point estimate

(noun)

a single value estimate for a population parameter

Related Terms

Examples of point estimate in the following topics:

  • Non-normal point estimates

    • We may apply the ideas of confidence intervals and hypothesis testing to cases where the point estimate or test statistic is not necessarily normal.
    • The point estimate tends towards some distribution that is not the normal distribution.
    • For each case where the normal approximation is not valid, our first task is always to understand and characterize the sampling distribution of the point estimate or test statistic.

  • Basic properties of point estimates

    • First, we determined that point estimates from a sample may be used to estimate population parameters.
    • We also determined that these point estimates are not exact: they vary from one sample to another.
    • While we could also quantify the standard error for other estimates – such as the median, standard deviation, or any other number of statistics – we will postpone these extensions until later chapters or courses.

  • Introduction to confidence intervals

    • A point estimate provides a single plausible value for a parameter.
    • However, a point estimate is rarely perfect; usually there is some error in the estimate.
    • Instead of supplying just a point estimate of a parameter, a next logical step would be to provide a plausible range of values for the parameter.
    • In Section 4.5, we generalize these methods for a variety of point estimates and population parameters that we will encounter in Chapter 5 and beyond.
    • This video introduces confidence intervals for point estimates, which are intervals that describe a plausible range for a population parameter.

  • Summary of Formulas

    • ( lower value,upper value ) = ( point estimate − error bound,point estimate + error bound )
    • error bound = upper value − point estimate OR error bound = (upper value − lower value)/2

  • Point estimates

    • The sample mean $\bar{x}$= 95.61 minutes is called a point estimate of the population mean: if we can only choose one value to estimate the population mean, this is our best guess.
    • What about generating point estimates of other population parameters, such as the population median or population standard deviation?
    • If $\bar{x}$ men = 87.65 and $\bar{x}$ women = 102.13, then what would be a good point estimate for the population difference?
    • If you had to provide a point estimate of the population IQR for the run time of participants, how might you make such an estimate using a sample?
    • 4.2: To obtain a point estimate of the IQR for the population, we could take the IQR of the sample.

  • Introduction to inference for other estimators

    • The sample mean is not the only point estimate for which the sampling distribution is nearly normal.
    • In this section, we introduce a number of examples where the normal approximation is reasonable for the point estimate.
    • Chapters 5 and 6 will revisit each of the point estimates you see in this section along with some other new statistics.
    • We make another important assumption about each point estimate encountered in this section: the estimate is unbiased.
    • A point estimate is unbiased if the sampling distribution of the estimate is centered at the parameter it estimates.

  • Hypothesis testing for nearly normal point estimates

    • Just as the confidence interval method works with many other point estimates, we can generalize our hypothesis testing methods to new point estimates.
    • Verify conditions to ensure the standard error estimate is reasonable and the point estimate is nearly normal and unbiased.
    • This point estimate is nearly normal and is an unbiased estimate of the actual difference in death rates.
    • $Z = \frac{point estimate null value}{SE_{point estimate}} = \frac{0.025 0}{0.013} = 1.92 (4.52)$
    • When a point estimate is nearly normal, we use the Z score of the point estimate as the test statistic.

  • Introduction to Estimation

    • One of the major applications of statistics is estimating population parameters from sample statistics.
    • This value of 0.53 is called a point estimate of the population proportion.
    • It is called a point estimate because the estimate consists of a single value or point.
    • Point estimates are usually supplemented by interval estimates called confidence intervals.
    • Therefore a point estimate of the difference between population means is 30.7.

  • Estimating the Target Parameter: Point Estimation

    • Point estimation involves the use of sample data to calculate a single value which serves as the "best estimate" of an unknown population parameter.
    • Point estimation involves the use of sample data to calculate a single value or point (known as a statistic) which serves as the "best estimate" of an unknown population parameter.
    • The point estimate of the mean is a single value estimate for a population parameter.
    • The most unbiased point estimate of a population mean (µ) is the sample mean ($\bar { x }$).
    • We use point estimators, such as the sample mean, to estimate or guess information about the data from a population.

  • The Density Scale

    • In addition to the points themselves, box plots allow one to visually estimate the interquartile range.
    • To see this, we compare the construction of histogram and kernel density estimators using these 6 data points:
    • Whenever a data point falls inside this interval, we place a box of height $\frac{1}{12}$.
    • For the kernel density estimate, we place a normal kernel with variance 2.25 (indicated by the red dashed lines) on each of the data points $x_i$.
    • The data points are the rug plot on the horizontal axis.