Table 3 Estimated MSE values for different estimators at \(p=4\) and \(\varphi =1\).

From: A bias-reduced estimator for generalized Poisson regression with application to carbon dioxide emission in Canada

\(\rho\)	n	GPMLE	GPRRE
\(\rho\)	n	–	\(\hat{k}^*_{1 }\)	\(\hat{k}^*_{2 }\)	\(\hat{k}^*_{3 }\)	\(\hat{k}^*_{4 }\)	\(\hat{k}^*_{5 }\)	\(\hat{k}^*_{6 }\)	\(\hat{k}^*_{7 }\)	\(\hat{k}^*_{8 }\)	\(\hat{k}^*_{9 }\)	\(\hat{k}^*_{10}\)	\(\hat{k}^*_{11}\)	\(\hat{k}^*_{12}\)	\(\hat{k}^*_{13}\)	\(\hat{k}^*_{14}\)	\(\hat{k}^*_{15}\)
0.80	50	3.6489	1.7840	1.5776	1.5776	1.4195	0.9476	2.0133	1.8727	0.6849	0.8922	0.7117	0.9642	0.5797	0.6368	0.9644	0.8964
	100	0.9571	0.6492	0.5691	0.5691	0.7714	0.5420	0.5889	0.6802	0.4448	0.6126	0.4506	0.4743	0.3659	0.3461	0.6071	0.5475
	150	0.5211	0.4269	0.4043	0.4043	0.4650	0.3448	0.3491	0.4144	0.3162	0.4171	0.3340	0.3172	0.3521	0.2613	0.4741	0.4124
	200	0.3610	0.3069	0.3052	0.3052	0.3308	0.2511	0.2481	0.3084	0.2418	0.3135	0.2635	0.2457	0.2823	0.1921	0.3709	0.3081
	300	0.2400	0.2221	0.2288	0.2288	0.2276	0.1769	0.1823	0.2165	0.1763	0.2208	0.1910	0.1810	0.2164	0.1308	0.2199	0.1776
	400	0.1715	0.1610	0.1617	0.1617	0.1666	0.1337	0.1469	0.1600	0.1355	0.1619	0.1470	0.1386	0.1408	0.1117	0.1413	0.1176
0.85	50	4.0078	1.5357	1.3720	1.3720	1.2153	0.8870	1.6035	1.6477	0.6760	0.8763	0.6878	0.8689	0.6007	0.6739	1.0125	0.9435
	100	1.1519	0.8641	0.7409	0.7409	0.9168	0.6134	0.7679	0.7883	0.4786	0.6855	0.4900	0.5219	0.5047	0.3725	0.5372	0.4799
	150	0.7483	0.5325	0.4773	0.4773	0.6375	0.4525	0.4510	0.5614	0.3912	0.5462	0.4183	0.4047	0.3171	0.2654	0.5123	0.4593
	200	0.5378	0.4299	0.3874	0.3874	0.4894	0.3439	0.3799	0.4228	0.3091	0.4245	0.3257	0.3116	0.2277	0.1866	0.2567	0.2326
	300	0.3416	0.2922	0.2702	0.2702	0.3250	0.2404	0.2701	0.2934	0.2308	0.3000	0.2503	0.2323	0.1575	0.1513	0.1454	0.1342
	400	0.2135	0.1843	0.1826	0.1826	0.2040	0.1601	0.1651	0.1956	0.1615	0.1984	0.1770	0.1642	0.1348	0.1156	0.1636	0.1359
0.90	50	8.5537	4.2505	3.7717	3.7717	2.1770	1.5578	4.8827	4.3108	0.8267	0.9296	0.7978	1.8232	0.6627	0.6689	1.0485	0.9703
	100	2.4749	1.4253	1.1802	1.1802	1.4381	0.9700	1.4313	1.4723	0.5925	0.7810	0.5282	0.8176	0.3843	0.3213	0.6477	0.6005
	150	1.0471	0.7850	0.6814	0.6814	0.8836	0.5627	0.7050	0.7439	0.4383	0.6591	0.4707	0.4947	0.3500	0.2567	0.3700	0.3248
	200	0.7964	0.5680	0.4881	0.4881	0.6836	0.4783	0.4960	0.5802	0.3985	0.5649	0.4164	0.4059	0.2599	0.1994	0.3289	0.2982
	300	0.4590	0.3283	0.2951	0.2951	0.4101	0.3073	0.2846	0.3714	0.2820	0.3807	0.3066	0.2783	0.1728	0.1421	0.2338	0.2061
	400	0.3178	0.2638	0.2490	0.2490	0.3004	0.2110	0.2468	0.2792	0.2096	0.2829	0.2376	0.2189	0.1496	0.1292	0.1337	0.1236
0.95	50	12.6088	6.2636	5.5080	5.5080	2.7403	2.2383	7.2900	6.4603	0.8256	0.7356	0.7104	2.6804	0.6402	0.6548	1.1497	1.0466
	100	3.7182	2.1997	1.7574	1.7574	2.0520	1.4411	2.1849	2.1261	0.7059	0.8197	0.5638	1.1552	0.5030	0.3381	0.6570	0.6037
	150	2.2661	1.2740	0.9779	0.9779	1.4555	1.0220	1.2351	1.3215	0.5961	0.8031	0.5244	0.7618	0.3775	0.2287	0.4988	0.4650
	200	1.4026	0.8972	0.7106	0.7106	1.0706	0.7598	0.8126	0.9046	0.5243	0.7493	0.4729	0.5770	0.3159	0.1718	0.3062	0.2874
	300	0.8113	0.5183	0.4321	0.4321	0.6760	0.4787	0.4579	0.5973	0.3942	0.5804	0.4209	0.4096	0.2264	0.1426	0.2343	0.2138
	400	0.6150	0.3725	0.3283	0.3283	0.5135	0.3682	0.3364	0.4776	0.3181	0.4711	0.3507	0.3344	0.1830	0.1164	0.2174	0.1886
0.99	50	73.1927	33.8598	30.9481	30.9481	2.3796	7.8464	41.4792	35.5031	0.7683	0.3623	0.4318	12.3884	0.4705	0.6210	1.3286	1.1616
	100	22.4155	9.5273	8.0536	8.0536	2.8515	5.2309	12.1525	12.4546	0.7808	0.2865	0.3609	5.6033	0.3500	0.3376	1.0869	0.9433
	150	10.7908	4.3459	3.4415	3.4415	2.6203	3.1024	5.4814	5.8097	0.7263	0.3877	0.3648	2.7016	0.3189	0.1933	0.7474	0.6645
	200	9.2668	4.1048	3.2091	3.2091	2.9107	3.0169	4.8104	5.0379	0.7521	0.4261	0.3924	2.4307	0.3128	0.1537	0.6041	0.5397
	300	4.9456	2.0607	1.4914	1.4914	2.0414	1.9294	2.4068	2.6616	0.7074	0.6138	0.4203	1.3836	0.2586	0.0926	0.3879	0.3532
	400	3.4664	1.5695	1.1006	1.1006	1.8078	1.5584	1.6910	1.9099	0.6938	0.7355	0.4782	1.0584	0.2535	0.0779	0.2325	0.2178

Bold values indicate the minimum MSE.

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Table 3 Estimated MSE values for different estimators at \(p=4\) and \(\varphi =1\).

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