What is Estimation: Definition and 205 Discussions

Estimation (or estimating) is the process of finding an estimate, or approximation, which is a value that is usable for some purpose even if input data may be incomplete, uncertain, or unstable. The value is nonetheless usable because it is derived from the best information available. Typically, estimation involves "using the value of a statistic derived from a sample to estimate the value of a corresponding population parameter". The sample provides information that can be projected, through various formal or informal processes, to determine a range most likely to describe the missing information. An estimate that turns out to be incorrect will be an overestimate if the estimate exceeded the actual result, and an underestimate if the estimate fell short of the actual result.

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  1. B

    Induction motor load estimation from a variable resistive load

    Hello, I'm trying to find out how much energy an induction motor pulls over a 24 hour period when connected to a resistive load. The only data I have are the specifcations of the motor, so I can estimate how much energy it will draw based on what capacity it might be running at. Really...
  2. L

    Archived Time estimation - mass spectrometer

    Hi everyone Homework Statement I want to separate isotopes of uranium with some kind of a mass spectrometer. The isotopes are Mass numbers 95 Atom numbers 235 and 238 Question: How long does it take to extract 1kg of the 235 isotope if I have a ray of charged ions (charge = e) when the...
  3. R

    System Parameter Estimation with Projection Algorithm

    I am recently trying to identify system parameters with projection algorithm, but faced a problem, and the dynamic model is the following: \ddot{y}(t)+a\cdot\dot{y}(t)=b\cdot e(t) The true value of a is 2.8, b is 0.1. While inputing volt e(t)=12sin(2\pi t)+5sin(2t), I can get a good...
  4. N

    Estimation of area using CLT

    Your help/input is much appreciated! Thanks in advance! :smile: Object A is in the unit square 0<x<1, 0<y<1. Consider a random point distributed uniformly over the square; let Y=1 if the point lies inside A and Y=0 otherwise. How could A be estimated from a sequence of n individual points unif...
  5. R

    Error Bounds for derivative estimation

    So we are estimated derivatives using a three point formula in class and the giving bounds for the error. I was given a table of x1=1.1, x2=1.2, x3=1.3, x4=1.4. I have to find an error bound to estimate the error for x=1.1 and 1.3 for f(x)=ex In class we did x=1.1 as follows...
  6. T

    Vertical Axis Wind Turbine Power Estimation

    Hello, Can some explain to me how to calculate the power coefficient of a vertical axis wind turbine. If you explain the steps invloved would be great or any external file location where I could refer. I have below information 1) Lift Coefficient. 2) Drag Coefficient. 3) Angle of...
  7. C

    Estimation for a Graph Theory problem

    I am thinking about this problem that come up in some of my work, I think this has been solved before, though I am not aware where I could find the solution. Here is the question: Suppose a graph has say 20 nodes with no edge initially, and at each instance, 4 (different) nodes are randomly...
  8. K

    Optics - Spectacles lens Power Estimation

    Hi, I'm Chaitanya, 4th year undergraduate student in biomedical engg. I have an idea of making a mobile phone application which measures the power of your spectacle glasses. The idea is we take an image with the phone's inbuilt camera. One of the spectacle lens will be held in front of the...
  9. F

    Hypothesis testing for ratio estimation

    Homework Statement Hi, this is a stats question, hope I'm asking it in the right place. I am estimating an animal populations health based on it's weight to length ratio, I have a population ratio (10grams/cm) from 5 years ago and a sample estimate made from recently gathered data. I am...
  10. N

    Estimation of the Operator norm

    Homework Statement L : R^n → R is defined L(x1 , . . . , xn ) = sum (xj) from j=1 to n. The problem statement asks me to find an estimation for the operation norm of L, where on R the norm ll . llp, 1 ≤ p ≤ ∞, is used and on R the absolute value.The Attempt at a Solution from, ll Lv lly ≤...
  11. R

    Creating a Heat Estimation for Spinning Electrodes on Iron Sheets

    Hi, I had been thinking and could not able find any answer myself. Actually, if two materials like copper or bronze(especially considerting electrode materials in seam weld design). If the electrodes are spnning on to a work sheet for weld, obviously heat would produce in the action. is...
  12. D

