Table 2. Ten GPR models’ parameter...

Table 2.

Ten GPR models’ parameter estimations for each city’s pre-owned residential housing price index

Estimate	CV1	CV2	CV3	CV4	CV5	CV6	CV7	CV8	CV9	CV10
Parameter	Beijing: isotropic exponential kernel, empty basis function and standardized predictors
$σ$	11.34644	10.88397	11.21652	11.25806	11.06121	11.35184	11.23226	11.36280	11.28581	11.29736
$σ_{l}$	1478.76297	1549.80495	1511.41873	1487.23894	1469.36263	1527.77996	1584.82872	1415.07405	1456.23803	1431.98451
$σ_{f}$	6996.28789	7058.99367	6964.91820	6985.32766	6985.61621	6995.05097	6992.20871	6984.68920	6997.99299	6986.10874
Parameter	Shanghai: isotropic exponential kernel, constant basis function and standardized predictors
$σ$	12.60171	12.65667	12.43396	12.46169	12.53081	12.30951	12.44506	12.68133	12.61629	12.73437
$β$	6716.31619	6722.91918	6726.56064	6716.64362	6722.22576	6767.73831	6709.08306	6728.25743	6718.44492	6741.19175
$σ_{l}$	76.71800	79.93348	105.42119	76.96624	77.65031	90.95637	83.80150	78.51796	76.06861	88.07812
$σ_{f}$	1734.47766	1744.49917	1771.82939	1731.23332	1737.49918	1752.39015	1736.88704	1739.06683	1735.42166	1772.84554
Parameter	Tianjing: isotropic exponential kernel, empty basis function and nonstandardized predictors
$σ$	8.12223	8.37052	8.41959	8.14719	8.47991	8.33426	8.26314	8.16722	8.36124	8.29159
$σ_{l}$	917896.68400	901786.73526	1118250.47428	907284.88983	897970.04107	906877.37576	905286.14179	903439.65243	909402.33100	968360.07350
$σ_{f}$	4059.19284	4054.76853	4068.70065	4073.58017	4057.06349	4054.87394	4057.33326	4054.47449	4056.23212	4044.77978
Parameter	Chongqing: nonisotropic Matern 3/2 kernel, constant basis function and nonstandardized predictors
$σ$	5.56727	4.92674	6.50467	4.28530	5.35656	5.54645	5.15887	4.11237	5.12630	4.26242
$β$	1586.83743	1580.41587	1540.93302	1580.81475	1573.37302	1570.65790	1576.28943	1592.85835	1584.82359	1591.20074
$σ_{1}$	6179.74452	49177165094822.20000	119205550.33128	2149.16216	5046068.48468	549422.88346	86565.88130	8264.27540	3572.51910	350.38719
$σ_{2}$	336.74491	309.43910	493.70744	262.24809	327.47981	313.34918	291.59866	1221.48760	303.39510	946.63918
$σ_{3}$	22830601.42381	50671823250.42500	346209.78951	22342314.86463	490489.89502	4896876.17514	1057550.17589	294.88070	1741581.29388	437.97748
$σ_{4}$	716.25275	612.09713	11909055.82648	615.48868	846.77062	505.22669	623.48021	1049.59618	582.52378	900.10337
$σ_{5}$	786574.36133	35564030.74322	881.36821	328699.26660	755193.56484	702460.44349	2050.46089	1881.80383	2267.40498	292678.05468
$σ_{6}$	157283006.40471	401551.22127	208620117.94988	2094464.49521	3422283.88256	1309663.50500	52978396.48421	1463779.80429	2184692.36164	1827.29584
$σ_{7}$	434384.33263	2207.38444	91449826.94185	1322.68043	2303.49598	2191.14959	2570.99901	2117640.48482	2859.70570	1208.41138
$σ_{8}$	51504378.45013	26348541.91946	97714088.99401	865739.50526	418217.83527	408326.24827	3158058.50326	1193899.85594	505382.64958	88386.51681
