Parameter estimation accounts for more than half of the mathematical statistics in the third year of the postgraduate entrance examination, so parameter estimation is the key. The first chapter of statistics is about the distribution of samples and statistics, which requires the numerical characteristics of statistics, and statistics are random variables. The distribution of statistics and its distribution parameters are common problems, which are often carried out by using the typical patterns and properties of distribution and the distribution of sample mean and sample variance of normal population. So remember the typical patterns of the above three distributions. There is a formula about three distributions, which is convenient for everyone to remember:
Find the chi-square (x2) of the normal sum of squares, and divide the chi-square by f;
If you want to get the t distribution, divide it into a positive n card;
The first formula means that the sum of squares of standard normal distribution can generate chi-square distribution, and two chi-square distributions can be divided by their dimensions to generate order F. The second formula means that the distribution can be obtained by dividing the standard normal distribution and chi-square distribution.
Moment estimator (value) and maximum likelihood estimator (value) of parameters are also often tested. Many students always feel helpless when they encounter such problems. The sample values given in the title are completely useless. In fact, such a topic is very simple. As long as we master the principles of moment estimation and maximum likelihood estimation, we can do it according to fixed procedures. The basic idea of moment method is to use the order origin moment of the sample as the order origin moment of the whole population. The problem-solving idea of the estimation moment estimation method is:
(1) When there is only one unknown parameter, we use the first-order origin moment of the sample, that is, the sample mean, to estimate the first-order origin moment of the population, that is, the expectation, and solve the unknown parameter, that is, its moment estimator.
(2) If there are two unknown parameters, then we should use the first moment to estimate them and the second moment to estimate them. Because of two unknowns, two equations are needed to solve. Solving the unknown parameters is the moment estimator. The outline only requires first and second moments.
The biggest difficulty of the maximum likelihood estimation method is to write the likelihood function correctly, which is written according to the distribution law or density function of the population. We will give you a memory formula.
Sample population exchange, moment method estimation is very convenient;
Calculate likelihood functions respectively, and obtain zero eggs by logarithmic derivation;
The first formula means that the moment estimation of parameters can be calculated by replacing the moment of the population with the moment of the sample; The second formula is to regard the unknown parameter in the likelihood function as a variable and find its stagnation point. In the concrete calculation, the logarithm is found on both sides of the likelihood function, and then the stagnation point of the parameter is found, which is the maximum likelihood estimation of the parameter.
How to review the mathematical statistics of in-service graduate students in capital university of economics and business? Through the introduction of the above content, I believe everyone has a certain understanding after reading it. If you have any questions, please consult our teachers online and they will give you detailed answers.
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