    Estimation of central temperature of a star

    Problem: Relatively low mass stars can be shown to have their radii dependent on their mass as; R\proptoM1/2 From this, show that the temperature in kelvin at the centre of such a star can be estimated to be \approx24\times106(M/Msolar)1/2 Relevant Equations...
  13. B

    Estimation with a log-likelihood function

    Homework Statement Hi, I am trying to solve a time series problem but I am stuck with a function I am not used to work with. I have a basic model AR(1) where e(t) has mean 0 and variance σ^2. The issue is that (e)t follows the density function attached to the post and it's causing me issues...
  14. M

    Least squares estimation with quadratic constraints (M*M = 0)

    Hello there, currently I am trying to solve a least squares problem of the following form: min_{M} ||Y - M*X||^2 where M is a 3x3 matrix and Y and X are 3xN matrices. However, the matrix M is of a special form. It is a rank 1 matrix which satisfies M*M = 0_{3x3} and the trace of M is zero...
  15. S

    Estimation, bias and mean squared error

    Homework Statement (x1,x2,...xn) is modeled as observed values of independent random variables X1,X2,...Xn each with the distribution 1/θ for x in [0,θ] and 0 otherwise. A proposed estimate of θ is m = max(x1,...xn) Calculate the distribution of the random variable M=max(X1,X2,...Xn) and...
  16. S

    Estimation, negative binomial variable

    Hey, there's this thing I can't wrap my head around. Let's say we have a negative binomial variable x, with parameters p and r. That is, x is the number of failures we get before the rth sucess, while looking at random bernolli variables with sucsess rate p. It can be shown that...
  17. S

    Function estimation subject to equality of densities

    Dear all, One of the main challenges in social science is inferring causality from nonexperimental data. Statistics can help. In a regression context regressing Y on T may not give the causal effect of T on Y due to unobserved confounding. A solution is finding a variable Z, called an...
  18. B

    I don't understand this estimation lemma example

    I don't understand this estimation lemma example :( We are given the 'curve', And part of the example is showing that the contour integral over the top semicircle C_R tends to zero. Apparently we use the estimation lemma and the fact that, |z^2 +1| \geq |z|^2 - 1 to show, \left|...
  19. I

    Minimum chi squared estimation

    hi i have some data (star counts) and i have a model and i want to perform min chi squared so if i call my data di, and my model mi with std dev = \sigmai = 1 then \chi^2 = \sum \frac{(di - mi)^2}{\sigma i^2} no my model is this mi = bi - Fo where bi is the background which has been...
  20. O

    MLE is biased: are there other estimation methods?

    hi all, i would appreciate any help you can offer for the following problem. consider coordinates x_1, x_2 in the plane for which ||x_1-x_2||=d. suppose that this pair of coordinates can be measured independently, and that the measurements are 2D normally distributed with means x_1, x_2 and...
  21. A

    Estimation of X in Gaussian Noise

    Given {X}=[x_1 x_2 ... x_n]^T where {x_i} \in \{ 0, a_1, a_2, a_3 \}^n, a_i \in \mathbb{C} and Z = \{z_1 z_2,...,z_n \} where z_i ~ N(0,\sigma^2) is a Complex Gaussian RV with mean 0 and variance sigma^2. Suppose we observe Y Y = HX+Z where H is known and its elements are independent...
  22. T

    Estimation of 1000w heating element contact temperature

    Hi All I recently purchased a 1000w heating element for coffee cups, http://www.ebay.com.au/itm/110668421004 that I will be using on a 240v AC source. I would like to know if a cup out of silicone will withstand direct contact with the element? From what I am reading normal silicone...
  23. K

    Estimation of angle of attack / sideslip from flight test data

    I'm working on doing some parameter identification for a small UAV model, but unfortunately due to the size of the aircraft, we are unable to measure alpha and beta directly. What we do have are X/Y/Z position and acceleration, velocity, roll/pitch/yaw angles, and roll/pitch/yaw rates. Is...
  24. R