$σ_{9}$	289.24758	282.27094	423.70755	242.89171	283.75746	288.84678	264.45721	334.87823	283.76100	358.16086
$σ_{f}$	171.92764	162.12951	195.82911	151.98030	166.74296	159.13466	159.44168	182.07565	161.32802	152.96275
Parameter	Shenzhen: isotropic Matern 5/2 kernel, empty basis function and standardized predictors
$σ$	56.90234	50.35853	43.96349	40.80814	53.80888	53.78936	53.43056	50.46201	54.90458	47.14572
$σ_{l}$	137.80039	5.02011	4.27545	4.08478	5.84916	6.07866	7.53360	4.96700	5.58126	4.56867
$σ_{f}$	102474.71802	4142.45441	3681.64696	3655.99229	4585.50482	4905.75759	5777.39136	4075.73372	4240.31194	3817.98637
Parameter	Guangzhou: isotropic Matern 5/2 kernel, linear basis function and standardized predictors
$σ$	35.68043	34.18927	24.26637	34.11388	35.07319	35.77847	34.52065	34.65384	35.83448	34.24232
$β_{0}$	4485.09877	4430.97531	4383.06173	4466.61728	4395.40741	4461.72840	4422.58025	4507.07407	4460.56790	4395.77778
$β_{1}$	−22.00451	204.20283	−51.03961	−40.10682	8.34190	−7.28323	−0.69112	−56.28909	−22.18170	−47.39137
$β_{2}$	−64.28505	−469.89481	102.95413	−10.60102	−32.16166	−64.93041	−82.15014	16.25216	−70.32153	−25.97377
$β_{3}$	143.68304	309.31510	−82.56766	111.21312	75.83371	123.12413	116.38854	118.48221	164.64201	184.78810
$β_{4}$	6.24641	−11.41629	95.92353	32.97490	21.68781	18.38982	−21.92609	−42.74598	−14.93738	−41.29688
$β_{5}$	−31.28362	9.24901	−47.84468	−54.63476	−120.49049	−47.24500	10.28977	−0.75441	−29.30189	26.58770
$β_{6}$	−232.27140	−238.26042	−172.98486	−255.27472	−187.78546	−229.54177	−242.82906	−244.53654	−244.58152	−435.32932
$β_{7}$	−11.33771	−7.90012	−19.14608	−42.01500	33.16940	−23.40106	24.85018	−20.72777	−5.30953	140.97066
$β_{8}$	−199.90394	−222.54370	−432.65164	−118.83366	−189.02693	−181.22494	−184.85978	−149.52617	−173.64549	−145.39190
$β_{9}$	1362.03626	1376.23692	1555.03505	1306.75678	1340.30623	1357.39790	1323.55188	1338.44435	1339.00020	1297.67889
$σ_{l}$	266648.70619	177047.86936	136094.68457	40617.41750	175184.11308	255379.07297	170519.28893	19638.07055	175799.13066	182805.47349
$σ_{f}$	0.00348	0.00579	0.00331	0.00509	0.00599	0.00335	0.00418	0.00448	0.00626	0.00440
Parameter	Hangzhou: isotropic exponential kernel, empty basis function and standardized predictors
$σ$	9.76159	9.56312	9.55361	9.67115	9.56680	9.50042	9.55300	9.76237	9.50078	9.59281
$σ_{l}$	1285.12787	1274.69808	1547.22868	1318.46341	1337.76567	1275.58168	1286.01475	1265.18415	1304.20902	1351.82417
$σ_{f}$	4945.14959	4944.55519	4972.09375	4964.27398	4950.56690	4947.07997	4941.23625	4947.08398	4948.16021	4934.15668
Parameter	Nanjing: isotropic exponential kernel, constant basis function and standardized predictors
$σ$	9.16982	9.00530	9.06427	9.07706	9.04644	9.10117	9.11421	9.30739	9.13766	9.21620
$β$	3892.37341	3913.27761	3893.10728	3892.44807	3881.41157	3886.87868	3892.75172	3893.17966	3894.86639	3851.13284
$σ_{l}$	93.19057	94.38255	93.95045	94.84893	93.50798	93.57927	93.60363	91.29244	110.31117	172.21773
