Point Estimation Problems And Solutions Pdf
Jennifer Kovachick
A point estimate or estimator is an estimated value of a population parameter."}},"@type":"Question","name":"How to find a point estimate?","acceptedAnswer":"@type":"Answer","text":"Different population parameters will have different estimators, which in turn will have different formulas for their estimation. You have to identify which parameter you're interested in, and use the formula of its respective estimator.","@type":"Question","name":"What is a point estimate example?","acceptedAnswer":"@type":"Answer","text":"An example of a point estimate is the sample mean, the estimator of the population mean.","@type":"Question","name":"What are the different types of point estimates?","acceptedAnswer":"@type":"Answer","text":"You have a point estimate for the population mean and another for population proportion. You also have a point estimate for the difference of two population means, and another for the difference of two population proportions.","@type":"Question","name":"Why do we use point estimation?","acceptedAnswer":"@type":"Answer","text":"We use point estimation because we typically don't know the actual value of the parameter we're interested in, so we have to make an estimation of it."]} #ab-fullscreen-popup display: none; Find study contentLearning Materials
However, they can gather data from small samples from the population, find their mean, and use that as a guide to guessing the parameter for the whole population. This is called point estimation.
The result of a point estimation of a parameter is a single value, usually referred to as the estimator, and it will usually have the same notation as the population parameter it represents plus a hat '^'.
Next, you will learn about two estimators that you will need to be familiar with, which are the sample mean and the estimator for the proportion. These are the best-unbiased estimators for their respective parameters.
Another estimator related to the mean is of the difference between of two means, \( \barx_1-\barx_2\). You may be interested in this estimator when you want to compare the same numerical characteristic between two populations, for example, comparing the average height between people who live in different countries.
When you want to calculate the proportion of the characteristic you are interested in, you will count all the elements in the sample that contain that characteristic, and each of these elements is a success.
A survey was conducted using a sample of \(300\) teacher trainees in a training school to determine what proportion of them view the services provided to them favorably. Out of \(150\) trainees, \(103\) of them responded that they viewed the services provided to them by the school as favorable. Find the point estimation for this data.
The point estimation here will be of the population proportion. The characteristic of interest is the teacher trainees having a favorable view about the services provided to them. So, all trainees with a favorable view are successes, \(x=103\). And \(n = 150\). that means
Another estimator related to the proportion is of the difference of two proportions, \( \hatp_1-\hatp_2\). You may be interested in this estimator when you want to compare proportions of two populations, for example, you may have two coins and suspect that one of them is unfair because it is landing on a head too frequently.
A researcher wants to estimate the proportion of students enrolled at a university who frequent the library of their respective college at least three times a week. The researcher surveyed \(200\) students of the science faculty who frequent their library, \(130\) of whom frequent it at least \(3\) times a week. She also surveyed \(300\) college students from the humanities faculty who frequent their library, of whom \(190\) frequent it at least \(3\) times a week.
c) The proportion of science students who frequent their library is greater than the proportion of humanities students who frequent their library. According to this information, you can say that it is more science students who frequent their library.
But the disadvantage of this estimation method is that you don't know how close or how far away from the true value of the parameter the estimator is. And this is where interval estimation comes in, which will consider what is called the margin of error, that information that allows you to appreciate the distance of the estimator to the parameter.
As you can imagine, it is in your interest that the estimated values of the parameters be as close as possible to the true values of the parameters, as this makes the statistical inferences more credible.
Different population parameters will have different estimators, which in turn will have different formulas for their estimation. You have to identify which parameter you're interested in, and use the formula of its respective estimator.
You have a point estimate for the population mean and another for population proportion. You also have a point estimate for the difference of two population means, and another for the difference of two population proportions.
In this paper, the major direct solutions to the three point perspective pose estimation problems are reviewed from a unified perspective beginning with the first solution which was published in 1841 by a German mathematician, continuing through the solutions published in the German and then American photogrammetry literature, and most recently in the current computer vision literature. The numerical stability of these three point perspective solutions are also discussed. We show that even in case where the solution is not near the geometric unstable region, considerable care must be exercised in the calculation. Depending on the order of the substitutions utilized, the relative error can change over a thousand to one. This difference is due entirely to the way the calculations are performed and not due to any geometric structural instability of any problem instance. We present an analysis method which produces a numerically stable calculation.
TY - JOUR
AU - Bernardo, Jos M.
TI - Objective Bayesian point and region estimation in location-scale models.
JO - SORT
PY - 2007
VL - 31
IS - 1
SP - 3
EP - 44
AB - Point and region estimation may both be described as specific decision problems. In point estimation, the action space is the set of possible values of the quantity on interest; in region estimation, the action space is the set of its possible credible regions. Foundations dictate that the solution to these decision problems must depend on both the utility function and the prior distribution. Estimators intended for general use should surely be invariant under one-to-one transformations, and this requires the use of an invariant loss function; moreover, an objective solution requires the use of a prior which does not introduce subjective elements. The combined use of an invariant information-theory based loss function, the intrinsic discrepancy, and an objective prior, the reference prior, produces a general solution to both point and region estimation problems. In this paper, estimation of the two parameters of univariate location-scale models is considered in detail from this point of view, with special attention to the normal model. The solutions found are compared with a range of conventional solutions.
LA - eng
KW - Inferencia paramtrica; Inferencia bayesiana; Estimador puntual; Intervalo de confianza; Decisin bayesiana; Estimacin por intervalos; confidence intervals; credible regions; decision theory; intrinsic discrepancy; intrinsic loss; location-scale models; noninformative prior; reference analysis; region estimation; point estimation
UR -
ER -
Inferencia paramtrica, Inferencia bayesiana, Estimador puntual, Intervalo de confianza, Decisin bayesiana, Estimacin por intervalos, confidence intervals, credible regions, decision theory, intrinsic discrepancy, intrinsic loss, location-scale models, noninformative prior, reference analysis, region estimation, point estimation
To begin, you should refrain from determining any level of % complete in Agile/Scrum. It is either "Done", or it is "Not Done". Those are the only two states you (and your team/department/organization) should be concerned with.
There is a critical factor that you must keep in mind regarding story points. They are for planning purposes only, to be used as needed to help both the PO and the Development Team determine how much work to forecast for completion in future sprints. Once a sprint begins, story points are meaningless. Ignore them completely. Only refer to them again when the sprint has ended, and you need to add up the # of story points that are done, in order to feed another sprint into your team's velocity calculation.
There are many organizations though that attempt to use story points and velocity as a performance metric on the team. This is completely wrong, since story points are valid only for planning purposes, and only germane to the team providing them.
I have been asked in the past to increase the velocity of teams I've served. My response has been to confirm that what they are asking for is for my teams to double their story point estimates. Of course, that isn't what they are asking for, but it is important to push back as much as possible on the misuse of such metrics.
As usual I have a different perspective. On your 8 point story where you got part of the work done, why would the estimate change for that story? Your team originally estimated based on delivering the entire story. Just because you have finished part of the work, why does that change the estimate to finish the entire thing? Why not carry the story over to your next sprint and finish it in it's entirety? As @Timothy points out, points are for planning purposes only and should not be used to "judge" the team. They planned a sprint based on what they knew at the time. I would bet that they found out things they didn't know that lead to their not finishing the story. If you absolutely have an aversion to moving things into another sprint, I suggest updating the original ticket to reflect what you actually accomplished and marking it done then create a new ticket for the remaining work that can be estimated again.
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