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Various aspects of the wavelet approach to nonparametric regression are considered, with the overall aim of extending the scope of wavelet techniques, to irregularlyspaced data, to regularly-spaced data sets of arbitrary size, to heteroscedastic and correlated data, and to data some of which may be downweighted or omitted as outliers. At the core of the(More)
among all candidate functions f . Here ρ is some convex function depending on the particular regression function we have in mind, TV(f) stands for the total variation of f , and λ > 0 is some tuning parameter. This framework is extended further to include binary or Poisson regression, and to include localized total variation penalties. The latter are needed(More)
In this paper we offer a unified approach to the problem of nonparametric regression on the unit interval. It is based on a universal, honest and non-asymptotic confidence region An which is defined by a set of linear inequalities involving the values of the functions at the design points. Interest will typically centre on certain simplest functions in An(More)
This paper considers the problem of specifying a simple approximating density function for a given data set (x1, . . . , xn). Simplicity is measured by the number of modes but several different definitions of approximation are introduced. The taut string method is used to control the numbers of modes and to produce candidate approximating densities.(More)
In the present study, the stereoselectivity of purified lipases from Candida rugosa, Chromobacterium viscosum, Pseudomonas species and Rhizopus arrhizus towards triacylglycerols in comparison to various structural analogs were investigated. Different triacylglycerol analogs with distinct polarities at position sn-2 of the glycerol backbone(More)
The ‘Signal plus Noise’ model for nonparametric regression can be extended to the case of observations taken at the vertices of a graph. This model includes many familiar regression problems. This article discusses the use of the edges of a graph to measure roughness in penalized regression. Distance between estimate and observation is measured at every(More)
In this paper we offer a unified approach to the problem of nonparametric regression on the unit interval. It is based on a universal, honest and non-asymptotic confidence region An which is defined by a set of linear inequalities involving the values of the functions at the design points. Interest will typically centre on certain simplest functions in An(More)
The temperature dependency of streams’ physical properties can have a significant effect on heat exchanger networks (HENs) design. An average value can be utilized during each temperature interval in order to determine the physical properties of the streams. Another method is the use of the physical properties’ values, which vary with regard to temperature(More)
The binding site of sn-1(3)-regioselective Rhizopus oryzae lipase (ROL) has been engineered to change the stereoselectivity of hydrolysis of triacylglycerol substrates and analogs. Two types of prochiral triradylglycerols were considered: 'flexible' substrates with ether, benzylether or ester groups, and 'rigid' substrates with amide or phenyl groups,(More)