$σ_{f}$	1369.19857	1349.25675	1372.45126	1369.86826	1362.07899	1369.59562	1369.08982	1368.53175	1383.41862	1368.59079
Parameter	Wuhan: isotropic Matern 3/2 kernel, linear basis function and nonstandardized predictors
$σ$	6.66189	6.66678	6.70195	6.59718	6.70471	6.62291	6.63637	6.71766	6.64260	6.73219
$β_{0}$	10.78421	12.30100	8.34022	9.92236	8.67804	9.90088	10.04611	4.80144	9.94509	9.61494
$β_{1}$	0.06340	−0.01005	0.08518	0.01621	0.10453	0.04171	0.10898	0.10672	0.07988	0.13736
$β_{2}$	0.02091	0.09498	−0.03409	0.08375	−0.00834	0.04736	−0.06268	−0.03537	−0.03054	−0.27797
$β_{3}$	−0.18118	−0.23945	−0.15890	−0.19974	−0.18776	−0.19678	−0.14400	−0.20213	−0.13627	0.15125
$β_{4}$	0.01215	0.22741	0.18200	0.20006	0.20754	0.16922	0.14618	0.19804	0.15205	−0.01339
$β_{5}$	0.07525	−0.12087	−0.23858	−0.32256	−0.46272	−0.20585	−0.23221	−0.21823	−0.20137	−0.11539
$β_{6}$	−0.38745	−0.25529	−0.14906	−0.02922	0.10892	−0.13963	−0.03333	−0.12452	−0.16991	−0.12346
$β_{7}$	0.52049	0.35388	0.44930	0.25959	0.13688	0.28213	0.16985	0.35542	0.28050	0.18125
$β_{8}$	−0.73962	−0.63818	−0.76253	−0.54932	−0.35954	−0.54483	−0.47243	−0.84189	−0.50952	−0.34950
$β_{9}$	1.61237	1.58255	1.62370	1.53765	1.45720	1.54332	1.51612	1.76027	1.53154	1.40643
$σ_{l}$	2.33523	2.33523	2.33523	2.33523	2.33523	2.33523	2.33523	2.33523	2.33523	2.33523
$σ_{f}$	11.75326	12.07343	11.78144	12.54297	11.67167	12.49449	11.78219	11.26843	12.26267	10.18165
Parameter	Chengdu: nonisotropic exponential kernel, empty basis function and standardized predictors
$σ$	4.39657	4.35434	4.36167	4.32293	4.30320	4.26143	4.33931	4.42181	4.36253	4.33344
$σ_{1}$	2941.14103	3113.62131	4126.33116	3394.64755	3035.25359	3326.19868	2772.82517	2531.98948	49868618.51215	3165.31256
$σ_{2}$	1753725.15362	12531925823.41980	7690572.75182	21414387728.08100	3174699.07872	1578935197.54663	3499884.40862	333960828.84330	10253919.14633	9210839.14545
$σ_{3}$	747467.03086	2423070835324.76000	16638.50742	3121288.20940	11177.08409	7834.78238	4377932.31528	1082289924.03462	2043.39925	10300.21350
$σ_{4}$	2379755.03833	262120010551.68600	16228.37347	7336002.13208	5164102.63706	43696532.85531	34097968.52278	3138950.57505	1221194.45053	15467880.24444
$σ_{5}$	2453.85132	3291.17006	44321565.23677	2436.22905	406210.35107	20672747.73771	32024331.46233	4066.28926	11228642956.61260	2222792.75629
$σ_{6}$	2051529.37133	111853876525.18900	4732922.50704	36742135.35967	904568.47167	2927.63719	505815505.38421	133094027.20823	8086.31028	2820.17721
$σ_{7}$	19314.05288	5450.59856	71139689.97648	265471447.04099	2618.58029	6603.49376	2507.52156	20225.60903	469870280.78414	2308567.46543
$σ_{8}$	22172970.43821	6546614768.15480	93380908.06771	163324014.66795	12089925.76055	2437685695.62122	1465150.15617	1426404.05317	1611.75648	6046398.86219
$σ_{9}$	622.38300	630.41588	892.41631	643.90420	634.75983	651.68949	623.51967	631.20710	766.86019	648.68741
$σ_{f}$	2403.72982	2402.25181	2408.48875	2414.05276	2402.35983	2390.71079	2399.17739	2397.75208	2407.90511	2406.04517