    Android- Gyro Sensor drift and Correct angle Estimation

    I am using LG Optimus 2x smartphone(Gyroscope and Accelerometer sensor) for positioning. I want to get correct rotation angles from gyroscope that can be used later on for body to Earth coordinate transformation. My question is that 1- How I can measure and remove the drift in gyro sensor. The...
  25. E

    Minimum MSE estimation derivation

    Hello, Would anyone be-able to recommend a good, easy to read article which outlines MMSE and its derivation. Specifically I am having trouble finding this term + \int x'xP(x|y)dx-\left \| \int xP(x|y)dx \right \|^2 from E({\left | \left | X-z \right | \right |}^2|Y=y)...
  26. D

    Estimation is over or under estimate

    Homework Statement If y''=-y^2, is this approximationg an over-estimation or an underestimation of the exact area? Homework Equations The Attempt at a Solution
  27. M

    Estimation of residual stress by finite element analysis

    I am trying to do a finite element analysis ofcold extrusion process of a tube wherein the steel tube is reduced from a larger outer diamter to a smaller one by extrusion process.The tube is held stationary and the die is pushed into the tube for a particular length and then retrieved.I am...
  28. R

    How do I calculate thermal conductance for a system with multiple materials?

    I am working on a project involving this setup (please refer to the pic). Basically compressed air at a constant flow rate flows through a 1/4" tube to the tube shown and gets heated by the star-wound heater and, this hot air heats the small inner vessel and then leaves the system. Now I am...
  29. O

    Spectrum estimation with noisy data, unbiased estimation of amplitudes needed

    hi everyone, i would be grateful for suggestions for the following problem: i have a set of measurements, discrete samples from a continuous function of time. with each measurement comes a estimate of its uncertainty (standard error). by doing a discrete Fourier transform, i have seen some...
  30. M

    Size estimation of CCD and ideal width of pointspread function

    Hi I have a problem to solve and I'm stack, so I would really appreciate your help if anyone can tell me how to answer the following question: "Consider a sky imaging system that has a 100m wide FoV measured at 1km from the camera; and that images a passenger airliner at a height of 2km as 10...
  31. D

    Estimation of dominant peak in frequency domain

    Homework Statement I have to develop an algorithm that can predict dominant peaks in the frequency domain, given a set of data in the time domain. I used FFT to check the frequency domain but apparently there are packet losses and irregular sampling intervals so FFT won't work. 2. The...
  32. D

    Trend Estimation: Analyzing Data to Determine Positive/Negative Trend

    Hi, I have a set of data. What I want to do is say with a 95% certainty this is a positive trend, or it is a negative trend. Basically I have a set of observations (X_i, Y_i) where i is in {1,2,3,4,5,6...} and X_i = i and Y_i is an observation. Right now I have the Variance, the...
  33. J

    How to calculate the bandwidth for a Kernel density estimation

    Hello everybody! Since some time I am trying the estimate the density of a set of numbers (in my case the numbers are distances to some object from a laser scanner). As I read, that the kernel density estimation technique is a basic approach for that kind of problem. Different Kernels can...
  34. Z

    Replication Method for Survey Estimation

    Hi all, What is a good way to use replication methods for estimation? For a dataset with no design information, only weighting remain. I know the basic principles of replication. Are there any considerations to use replication effectively? There is a public data of 15,000 people from the...
  35. S

    Taylor's Theorem: f(x) & Error Estimation

    Homework Statement f(x) = (1+x)^(1/3) Use taylor's theorem to write down an expression for the error R_3(x) = f(x) - P_3(x). In what interval does the unknown constant c lie? I can't find what value is x where c lies between x and a. Homework Equations in previous question, we are required to...
  36. M

    River Width Estimation Problem

    1. Jean camps beside a wide river and wonders how wide it is. She spots a large rock on the bank directly across from her. She then walks upstream until she judges that the angle between her and the rock, which she can still see clearly, is now at an angle of 30 downstream (as shown in the...
  37. T

