  Asteroseismic time-series data have imprints of stellar oscillation modes,
whose detection and characterization through time-series analysis allows us to
probe stellar interior physics. Such analyses usually occur in the Fourier
domain by computing the Lomb-Scargle (LS) periodogram, an estimator of the
power spectrum underlying unevenly-sampled time-series data. However, the LS
periodogram suffers from the statistical problems of (1) inconsistency (or
noise) and (2) bias due to high spectral leakage. Here, we develop a multitaper
power spectrum estimator using the Non-Uniform Fast Fourier Transform (mtNUFFT)
to tackle the inconsistency and bias problems of the LS periodogram. Using a
simulated light curve, we show that the mtNUFFT power spectrum estimate of
solar-like oscillations has lower variance and bias than the LS estimate. We
also apply our method to the Kepler-91 red giant, and combine it with PBjam
peakbagging to obtain mode parameters and a derived age estimate of $3.97 \pm
0.52$ Gyr. PBjam allows the improvement of age precision relative to the $4.27
\pm 0.75$ Gyr APOKASC-2 (uncorrected) estimate, whereas partnering mtNUFFT with
PBjam speeds up peakbagging thrice as much as LS. This increase in efficiency
has promising implications for Galactic archaeology, in addition to stellar
structure and evolution studies. Our new method generally applies to
time-domain astronomy and is implemented in the public Python package tapify,
available at https://github.com/aaryapatil/tapify.
