Binary-search-tree sort 7∈ b Create an empty Bst for i=i to n do trEe-INSert(,AiD) Perform an inorder tree walk of t Example:

Symbol-table problem Symbol table T holding n records

How fast can we sort? All the sorting algorithms we have seen so far are comparison sorts: only use comparisons to determine the relative order of elements E. g, insertion sort, merge sort, quicksort heapsort The best worst-case running time that weve seen for comparison sorting is O(nIgn) Is o(nlgn) the best we can do?

The divide-and-conquer design paradigm 1. Divide the problem(instance) into subproblems 2. Conquer the subproblems by solving them recursively 3. Combine subproblem solutions

Welcome to Introduction to Algorithms, Fall 2001 Handouts 1. Course Information 2. Calendar 3. Registration (MIT students only) 4. References 5. Objectives and Outcomes 6. Diagnostic Survey

Ch. 9 Heteroscedasticity Regression disturbances whose variance are not constant across observations are heteroscedastic. In the heteroscedastic model we assume that

Ch. 7 Violations of the ideal conditions 1 ST pecification 1.1 Selection of variables Consider a initial model. which we assume that Y=x1/1+E, It is not unusual to begin with some formulation and then contemplate adding more variable(regressors) to the model

Ch. 5 Hypothesis Testing The current framework of hypothesis testing is largely due to the work of Neyman and Pearson in the late 1920s, early 30s, complementing Fisher's work on estimation. As in estimation, we begin by postulating a statistical model but instead of seeking an estimator of 6 in e we consider the question whether

Ch. 3 Estimation 1 The Nature of statistical Inference It is argued that it is important to develop a mathematical model purporting to provide a generalized description of the data generating process. A prob bility model in the form of the parametric family of the density functions p=f(:0),0E e and its various ramifications formulated in last chapter

Ch. 24 Johansen's mle for Cointegration We have so far considered only single-equation estimation and testing for cointe- gration. While the estimation of single equation is convenient and often consis- tent, for some purpose only estimation of a system provides sufficient information This is true, for example, when we consider the estimation of multiple cointe- grating vectors, and inference about the number of such vectors. This chapter examines methods of finding the cointegrating rank and derive the asymptotic