Hajek–Renyi-type inequality for $(\alpha , \beta )$ -mixing sequences and its application to change-point model

Journal of Inequalities and Applications

Table 1 MSE of the estimator ${\hat{\tau}}_{n}(\theta )$ with different θ and $\delta _{n}$

	$\delta _{n}$	n = 50	n = 150	n = 300	n = 600
θ = 0.1	$n^{-0.2}$	0.369224	0.091402	0.027506	0.006292
	$n^{-0.1}$	0.225240	0.025418	0.003985	0.000768
	$n^{0}$	0.073288	0.004294	0.001141	0.000066
θ = 0.3	$n^{-0.2}$	0.513416	0.116556	0.035649	0.010550
	$n^{-0.1}$	0.284935	0.031244	0.004464	0.000906
	$n^{0}$	0.098712	0.005237	0.000523	0.000054
θ = 0.5	$n^{-0.2}$	0.817272	0.196381	0.069204	0.026228
	$n^{-0.1}$	0.476872	0.048981	0.007227	0.001232
	$n^{0}$	0.181479	0.004279	0.000447	0.000064

	\(\delta _{n}\)	n = 50	n = 150	n = 300	n = 600
θ = 0.1	\(n^{-0.2}\)	0.369224	0.091402	0.027506	0.006292
	\(n^{-0.1}\)	0.225240	0.025418	0.003985	0.000768
	\(n^{0}\)	0.073288	0.004294	0.001141	0.000066
θ = 0.3	\(n^{-0.2}\)	0.513416	0.116556	0.035649	0.010550
	\(n^{-0.1}\)	0.284935	0.031244	0.004464	0.000906
	\(n^{0}\)	0.098712	0.005237	0.000523	0.000054
θ = 0.5	\(n^{-0.2}\)	0.817272	0.196381	0.069204	0.026228
	\(n^{-0.1}\)	0.476872	0.048981	0.007227	0.001232
	\(n^{0}\)	0.181479	0.004279	0.000447	0.000064