Marcinkiewicz strong laws for linear statistics

By Z. Bai, P. Cheng. 2000

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On the strong convergence for weighted sums of random variables (2011, background): “ Bai and Cheng (2000) proved the strong law of large numbers for weighted sums”
Strong Limit Theorems for Weighted Sums of Negatively Associated Random Variables (2008, background): “Theorem 2.2 extends the work of Cuzick [12] and Bai and Cheng [ 3 ] independent to the NA setting; furthermore; the ranges for p, α, and β have been extended.”
A Strong Limit Theorem for Weighted Sums of Sequences of Negatively Dependent Random Variables (2010, result): “Our results extend and improve the corresponding results of Bai and Cheng 2000 from the i.i.d. case to ND sequences.”
Strong laws for weighted sums of $$\psi $$ψ-mixing random variables and applications in errors-in-variables regression models (2017, background): “Bai and Cheng (2000) extended and generalized the result of Cuzick (1995) to theMarcinkiewicz type strong law, and Chen and Gan (2007) generalized the result of Bai and Cheng (2000) in some directions. Huang et al. (2014) extended the corresponding result of Bai and Cheng (2000) to φ-mixing random v”