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Quantifying the uncertainty of estimated parameters in high dimensional sparse models gives critical insights and valuable information in analyzing various types of big data. Yet it possesses some unique difficulties and has been drawing numerous research attention over the past years. The goal of high dimensional inference is to provide accurate point estimators of the unknown parameters with tractable limiting distributions, which leads to confidence intervals, significance testing, and other uncertainty measures. In this dissertation, we propose a novel estimation procedure, along with a non-parametric variance estimator, which is adaptive to a wide range of regression models and outcome types to draw reliable inferences for the model parameters. Comparisons are made with several existing methods, and advantages of our procedure are shown both in simulation studies and real data applications. Our method is successfully applied to multiple genomic data sets with continuous, binary, and survival outcomes.

This dissertation presents infrared nano-spectroscopy and nano-imaging studies of graphene plasmons using scattering -type scanning near-field microscope - a unique technique allowing efficient excitation and high-resolution imaging of graphene plasmons. With this technique, we show in real space that common graphene/SiO₂/Si back-gated structure support propagating surface plasmons in the infrared frequencies. The observed plasmons are highly confined surface modes with a wavelength around 200 nm that are conveniently tunable by the back gate voltages. In addition, we perform spectroscopic studies on graphene by varying the probing frequencies. The spectroscopy results not only show direct signature of graphene plasmons but also provide evidence of strong coupling between graphene plasmons and SiO₂ optical phonons. Furthermore, we investigate the plasmonic properties of bernal-stacking bilayer graphene (BLG) and find that BLG supports gate- tunable infrared plasmons with higher confinement compared to graphene and randomly stacked graphene layers. Moreover, BLG plasmons can be turned off completely in wide gate voltage close to the charge neutrality point. Those unique plasmonic properties are attributed to both interlayer tunneling and bandgap opening inBLG. Finally, we are able to map and characterize grain boundaries inside graphene film fabricated with chemical vapor deposition (CVD) method by launching surface plasmons. We found grain boundaries, as well as other line defects in CVD graphene, trigger distinct plasmonic twin fringes patterns due to plasmon interference. Theoretical modeling and analysis unveil unique electronic properties associated with grain boundaries