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Residual errors in shear measurements, after corrections for instrumentsystematics and atmospheric effects, can impact cosmological parameters derivedfrom weak lensing observations. Here we combine convergence maps from our suiteof ray-tracing simulations with random realizations of spurious shear. Thisallows us to quantify the errors and biases of the triplet$(\Omega_m,w,\sigma_8)$ derived from the power spectrum (PS), as well as fromthree different sets of non-Gaussian statistics of the lensing convergencefield: Minkowski functionals (MF), low--order moments (LM), and peak counts(PK). Our main results are: (i) We find an order of magnitude smaller biasesfrom the PS than in previous work. (ii) The PS and LM yield biases much smallerthan the morphological statistics (MF, PK). (iii) For strictly Gaussianspurious shear with integrated amplitude as low as its current estimate of$\sigma^2_{sys}\approx 10^{-7}$, biases from the PS and LM would be unimportanteven for a survey with the statistical power of LSST. However, we find that forsurveys larger than $\approx 100$ deg$^2$, non-Gaussianity in the noise (notincluded in our analysis) will likely be important and must be quantified toassess the biases. (iv) The morphological statistics (MF,PK) introduceimportant biases even for Gaussian noise, which must be corrected in largesurveys. The biases are in different directions in $(\Omega_m,w,\sigma_8)$parameter space, allowing self-calibration by combining multiple statistics.Our results warrant follow-up studies with more extensive lensing simulationsand more accurate spurious shear estimates.

The impact of spurious shear on cosmological parameter estimates from weak lensing observables