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In this thesis we examine the theoretical origin and statistical features of the Cosmic Microwave Background radiation. We particularly focus on the CMB power spectra and cosmological parameter estimation from QUaD CMB experiment data in order to derive implications for the concordance cosmological model. In chapter 4 we present a detailed parameter estimation analysis of the combined polarization and temperature power spectra from the second and third season observations of the QUaD experiment. QUaD has for the first time detected multiple acoustic peaks in the polarization spectrum, allowing meaningful parameter analyses from the polarization data alone. In a standard 6-parameter ACDM parameter estimation analysis we find the QUaD TT power spectrum to be in very good agreement with previous results. However, the QUaD polarization data shows some tension with ACDM model. The origin of this 1−2σ tension remains unclear, and may point to new physics, residual systematics or simple random chance. Combining polarization and temperature data we find an acceptable fit, and show that our results are dominated by the polarization signal. We combine QUaD with the five-year data from the WMAP satellite and the SDSS Luminous Red Galaxies 4th data release power spectrum, and extend our analysis to constrain the tensor-to-scalar ratio and the primordial isocurvature perturbations. Our analysis sets a benchmark for future polarization experiments. In chapter 5 we outline and test a new semi-analytical approach for the estimation of the pseudo- temperature and polarization CMB power spectra for experiments with incomplete sky coverage. We propose a method for constructing the mode-mode coupling matrices which connect the temperature and polarization pseudo-Cℓ’s to the unbiased all-sky bandpowers in the flat sky approximation. We apply this method to the apodization masks of the QUaD CMB experiment and we show that the true underlying bandpowers can be reconstructed from the simulated QUaD-like pseudo-Cℓ’s to high precision. We further investigate the possibility of extending the proposed analytical flat sky approach to the exact calculation of the PCL covariance matrices over a large range of multipoles and we find that the numerical calculation is extremely computationally expensive. The flat sky pseudo-Cℓ and covariances methods presented in this chapter are still work in progress and require more testing.