Estimate	CV1	CV2	CV3	CV4	CV5	CV6	CV7	CV8	CV9	CV10
Parameter	Beijing: isotropic exponential kernel, empty basis function and standardized predictors
$σ$	11.34644	10.88397	11.21652	11.25806	11.06121	11.35184	11.23226	11.36280	11.28581	11.29736
$σ_{l}$	1478.76297	1549.80495	1511.41873	1487.23894	1469.36263	1527.77996	1584.82872	1415.07405	1456.23803	1431.98451
$σ_{f}$	6996.28789	7058.99367	6964.91820	6985.32766	6985.61621	6995.05097	6992.20871	6984.68920	6997.99299	6986.10874
Parameter	Shanghai: isotropic exponential kernel, constant basis function and standardized predictors
$σ$	12.60171	12.65667	12.43396	12.46169	12.53081	12.30951	12.44506	12.68133	12.61629	12.73437
$β$	6716.31619	6722.91918	6726.56064	6716.64362	6722.22576	6767.73831	6709.08306	6728.25743	6718.44492	6741.19175
$σ_{l}$	76.71800	79.93348	105.42119	76.96624	77.65031	90.95637	83.80150	78.51796	76.06861	88.07812
$σ_{f}$	1734.47766	1744.49917	1771.82939	1731.23332	1737.49918	1752.39015	1736.88704	1739.06683	1735.42166	1772.84554
Parameter	Tianjing: isotropic exponential kernel, empty basis function and nonstandardized predictors
$σ$	8.12223	8.37052	8.41959	8.14719	8.47991	8.33426	8.26314	8.16722	8.36124	8.29159
$σ_{l}$	917896.68400	901786.73526	1118250.47428	907284.88983	897970.04107	906877.37576	905286.14179	903439.65243	909402.33100	968360.07350
$σ_{f}$	4059.19284	4054.76853	4068.70065	4073.58017	4057.06349	4054.87394	4057.33326	4054.47449	4056.23212	4044.77978
Parameter	Chongqing: nonisotropic Matern 3/2 kernel, constant basis function and nonstandardized predictors
$σ$	5.56727	4.92674	6.50467	4.28530	5.35656	5.54645	5.15887	4.11237	5.12630	4.26242
$β$	1586.83743	1580.41587	1540.93302	1580.81475	1573.37302	1570.65790	1576.28943	1592.85835	1584.82359	1591.20074
$σ_{1}$	6179.74452	49177165094822.20000	119205550.33128	2149.16216	5046068.48468	549422.88346	86565.88130	8264.27540	3572.51910	350.38719
$σ_{2}$	336.74491	309.43910	493.70744	262.24809	327.47981	313.34918	291.59866	1221.48760	303.39510	946.63918
$σ_{3}$	22830601.42381	50671823250.42500	346209.78951	22342314.86463	490489.89502	4896876.17514	1057550.17589	294.88070	1741581.29388	437.97748
$σ_{4}$	716.25275	612.09713	11909055.82648	615.48868	846.77062	505.22669	623.48021	1049.59618	582.52378	900.10337
$σ_{5}$	786574.36133	35564030.74322	881.36821	328699.26660	755193.56484	702460.44349	2050.46089	1881.80383	2267.40498	292678.05468
$σ_{6}$	157283006.40471	401551.22127	208620117.94988	2094464.49521	3422283.88256	1309663.50500	52978396.48421	1463779.80429	2184692.36164	1827.29584
$σ_{7}$	434384.33263	2207.38444	91449826.94185	1322.68043	2303.49598	2191.14959	2570.99901	2117640.48482	2859.70570	1208.41138
$σ_{8}$	51504378.45013	26348541.91946	97714088.99401	865739.50526	418217.83527	408326.24827	3158058.50326	1193899.85594	505382.64958	88386.51681
$σ_{9}$	289.24758	282.27094	423.70755	242.89171	283.75746	288.84678	264.45721	334.87823	283.76100	358.16086
