A local linear kernel estimator of the regression function x 7→ g(x) := E[Yi|Xi = x], x ∈ R , of a stationary (d+1)-dimensional spatial process {(Yi,Xi), i ∈ Z } observed over a rectangular domain of the form In := {i = (i1, . . . , iN ) ∈ Z N |1 ≤ ik ≤ nk, k = 1, . . . ,N}, n = (n1, . . . , nN ) ∈ Z N , is proposed and investigated. Under mild regularity assumptions, asymptotic normality of th...

We propose a tuning method for statistical machine translation, based on the pairwise ranking approach. Hopkins and May (2011) presented a method that uses a binary classifier. In this work, we use linear regression and show that our approach is as effective as using a binary classifier and converges faster.

We consider the estimation of the slope function in functional linear regression, where scalar responses are modeled in dependence of random functions. Cardot and Johannes [2010] have shown that a thresholded projection estimator can attain up to a constant minimax-rates of convergence in a general framework which allows to cover the prediction problem with respect to the mean squared predictio...

One of the most widely used statistical techniques is simple linear regression. This technique is used to relate a measured response variable, Y, to a single measured predictor (explanatory) variable, X, by means of a straight line. It uses the principle of least squares to come up with values of the “best” slope and intercept for a straight line that approximates the relationship. By means of ...

Machine learning and statistics typically focus on building models that capture the vast majority of the data, possibly ignoring a small subset of data as “noise” or “outliers.” By contrast, here we consider the problem of jointly identifying a significant (but perhaps small) segment of a population in which there is a highly sparse linear regression fit, together with the coefficients for the ...

Rationale Frequently decision-making situations require modeling of relationships among business variables. For instance, the amount of sale of a product may be related to its advertising expenditures for marketing, the health of the economy as measured by the stock market performance, and the number of sales people etc? The regression analysis provides tools for modeling a "response" variable ...