ observations of the variable $y$, with each observation, $i$, weighted by $w(i)$. Each $w(i)$ weight falls between zero and 1, with the sum of the weights, ...
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26 views

how to use global weights to update local ones

I have a population of data points. Each data point expresses a different name. Each such name belongs to a different ethnicity, say {A, B, C, D, E}, with a probability. The sum of probabilities for a ...
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27 views

Aggregating based on inverse probability weight

I have a data set that includes life quality indices for many cities. I want to aggregate the indices to the metropolitan level. Since some cities in each metro area are missing, the data set provides ...
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37 views

How do I determine the appropriate “weight” of a point in fantasy basketball?

For fantasy basketball, I want to quantify a player's output based on his Points, Rebounds, Assists, Steals, 3s, and Blocks production. Let's pretend that over the course of an imaginary basketball ...
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1answer
469 views

Degrees of freedom for a weighted average

And yet another for the long list of degrees-of-freedom questions! Given an i.i.d. sample $x_1,..., x_n$ from an arbitrary real-valued distribution with expectation $\mu$, the sample mean can be ...
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1answer
300 views

Using the eigenvalues from PCA in k-nearest-neighbours

I'm quite new to this StackExchange, only been a lurker till now, but my StackOverflow fellows have said you'd be the best people to ask about this. Anyway, enough introduction. I'm using the ...
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1answer
92 views

Comparing two lists to measure for similarity

The problem I am trying to solve is finding the probability that two people are the same by cross-referencing the associates of the two people. For example, if person A is associated with the ...
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58 views

How to bootstrap confidence of a weighted measure?

I have a large data set of 20M observations with 20+ measures for each observation (people). Additionally I have a set of weights that reflect the racial population where each person lives. For ...
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3answers
905 views

Weighted standard deviation of average

For two groups (a and b) with unequal numbers of observations (n=10 and n=30), I have given their means and sd. Calculating the weighted mean is pretty straight forward. But how can I derive the sd of ...
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1answer
93 views

Standard error of a weighted mean when observations are not independent

I have a situation where I have a bunch of noisy observations with known (and normal) sampling error and a non-trivial co-variance structure between the observations. In an uncorrelated setting, I'd ...
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1answer
39 views

Estimate the parameters of an ellipse in the presence of large outliers

I have a number of points $x_1,\ldots,x_m\in\mathbb{R}^n$ with weights $w_1,\ldots,w_m$ between 0 and 1. There is an ellipse which contains a very high concentration of points with weights close to ...
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2k views

How to compute weighted means and SDs?

I want to calculate volume weighted average price and standard deviation for the following dataset: ...
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2answers
188 views

Confusion regarding weighted average

This is a pretty simple question and I'm wondering how to go about finding a solution. I have the following data. ...
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1answer
138 views

Given weighted mean and raw data, derive weights to minimize error

Imagine I have a set of data from an experiment: Observed Measurement 1: 5 Observed Measurement 2: 6 Observed Measurement 3: 7 Observed Measurement 4: 8 Observed Measurement 5: 9 I have a target ...
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1answer
2k views

Weighted Variance, one more time

Unbiased weighted variance was already addressed here and elsewhere but there still seems to be a surprising amount of confusion. There appears to be a consensus toward the formula presented in the ...
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123 views

Best fit of weighted mean?

The title might be somewhat misleading. I am trying to solve the following optimization problem and do not find any clues. Can any one help? I have a sequence of $n$ observation $s_i$. Each ...
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1answer
189 views

Is there a more elegent solution for exponentially weighted-mean in R? [closed]

OK so I have a working code to do what I want but I am new to R and feel like my solution is very clunky and there is likely a more efficient way to get the same result. I have a set of data that ...
2
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1answer
92 views

Computing lowess mean value

I am trying to reimplement the lowess algorithm in java. I read the matlab page explaining lowess with the following steps: Compute the regression weights for each data point in the span. A ...
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1answer
230 views

How does a Daniell kernel differ from a two sided average?

As far as I can understand, the Daniell kernel, is simply $K(j/M)=\frac{1}{2M+1}1(|j|\leq M)$. Namely, this is a two sided average. Why do people call this an untruncated kernel and differentiate ...
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2answers
146 views

Always get confused by “probabilities and weighted probabilities” type of questions as cant differentiate between two

Urn 1 contains 5 white balls and 7 black balls. Urn 2 contains 3 whites and 12 black. A fair coin is flipped; if it is Heads, a ball is drawn from Urn 1, and if it is Tails, a ball is drawn from Urn ...
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2k views

Bias correction in weighted variance

For unweighted variance $$\text{Var}(X):=\frac{1}{n}\sum_i(x_i - \mu)^2$$ there exists the bias corrected sample variance, when the mean was estimated from the same data: ...
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1answer
356 views

Optimize Weights used in a Weighted Average

I want to calculate a weighted average, mostly for illustration purposes. However, I have an outcome variable that is Y/N and would like to optimize the weights relative to this outcome. What are ...
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186 views

Voting system that uses confidence for each voter

Let's say, we have simple "yes/no" question that we want to know answer to. And there are N people "voting" for correct answer. Every voter has a history - list of 1's and 0's, showing whether they ...