$σ_{f}$	171.92764	162.12951	195.82911	151.98030	166.74296	159.13466	159.44168	182.07565	161.32802	152.96275
Parameter	Shenzhen: isotropic Matern 5/2 kernel, empty basis function and standardized predictors
$σ$	56.90234	50.35853	43.96349	40.80814	53.80888	53.78936	53.43056	50.46201	54.90458	47.14572
$σ_{l}$	137.80039	5.02011	4.27545	4.08478	5.84916	6.07866	7.53360	4.96700	5.58126	4.56867
$σ_{f}$	102474.71802	4142.45441	3681.64696	3655.99229	4585.50482	4905.75759	5777.39136	4075.73372	4240.31194	3817.98637
Parameter	Guangzhou: isotropic Matern 5/2 kernel, linear basis function and standardized predictors
$σ$	35.68043	34.18927	24.26637	34.11388	35.07319	35.77847	34.52065	34.65384	35.83448	34.24232
$β_{0}$	4485.09877	4430.97531	4383.06173	4466.61728	4395.40741	4461.72840	4422.58025	4507.07407	4460.56790	4395.77778
$β_{1}$	−22.00451	204.20283	−51.03961	−40.10682	8.34190	−7.28323	−0.69112	−56.28909	−22.18170	−47.39137
$β_{2}$	−64.28505	−469.89481	102.95413	−10.60102	−32.16166	−64.93041	−82.15014	16.25216	−70.32153	−25.97377
$β_{3}$	143.68304	309.31510	−82.56766	111.21312	75.83371	123.12413	116.38854	118.48221	164.64201	184.78810
$β_{4}$	6.24641	−11.41629	95.92353	32.97490	21.68781	18.38982	−21.92609	−42.74598	−14.93738	−41.29688
$β_{5}$	−31.28362	9.24901	−47.84468	−54.63476	−120.49049	−47.24500	10.28977	−0.75441	−29.30189	26.58770
$β_{6}$	−232.27140	−238.26042	−172.98486	−255.27472	−187.78546	−229.54177	−242.82906	−244.53654	−244.58152	−435.32932
$β_{7}$	−11.33771	−7.90012	−19.14608	−42.01500	33.16940	−23.40106	24.85018	−20.72777	−5.30953	140.97066
$β_{8}$	−199.90394	−222.54370	−432.65164	−118.83366	−189.02693	−181.22494	−184.85978	−149.52617	−173.64549	−145.39190
$β_{9}$	1362.03626	1376.23692	1555.03505	1306.75678	1340.30623	1357.39790	1323.55188	1338.44435	1339.00020	1297.67889
$σ_{l}$	266648.70619	177047.86936	136094.68457	40617.41750	175184.11308	255379.07297	170519.28893	19638.07055	175799.13066	182805.47349
$σ_{f}$	0.00348	0.00579	0.00331	0.00509	0.00599	0.00335	0.00418	0.00448	0.00626	0.00440
Parameter	Hangzhou: isotropic exponential kernel, empty basis function and standardized predictors
$σ$	9.76159	9.56312	9.55361	9.67115	9.56680	9.50042	9.55300	9.76237	9.50078	9.59281
$σ_{l}$	1285.12787	1274.69808	1547.22868	1318.46341	1337.76567	1275.58168	1286.01475	1265.18415	1304.20902	1351.82417
$σ_{f}$	4945.14959	4944.55519	4972.09375	4964.27398	4950.56690	4947.07997	4941.23625	4947.08398	4948.16021	4934.15668
Parameter	Nanjing: isotropic exponential kernel, constant basis function and standardized predictors
$σ$	9.16982	9.00530	9.06427	9.07706	9.04644	9.10117	9.11421	9.30739	9.13766	9.21620
$β$	3892.37341	3913.27761	3893.10728	3892.44807	3881.41157	3886.87868	3892.75172	3893.17966	3894.86639	3851.13284
$σ_{l}$	93.19057	94.38255	93.95045	94.84893	93.50798	93.57927	93.60363	91.29244	110.31117	172.21773
$σ_{f}$	1369.19857	1349.25675	1372.45126	1369.86826	1362.07899	1369.59562	1369.08982	1368.53175	1383.41862	1368.59079
