Question

In: Statistics and Probability

1 a)Describe features of the covariance correlation matrix    b) How is a log likelihood ratio...

1 a)Describe features of the covariance correlation matrix

   b) How is a log likelihood ratio test is constructed to assess the adequacy of a given model

Solutions

Expert Solution

1.

  • a covariance matrix (also known as dispersionmatrix or variancecovariance matrix) is a matrix whose element in the i, j position is the covariance between the i-th and j-th elements of a random vector. A random vector is a random variable with multiple dimensions.
  • A measure used to represent how strongly two random variables are related known as correlation. Covariance is nothing but a measure of correlation. On the contrary, correlation refers to the scaled form of covariance. Correlation is dimensionless, i.e. it is a unit-free measure of the relationship betweenvariables.
  • A correlation matrix is a table showing correlationcoefficients between sets of variables. Each random variable (Xi) in the table is correlated with each of the other values in the table (Xj).

2.

Likelihood Ratio Tests are a powerful, very general method of testing model when unknown parameters are replaced by their maximum likelihood estimates.

For construction refer to:- https://ocw.mit.edu/courses/mathematics/18-443-statistics-for-applications-spring-2015/lecture-notes/MIT18_443S15_LEC10.pdf


Related Solutions

1) Define the following statistic tests       a)   A log likelihood ratio test       b)   Wald's...
1) Define the following statistic tests       a)   A log likelihood ratio test       b)   Wald's test 2) How is a log likelihood ratio test is constructed to assess theadequacy of a given model 3) Describe features of the covariance correlation matrix
7) COVARIANCE AND CORRELATION COEFFICIENT. What is covariance? How is covariance and correlation coefficients linked? How...
7) COVARIANCE AND CORRELATION COEFFICIENT. What is covariance? How is covariance and correlation coefficients linked? How does the concept of covariance link to the Timura depiction of an efficient frontier oriented “silver bullet” In addition, draw a graphic that explains your thinking using real estate, international, private equity, venture capital, etc.
What information does the eigendecomposition of the data/population correlation or covariance matrix offer?
What information does the eigendecomposition of the data/population correlation or covariance matrix offer?
1. How logistic regression maps all outcome to either 0 or 1. The equation for log-likelihood...
1. How logistic regression maps all outcome to either 0 or 1. The equation for log-likelihood function (LLF) is : LLF = Σi( i log( ( i)) + (1 − i) log(1 − ( i))). y p x y p x How logistic regression uses this in maximum likelihood estimation? 2. We can apply PCA to reduce features in a data set for model construction. But, why do we still need regularization? What is the difference between lasso and ridge...
How do you use R to derive the parameters maximizes the log-likelihood?
How do you use R to derive the parameters maximizes the log-likelihood?
How to find exact and conditional log likelihood for MA(1) model. Find ML estimates. (For Nile...
How to find exact and conditional log likelihood for MA(1) model. Find ML estimates. (For Nile data in R but if you tell me the process I’ll apply it to that data)   
How logistic regression maps all outcome to either 0 or 1. The equation for log-likelihood function...
How logistic regression maps all outcome to either 0 or 1. The equation for log-likelihood function (LLF) is : LLF = Σi( i log( ( i)) + (1 − i) log(1 − ( i))). y p x y p x How logistic regression uses this in maximum likelihood estimation?
1) Describe the structural features of peptide b-turns and how are they distinctly different from b-sheets....
1) Describe the structural features of peptide b-turns and how are they distinctly different from b-sheets. 2) Describe a spectroscopic technique for characterizing b-turn secondary structures in peptides.
2. Two stocks A and B have expected returns, and a variance-covariance matrix of returns given...
2. Two stocks A and B have expected returns, and a variance-covariance matrix of returns given in Table 1. Table 1 Stock A Stock B E(R) 0.14 0.08 Variance-covariance matrix: Stock A Stock B Stock A 0.04 0.012 Stock B 0.012 0.0225 a) What is the correlation coefficient between the returns on stock A and stock B? b) What is the expected return and standard deviation of portfolio S which is invested 80% in stock A and 20% in stock...
v(a) Using examples, outline the differences between correlation and causation. (b) The Excel correlation matrix below...
v(a) Using examples, outline the differences between correlation and causation. (b) The Excel correlation matrix below shows correlation coefficients between cheapest economy and business class fares, flight times and flight distances for non-stop round-trip flights in December 2019 to 12 medium- and long-haul destinations from Manchester Airport (source: flights.google.com, accessed 4th November 2019). Economy Fare Business Fare Time Distance Economy Fare 1.000 Business Fare 0.854 1.000 Time 0.663 0.494 1.000 Distance 0.520 0.317 0.971 1.000 (i) Explain how this correlation...
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT