By Li G., Datta S.
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Extra resources for A bootastrap approach to non-parametric regression for right censored data
We examine first the intercountry life-cycle savings model and its basic regression results. We then examine in turn the application of the singleand multiple-row diagnostics. Ttre Model and Regression Results. According to the life-cycle hypothesis, savings rates should be smaller if nonmembers of the labor force constitute a large part of the population. Income is not expected to be important, since age distribution and the rate of income growth constitute the core of life-cycle savings behavior.
The calculation of each deletion diagnostic results in a series of n values. The hat-matrix diagonals, for example, form a set of size n, as do DFFIT and thep series of DFBETA. Following Tukey (1977) we compute the interquartile range s’ for each series and indicate as extreme those values that exceed (7/2)5. 1% of the time. Thus, these limits can be viewed as a convenient point of departure in the absence of a more exact distribution theory. I2 Gaps. With either internal or external scaling, we are always alerted when a noticeable gap appears in the series of a diagnostic measure; that is, when one or more values of the diagnostic measure show themselves to be singularly different from the rest.
In what follows, then, we call the ith observation a leveragepoint when hi exceeds 2 p / n . The term leverage is reserved for use in this context. Note that when hi= 1, we havepi=yi; that is, ei=O. This is equivalent to saying that, in some coordinate system, one parameter is determined completely byy, or, in effect, dedicated to one data point. A proof of this result is given in Appendix 2A where it is also shown that det[X‘(i)X(i)]=(I -hi)det(XTX). 20) 18 DETECTING INFLUENTIAL OBSERVATIONS AND OUTLIERS Clearly when hi = 1 the new matrix X ( i ) , formed by deleting the ith row, is singular and we cannot obtain the usual least-squares estimates.