Parameter	Wuhan: isotropic Matern 3/2 kernel, linear basis function and nonstandardized predictors
$σ$	6.66189	6.66678	6.70195	6.59718	6.70471	6.62291	6.63637	6.71766	6.64260	6.73219
$β_{0}$	10.78421	12.30100	8.34022	9.92236	8.67804	9.90088	10.04611	4.80144	9.94509	9.61494
$β_{1}$	0.06340	−0.01005	0.08518	0.01621	0.10453	0.04171	0.10898	0.10672	0.07988	0.13736
$β_{2}$	0.02091	0.09498	−0.03409	0.08375	−0.00834	0.04736	−0.06268	−0.03537	−0.03054	−0.27797
$β_{3}$	−0.18118	−0.23945	−0.15890	−0.19974	−0.18776	−0.19678	−0.14400	−0.20213	−0.13627	0.15125
$β_{4}$	0.01215	0.22741	0.18200	0.20006	0.20754	0.16922	0.14618	0.19804	0.15205	−0.01339
$β_{5}$	0.07525	−0.12087	−0.23858	−0.32256	−0.46272	−0.20585	−0.23221	−0.21823	−0.20137	−0.11539
$β_{6}$	−0.38745	−0.25529	−0.14906	−0.02922	0.10892	−0.13963	−0.03333	−0.12452	−0.16991	−0.12346
$β_{7}$	0.52049	0.35388	0.44930	0.25959	0.13688	0.28213	0.16985	0.35542	0.28050	0.18125
$β_{8}$	−0.73962	−0.63818	−0.76253	−0.54932	−0.35954	−0.54483	−0.47243	−0.84189	−0.50952	−0.34950
$β_{9}$	1.61237	1.58255	1.62370	1.53765	1.45720	1.54332	1.51612	1.76027	1.53154	1.40643
$σ_{l}$	2.33523	2.33523	2.33523	2.33523	2.33523	2.33523	2.33523	2.33523	2.33523	2.33523
$σ_{f}$	11.75326	12.07343	11.78144	12.54297	11.67167	12.49449	11.78219	11.26843	12.26267	10.18165
Parameter	Chengdu: nonisotropic exponential kernel, empty basis function and standardized predictors
$σ$	4.39657	4.35434	4.36167	4.32293	4.30320	4.26143	4.33931	4.42181	4.36253	4.33344
$σ_{1}$	2941.14103	3113.62131	4126.33116	3394.64755	3035.25359	3326.19868	2772.82517	2531.98948	49868618.51215	3165.31256
$σ_{2}$	1753725.15362	12531925823.41980	7690572.75182	21414387728.08100	3174699.07872	1578935197.54663	3499884.40862	333960828.84330	10253919.14633	9210839.14545
$σ_{3}$	747467.03086	2423070835324.76000	16638.50742	3121288.20940	11177.08409	7834.78238	4377932.31528	1082289924.03462	2043.39925	10300.21350
$σ_{4}$	2379755.03833	262120010551.68600	16228.37347	7336002.13208	5164102.63706	43696532.85531	34097968.52278	3138950.57505	1221194.45053	15467880.24444
$σ_{5}$	2453.85132	3291.17006	44321565.23677	2436.22905	406210.35107	20672747.73771	32024331.46233	4066.28926	11228642956.61260	2222792.75629
$σ_{6}$	2051529.37133	111853876525.18900	4732922.50704	36742135.35967	904568.47167	2927.63719	505815505.38421	133094027.20823	8086.31028	2820.17721
$σ_{7}$	19314.05288	5450.59856	71139689.97648	265471447.04099	2618.58029	6603.49376	2507.52156	20225.60903	469870280.78414	2308567.46543
$σ_{8}$	22172970.43821	6546614768.15480	93380908.06771	163324014.66795	12089925.76055	2437685695.62122	1465150.15617	1426404.05317	1611.75648	6046398.86219
$σ_{9}$	622.38300	630.41588	892.41631	643.90420	634.75983	651.68949	623.51967	631.20710	766.86019	648.68741
$σ_{f}$	2403.72982	2402.25181	2408.48875	2414.05276	2402.35983	2390.71079	2399.17739	2397.75208	2407.90511	2406.04517

Source: Table by authors

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