Machine Learning | parameter point estimates and basic questions (point and interval estimation) | 5mins Getting Started | Commission shall study notes (XXII)

Parameters point estimate

• Background: The statistic evaluation of a study of the nature and quality of statistical inference, depends entirely on the nature of the sampling distribution

• The basic problem of statistical inference

  (1) The parameter estimation problem: the distribution function of the form X generally known, but one or more unknown parameters, need to be estimated by means of which the sample X

  (2) hypothesis testing problem: the overall form of the distribution function of X is completely unknown, or only know the form, but do not know its parameters, in order to infer the general characteristics of some unknown, made certain assumptions about the overall

Parameter estimation problem

• Implementation: assuming the population distribution in the form of known, unknown or just a few parameters, using the information obtained from the total sample to estimate the overall function of certain parameters or certain parameter.

• General formulation (define): There is a statistical population, the overall distribution function $F(x,\theta)$ , wherein $\theta$ is the unknown parameter ( $\theta$ can be vectors). Now from the overall sample, the sample was $X_1,X_2,...,X_n$, Should be based on the parameters of the sample $\theta$ to make estimates, or estimates $\theta$ is a known function $g(\theta)$ . Such problem is called parameter estimation.

• Parameter estimation of two forms: point and interval estimation

  eg if we want to estimate the average height of a team of boys. (Assuming that height is normally distributed $N (\ mu, 0.1 ^ 2)$）

  Now select from the overall capacity of the sample 5, our task is to find the estimated population mean based on a sample selected (number 5). And all of this information is composed of the number 5.

  This number is provided 5: 1.65 1.67 1.68 1.78 1.69

  estimate $\ mu$ is 1.68, which is thepoint estimate

  estimate $\ mu$ is the interval [1.57,1.84] inside, which isthe interval estimate.