Multiple linear regression with constrained coefficients: Application of the lagrange multiplier

In this paper, we present two unfamiliar novel estimation techniques (UNET) for the constrained regression coefficients in the frame-work of a standard multiple linear regression model. Estimation of a linear regression problem with constraints on the regression coefficients are firstly derived by minimising a formulated goal function that minimises the total sum of the squared errors, plus the sum of the linear constraints multiplied by a Lagrangian. We also show that the solution to the system of equations can be obtained without differentiating the goal function, rather expressed in terms of the known matrices. This is achieved by employing properties of a blocked linear system. The UNET is justified by a numerical simulated system of linear equations in 3-dimensions. The UNET yields estimates that are comparable to those generated by the Schur complement principle

Evidence of electron neutrino appearance in a muon neutrino beam

The T2K Collaboration reports evidence for electron neutrino appearance at the atmospheric mass splitting, |Δm232|≈2.4×10−3  eV2. An excess of electron neutrino interactions over background is observed from a muon neutrino beam with a peak energy of 0.6 GeV at the Super-Kamiokande (SK) detector 295 km from the beam’s origin. Signal and background predictions are constrained by data from near detectors located 280 m from the neutrino production target. We observe 11 electron neutrino candidate events at the SK detector when a background of 3.3±0.4(syst) events is expected. The background-only hypothesis is rejected with a p value of 0.0009 (3.1σ), and a fit assuming νμ→νe oscillations with sin22θ23=1, δCP=0 and |Δm232|=2.4×10−3  eV2 yields sin22θ13=0.088+0.049−0.039(stat+syst)

Search for dinucleon decay into pions at Super-Kamiokande

A search for dinucleon decay into pions with the Super-Kamiokande detector has been performed with an exposure of 282.1 kiloton-years. Dinucleon decay is a process that violates baryon number by two units. We present the first search for dinucleon decay to pions in a large water Cherenkov detector. The modes $^{16}$O$(pp) \rightarrow$ $^{14}$C$\pi^{+}\pi^{+}$, $^{16}$O$(pn) \rightarrow$ $^{14}$N$\pi^{+}\pi^{0}$, and $^{16}$O$(nn) \rightarrow$ $^{14}$O$\pi^{0}\pi^{0}$ are investigated. No significant excess in the Super-Kamiokande data has been found, so a lower limit on the lifetime of the process per oxygen nucleus is determined. These limits are: $\tau_{pp\rightarrow\pi^{+}\pi^{+}} > 7.22 \times 10^{31}$ years, $\tau_{pn\rightarrow\pi^{+}\pi^{0}} > 1.70 \times 10^{32}$ years, and $\tau_{nn\rightarrow\pi^{0}\pi^{0}} > 4.04 \times 10^{32}$ years. The lower limits on each mode are about two orders of magnitude better than previous limits from searches for dinucleon decay in iron.Comment: 20 pages, 17 figures. Accepted for publication in Physical Review D on March 30, 201