    Kalman Filter for State Estimation

    Hi, I am not sure if this is the right forum to post this. I am working on a Kalman Filter for battery state of discharge estimation during discharging process. I am using a Linearized Discrete Time Kalman Filter to estimate the State of Discharge/SOD (how much % of charge has been taken...
  38. Z

    Grain size estimation in glacing angle XRD

    Hello everyone, I met a problem in XRD. Using theta-2theta mode I can not find crystalline peaks in my thin film sample because most within it is amorphous phase. However, I get three clear peaks using the glacing mode,i.e. theta-theta mode. Now i want to calculate the grain size in terms...
  39. J

    Estimating Energy Potential from Medical Waste Incinerator Heat?

    Dear All, What is the best approach to estimating energy from incinerator waste heat? Note that it is medical waste being incinerated. Thank you so much.
  40. V

    Estimation of reflected electron beam power falling on a target

    Hi, I need to calculate an estimate of the reflected electron beam power in the form of back scattered electrons and secondary electron emissions from a tungsten/Graphite target. The Electron source is a 25kV source with operated at a power of around 25kW. The tungsten. graphite blocks are...
  41. E

    Bayesian Estimation: Posterior Mean Estimator

    Homework Statement X_1 , \dots ,X_n \sim U[0, \theta] iid. \theta \sim U[0,1] derive the Bayesian posterior mean estimator Homework Equations f(\theta |\vec{X}) = \frac{f( \vec{X}|\theta)f(\theta )}{f( \vec{X})} The Attempt at a Solution My line of thinking... First, the marginal...
  42. J

    How Can Solving Linear Estimation Problems Serve as a Learning Tool?

    Problem is solved. :)
  43. Telemachus

    Taylor polynomial of third degree and error estimation

    Homework Statement It seems that I'm a little bit lost about this exercise. It says: Find the taylors polynomial of third degree centered at the origin for z=\cos y \sin x. Estimate the error for: \Delta x=-0.15,\Delta y=0.2. So, I did the first part (the easy one), the taylors polynomial for...
  44. B

    Ill-posed inverse problem (linear operator estimation)

    Ok this kind of question seems to come up a lot in research and applications but has me completely stumped. Say we have a dynamical system x_{t+1} = Ax_t where for simplicity we'll assume A is a constant symmetric real matrix but otherwise unknown. 1. What is the "best" estimate of A, when...
  45. F

    Estimation of diffuse and direct radiation starting from the global radiation

    I don’t know if this one is the appropriate forum for the following question. If for this question it is better another section of the forum, point out to me, please. I know the global radiation on a south oriented surface, in a German locality. Do you know methods to estimate the direct...
  46. K

    Estimation of number of Carbon atoms in bacterium

    Homework Statement Minimal growth medium for bacteria such as E. coli includes various salts with characteristic concentrations of mM and carbon source. This carbon source is typically glucose and it is used at 0.2% ( a concentration of 0.2g/100mL). a) Make an estimate of the number of...
  47. R

    Can we easily extract effective masses from Si band structure?

    can we estimate effective masses of electron and hole from the band structure if yes how? can somebody explain with reference to Si band structure?
  48. H

    Numerical Estimation problem

    Homework Statement "Estimate the mass of water in all the World’s oceans." Homework Equations I know the following: Two-thirds of the Earth is sea. The density of seawater is 1025 kg/m3. Radius of the Earth = 6.3*106m. The Attempt at a Solution Let's assume that the...
  49. H

    Numerical Estimation of the momentum of free electrons

    Homework Statement This is a problem in numerical estimation. Estimate a typical maximum momentum pmax for the free electrons in a metal where pmax = \left(\frac{3nh^{3}}{8\pi}\right)^{1/3} (In estimating n, the number density of free electrons, assume there is one such electron...
  50. G

    Drag Estimation for a Subsonic Aircraft

    1. Homework Statement The small scale drawing given in the Annexure shows the general arrangement and dimensional data on an early version of the English Electric “Canberra” B.1 bomber, powered by two Rolls Royce “Avon” jet engines. It was and is an extremely successful aircraft, designed by W...
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