# least-squares estimate

## least-squares estimate

[¦lēst ′skwerz ‚es·tə·mət]
(statistics)
An estimate obtained by the least-squares method.
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.
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By minimizing the trace of E'E, Theil shows that the orthogonal least-squares estimate of the price index is the eigenvector corresponding to [lambda], the largest eigenvalue of CC'.
The MSEs of all parameter estimates (and model predictions) are decreased when a single variable in the EM is deleted whose true parameter value is smaller in magnitude than the theoretical standard deviation of its least-squares estimate;
Here we use the incidence data starting on April 18 and continuing past April 30 to obtain a least-squares estimate of the minimum point [t.sub.min] of the incidence curve.
The best least-squares estimate for the parameter Y of the nonexistent laboratory-effects model (1) is the weighted mean [x.sub.W] = [[SIGMA].sub.i] [w.sub.i] [x.sub.i] / [[SIGMA].sub.i] [w.sub.i], where [w.sub.i] = 1/[u.sup.2]([x.sub.i]) for i = 1, 2,..., n.
[b.sub.1] = the least-squares estimate of the population regression coefficient for X
But its least-squares estimate would almost certainly be biased or inconsistent, even if the form of the equation were correct, becasue the bond rate is almost certainly not exogenous and hence not independent of the equation's disturbances.
Starting from some initial estimates [[??].sup.(0)], at each iteration t until it converges, this algorithm computes the residuals [r.sup.(t - 1).sub.i] and the associated weights [w.sup.(t - 1).sub.i] = w[[r.sup.(t - 1).sub.i]] from the previous iteration and yields new weighted least-squares estimates.
Restricted least-squares estimates of age composition from length composition.
Weighted least-squares estimates are not possible if P [is less than or equal to] 0 or P [is greater than or equal to] 1.
In particular, if the individual-specific error component is correlated with X, then least-squares estimates of [Beta] from cross-sectional data will be inconsistent.(2) Using least-squares estimates [Mathematical Expression Omitted] of [Beta] to estimate the portion of the log wage variance due to industry, we use a measure with(3)
However, if the data [v.sub.rt] are contaminated by outliers, these least-squares estimates are unduly susceptible to sampling variation and may be quite unstable.
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